chore: Remove trailing whitespace (#129 )

Switch to the convention of using no trailing whitespace, even on blank lines. Also remove some unintended trailing whitespace on non-blank lines and fix a few typos. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#129 Reviewed-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-authored-by: Glen Whitney <glen@studioinfinity.org> Co-committed-by: Glen Whitney <glen@studioinfinity.org>
feat: Point coordinate regulators (#118 )
2025-11-11 00:47:40 +00:00 · 2025-10-13 22:52:02 +00:00 · 2025-09-18 23:31:17 +00:00 · 2025-08-11 03:33:19 +00:00 · 2025-08-07 23:24:07 +00:00 · 2025-08-04 23:34:33 +00:00
80 changed files with 3015 additions and 7167 deletions
--- a/.forgejo/setup-trunk/action.yaml
+++ b/.forgejo/setup-trunk/action.yaml
@ -10,7 +10,7 @@ runs:
  using: "composite"
  steps:
    - run: rustup target add wasm32-unknown-unknown
-    
+
    # install the Trunk binary to `ci-bin` within the workspace directory, which
    # is determined by the `github.workspace` label and reflected in the
    # `GITHUB_WORKSPACE` environment variable. then, make the `trunk` command
--- a/.forgejo/workflows/continuous-integration.yaml
+++ b/.forgejo/workflows/continuous-integration.yaml
@ -24,6 +24,6 @@ jobs:
      # workspace directory (action variable `github.workspace`, environment
      # variable `$GITHUB_WORKSPACE`):
      - uses: https://code.forgejo.org/actions/checkout@v4
-      
+
      - uses: ./.forgejo/setup-trunk
-      - run: RUSTFLAGS='-D warnings' cargo test
+      - run: RUSTFLAGS='-D warnings' cargo test
--- a/README.md
+++ b/README.md
@ -12,11 +12,11 @@ Note that currently this is just the barest beginnings of the project, more of a

 ### Implementation goals

-* Comfortable, intuitive UI
+* Provide a comfortable, intuitive UI

-* Able to run in browser (so implemented in WASM-compatible language)
+* Allow execution in browser (so implemented in WASM-compatible language)

-* Produce scalable graphics of 3D diagrams, and maybe STL files (or other fabricatable file format) as well.
+* Produce scalable graphics of 3D diagrams, and maybe STL files (or other fabricatable file format) as well

 ## Prototype

@ -24,44 +24,66 @@ The latest prototype is in the folder `app-proto`. It includes both a user inter

 ### Install the prerequisites

-1. Install [`rustup`](https://rust-lang.github.io/rustup/): the officially recommended Rust toolchain manager
-   * It's available on Ubuntu as a [Snap](https://snapcraft.io/rustup)
-2. Call `rustup default stable` to "download the latest stable release of Rust and set it as your default toolchain"
-   * If you forget, the `rustup` [help system](https://github.com/rust-lang/rustup/blob/d9b3601c3feb2e88cf3f8ca4f7ab4fdad71441fd/src/errors.rs#L109-L112) will remind you
-3. Call `rustup target add wasm32-unknown-unknown` to add the [most generic 32-bit WebAssembly target](https://doc.rust-lang.org/nightly/rustc/platform-support/wasm32-unknown-unknown.html)
-4. Call `cargo install wasm-pack` to install the [WebAssembly toolchain](https://rustwasm.github.io/docs/wasm-pack/)
-5. Call `cargo install trunk` to install the [Trunk](https://trunkrs.dev/) web-build tool
+1. Install [`rustup`](https://rust-lang.github.io/rustup/): the officially recommended Rust toolchain manager.
+   - It's available on Ubuntu as a [Snap](https://snapcraft.io/rustup).
+2. Call `rustup default stable` to "download the latest stable release of Rust and set it as your default toolchain".
+   - If you forget, the `rustup` [help system](https://github.com/rust-lang/rustup/blob/d9b3601c3feb2e88cf3f8ca4f7ab4fdad71441fd/src/errors.rs#L109-L112) will remind you.
+3. Call `rustup target add wasm32-unknown-unknown` to add the [most generic 32-bit WebAssembly target](https://doc.rust-lang.org/nightly/rustc/platform-support/wasm32-unknown-unknown.html).
+4. Call `cargo install wasm-pack` to install the [WebAssembly toolchain](https://rustwasm.github.io/docs/wasm-pack/).
+5. Call `cargo install trunk` to install the [Trunk](https://trunkrs.dev/) web-build tool.
+   - In the future, `trunk` can be updated with the same command. (You may need the `--locked` flag if your ambient version of `rustc` does not match that required by `trunk`.)
 6. Add the `.cargo/bin` folder in your home directory to your executable search path
-   * This lets you call Trunk, and other tools installed by Cargo, without specifying their paths
-   * On POSIX systems, the search path is stored in the `PATH` environment variable
+   - This lets you call Trunk, and other tools installed by Cargo, without specifying their paths.
+   - On POSIX systems, the search path is stored in the `PATH` environment variable.
+   - Alternatively, if you don't want to adjust your `PATH`, you can install `trunk` in another directory `DIR` via `cargo install --root DIR trunk`.

 ### Play with the prototype

-1. From the `app-proto` folder, call `trunk serve --release` to build and serve the prototype
-   * *The crates the prototype depends on will be downloaded and served automatically*
-   * *For a faster build, at the expense of a much slower prototype, you can call `trunk serve` without the `--release` flag*
-   * *If you want to stay in the top-level folder, you can call `trunk serve --config app-proto [--release]`* from there instead.
-3. In a web browser, visit one of the URLs listed under the message `INFO 📡 server listening at:`
-   * *Touching any file in the `app-proto` folder will make Trunk rebuild and live-reload the prototype*
-4. Press *ctrl+C* in the shell where Trunk is running to stop serving the prototype
+1. From the `app-proto` folder, call `trunk serve --release` to build and serve the prototype.
+   - The crates the prototype depends on will be downloaded and served automatically.
+   - For a faster build, at the expense of a much slower prototype, you can call `trunk serve` without the `--release` flag.
+   - If you want to stay in the top-level folder, you can call `trunk serve --config app-proto [--release]` from there instead.
+3. In a web browser, visit one of the URLs listed under the message `INFO 📡 server listening at:`.
+   - Touching any file in the `app-proto` folder will make Trunk rebuild and live-reload the prototype.
+4. Press *ctrl+C* in the shell where Trunk is running to stop serving the prototype.

 ### Run the engine on some example problems

-1. Go into the `app-proto` folder
-2. Call `./run-examples`
-   * *For each example problem, the engine will print the value of the loss function at each optimization step*
-   * *The first example that prints is the same as the Irisawa hexlet example from the Julia version of the engine prototype. If you go into `engine-proto/gram-test`, launch Julia, and then*
-     
+1. Use `sh` to run the script `tools/run-examples.sh`.
+   - The script is location-independent, so you can do this from anywhere in the dyna3 repository.
+   - The call from the top level of the repository is:
+
+     ```bash
+     sh tools/run-examples.sh
+     ```
+   - For each example problem, the engine will print the value of the loss function at each optimization step.
+   - The first example that prints is the same as the Irisawa hexlet example from the Julia version of the engine prototype. If you go into `engine-proto/gram-test`, launch Julia, and then execute
+
     ```julia
     include("irisawa-hexlet.jl")
     for (step, scaled_loss) in enumerate(history_alt.scaled_loss)
       println(rpad(step-1, 4), " | ", scaled_loss)
     end
     ```
-     
-     *you should see that it prints basically the same loss history until the last few steps, when the lower default precision of the Rust engine really starts to show*
+
+     you should see that it prints basically the same loss history until the last few steps, when the lower default precision of the Rust engine really starts to show.

 ### Run the automated tests

-1. Go into the `app-proto` folder
-2. Call `cargo test`
+1. Go into the `app-proto` folder.
+2. Call `cargo test`.
+
+### Deploy the prototype
+
+1. From the `app-proto` folder, call `trunk build --release`.
+   - Building in [release mode](https://doc.rust-lang.org/cargo/reference/profiles.html#release) produces an executable which is smaller and often much faster, but harder to debug and more time-consuming to build.
+   - If you want to stay in the top-level folder, you can call `trunk build --config app-proto --release` from there instead.
+2. Use `sh` to run the packaging script `tools/package-for-deployment.sh`.
+   - The script is location-independent, so you can do this from anywhere in the dyna3 repository.
+   - The call from the top level of the repository is:
+     ```bash
+     sh tools/package-for-deployment.sh
+     ```
+   - This will overwrite or replace the files in `deploy/dyna3`.
+3. Put the contents of `deploy/dyna3` in the folder on your server that the prototype will be served from.
+   - To simplify uploading, you might want to combine these files into an archive called `deploy/dyna3.zip`. Git has been set to ignore this path.
--- a/app-proto/Cargo.lock
+++ b/app-proto/Cargo.lock
@ -20,6 +20,21 @@ version = "0.2.18"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "5c6cb57a04249c6480766f7f7cef5467412af1490f8d1e243141daddada3264f"

+[[package]]
+name = "android-tzdata"
+version = "0.1.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e999941b234f3131b00bc13c22d06e8c5ff726d1b6318ac7eb276997bbb4fef0"
+
+[[package]]
+name = "android_system_properties"
+version = "0.1.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "819e7219dbd41043ac279b19830f2efc897156490d7fd6ea916720117ee66311"
+dependencies = [
+ "libc",
+]
+
 [[package]]
 name = "approx"
 version = "0.5.1"
@ -35,6 +50,21 @@ version = "1.3.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "0c4b4d0bd25bd0b74681c0ad21497610ce1b7c91b1022cd21c80c6fbdd9476b0"

+[[package]]
+name = "base64"
+version = "0.22.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "72b3254f16251a8381aa12e40e3c4d2f0199f8c6508fbecb9d91f575e0fbb8c6"
+
+[[package]]
+name = "block-buffer"
+version = "0.10.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "3078c7629b62d3f0439517fa394996acacc5cbc91c5a20d8c658e77abd503a71"
+dependencies = [
+ "generic-array",
+]
+
 [[package]]
 name = "bumpalo"
 version = "3.16.0"
@ -68,6 +98,35 @@ version = "1.0.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "baf1de4339761588bc0619e3cbc0120ee582ebb74b53b4efbf79117bd2da40fd"

+[[package]]
+name = "charming"
+version = "0.5.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "73ffae2e616ae7d66b2e9ea369f1c7650042bdcdc1dc08b04b027107007b4f09"
+dependencies = [
+ "handlebars",
+ "js-sys",
+ "serde",
+ "serde-wasm-bindgen",
+ "serde_json",
+ "serde_with",
+ "wasm-bindgen",
+ "web-sys",
+]
+
+[[package]]
+name = "chrono"
+version = "0.4.41"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c469d952047f47f91b68d1cba3f10d63c11d73e4636f24f08daf0278abf01c4d"
+dependencies = [
+ "android-tzdata",
+ "iana-time-zone",
+ "num-traits",
+ "serde",
+ "windows-link",
+]
+
 [[package]]
 name = "console_error_panic_hook"
 version = "0.1.7"
@ -78,12 +137,125 @@ dependencies = [
 "wasm-bindgen",
 ]

+[[package]]
+name = "core-foundation-sys"
+version = "0.8.7"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "773648b94d0e5d620f64f280777445740e61fe701025087ec8b57f45c791888b"
+
+[[package]]
+name = "cpufeatures"
+version = "0.2.17"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "59ed5838eebb26a2bb2e58f6d5b5316989ae9d08bab10e0e6d103e656d1b0280"
+dependencies = [
+ "libc",
+]
+
+[[package]]
+name = "crypto-common"
+version = "0.1.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1bfb12502f3fc46cca1bb51ac28df9d618d813cdc3d2f25b9fe775a34af26bb3"
+dependencies = [
+ "generic-array",
+ "typenum",
+]
+
+[[package]]
+name = "darling"
+version = "0.20.11"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "fc7f46116c46ff9ab3eb1597a45688b6715c6e628b5c133e288e709a29bcb4ee"
+dependencies = [
+ "darling_core",
+ "darling_macro",
+]
+
+[[package]]
+name = "darling_core"
+version = "0.20.11"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "0d00b9596d185e565c2207a0b01f8bd1a135483d02d9b7b0a54b11da8d53412e"
+dependencies = [
+ "fnv",
+ "ident_case",
+ "proc-macro2",
+ "quote",
+ "strsim",
+ "syn",
+]
+
+[[package]]
+name = "darling_macro"
+version = "0.20.11"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "fc34b93ccb385b40dc71c6fceac4b2ad23662c7eeb248cf10d529b7e055b6ead"
+dependencies = [
+ "darling_core",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "deranged"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9c9e6a11ca8224451684bc0d7d5a7adbf8f2fd6887261a1cfc3c0432f9d4068e"
+dependencies = [
+ "powerfmt",
+ "serde",
+]
+
+[[package]]
+name = "derive_builder"
+version = "0.20.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "507dfb09ea8b7fa618fcf76e953f4f5e192547945816d5358edffe39f6f94947"
+dependencies = [
+ "derive_builder_macro",
+]
+
+[[package]]
+name = "derive_builder_core"
+version = "0.20.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "2d5bcf7b024d6835cfb3d473887cd966994907effbe9227e8c8219824d06c4e8"
+dependencies = [
+ "darling",
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "derive_builder_macro"
+version = "0.20.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ab63b0e2bf4d5928aff72e83a7dace85d7bba5fe12dcc3c5a572d78caffd3f3c"
+dependencies = [
+ "derive_builder_core",
+ "syn",
+]
+
+[[package]]
+name = "digest"
+version = "0.10.7"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9ed9a281f7bc9b7576e61468ba615a66a5c8cfdff42420a70aa82701a3b1e292"
+dependencies = [
+ "block-buffer",
+ "crypto-common",
+]
+
 [[package]]
 name = "dyna3"
 version = "0.1.0"
 dependencies = [
+ "charming",
 "console_error_panic_hook",
 "dyna3",
+ "enum-iterator",
 "itertools",
 "js-sys",
 "lazy_static",
@ -100,12 +272,48 @@ version = "1.13.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "60b1af1c220855b6ceac025d3f6ecdd2b7c4894bfe9cd9bda4fbb4bc7c0d4cf0"

+[[package]]
+name = "enum-iterator"
+version = "2.3.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a4549325971814bda7a44061bf3fe7e487d447cba01e4220a4b454d630d7a016"
+dependencies = [
+ "enum-iterator-derive",
+]
+
+[[package]]
+name = "enum-iterator-derive"
+version = "1.5.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "685adfa4d6f3d765a26bc5dbc936577de9abf756c1feeb3089b01dd395034842"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
 [[package]]
 name = "equivalent"
 version = "1.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "5443807d6dff69373d433ab9ef5378ad8df50ca6298caf15de6e52e24aaf54d5"

+[[package]]
+name = "fnv"
+version = "1.0.7"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "3f9eec918d3f24069decb9af1554cad7c880e2da24a9afd88aca000531ab82c1"
+
+[[package]]
+name = "generic-array"
+version = "0.14.7"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "85649ca51fd72272d7821adaf274ad91c288277713d9c18820d8499a7ff69e9a"
+dependencies = [
+ "typenum",
+ "version_check",
+]
+
 [[package]]
 name = "getrandom"
 version = "0.2.15"
@ -117,6 +325,28 @@ dependencies = [
 "wasi",
 ]

+[[package]]
+name = "handlebars"
+version = "6.3.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "759e2d5aea3287cb1190c8ec394f42866cb5bf74fcbf213f354e3c856ea26098"
+dependencies = [
+ "derive_builder",
+ "log",
+ "num-order",
+ "pest",
+ "pest_derive",
+ "serde",
+ "serde_json",
+ "thiserror",
+]
+
+[[package]]
+name = "hashbrown"
+version = "0.12.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8a9ee70c43aaf417c914396645a0fa852624801b24ebb7ae78fe8272889ac888"
+
 [[package]]
 name = "hashbrown"
 version = "0.14.5"
@ -127,6 +357,12 @@ dependencies = [
 "allocator-api2",
 ]

+[[package]]
+name = "hex"
+version = "0.4.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7f24254aa9a54b5c858eaee2f5bccdb46aaf0e486a595ed5fd8f86ba55232a70"
+
 [[package]]
 name = "html-escape"
 version = "0.2.13"
@ -136,6 +372,47 @@ dependencies = [
 "utf8-width",
 ]

+[[package]]
+name = "iana-time-zone"
+version = "0.1.63"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b0c919e5debc312ad217002b8048a17b7d83f80703865bbfcfebb0458b0b27d8"
+dependencies = [
+ "android_system_properties",
+ "core-foundation-sys",
+ "iana-time-zone-haiku",
+ "js-sys",
+ "log",
+ "wasm-bindgen",
+ "windows-core",
+]
+
+[[package]]
+name = "iana-time-zone-haiku"
+version = "0.1.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f31827a206f56af32e590ba56d5d2d085f558508192593743f16b2306495269f"
+dependencies = [
+ "cc",
+]
+
+[[package]]
+name = "ident_case"
+version = "1.0.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b9e0384b61958566e926dc50660321d12159025e767c18e043daf26b70104c39"
+
+[[package]]
+name = "indexmap"
+version = "1.9.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "bd070e393353796e801d209ad339e89596eb4c8d430d18ede6a1cced8fafbd99"
+dependencies = [
+ "autocfg",
+ "hashbrown 0.12.3",
+ "serde",
+]
+
 [[package]]
 name = "indexmap"
 version = "2.5.0"
@ -143,7 +420,8 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "68b900aa2f7301e21c36462b170ee99994de34dff39a4a6a528e80e7376d07e5"
 dependencies = [
 "equivalent",
- "hashbrown",
+ "hashbrown 0.14.5",
+ "serde",
 ]

 [[package]]
@ -155,6 +433,12 @@ dependencies = [
 "either",
 ]

+[[package]]
+name = "itoa"
+version = "1.0.15"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "4a5f13b858c8d314ee3e8f639011f7ccefe71f97f96e50151fb991f267928e2c"
+
 [[package]]
 name = "js-sys"
 version = "0.3.70"
@ -192,6 +476,12 @@ dependencies = [
 "rawpointer",
 ]

+[[package]]
+name = "memchr"
+version = "2.7.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "78ca9ab1a0babb1e7d5695e3530886289c18cf2f87ec19a575a0abdce112e3a3"
+
 [[package]]
 name = "minicov"
 version = "0.3.5"
@ -248,6 +538,12 @@ dependencies = [
 "num-traits",
 ]

+[[package]]
+name = "num-conv"
+version = "0.1.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "51d515d32fb182ee37cda2ccdcb92950d6a3c2893aa280e540671c2cd0f3b1d9"
+
 [[package]]
 name = "num-integer"
 version = "0.1.46"
@ -257,6 +553,21 @@ dependencies = [
 "num-traits",
 ]

+[[package]]
+name = "num-modular"
+version = "0.6.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "17bb261bf36fa7d83f4c294f834e91256769097b3cb505d44831e0a179ac647f"
+
+[[package]]
+name = "num-order"
+version = "1.2.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "537b596b97c40fcf8056d153049eb22f481c17ebce72a513ec9286e4986d1bb6"
+dependencies = [
+ "num-modular",
+]
+
 [[package]]
 name = "num-rational"
 version = "0.4.2"
@ -289,6 +600,57 @@ version = "1.0.15"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "57c0d7b74b563b49d38dae00a0c37d4d6de9b432382b2892f0574ddcae73fd0a"

+[[package]]
+name = "pest"
+version = "2.8.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "198db74531d58c70a361c42201efde7e2591e976d518caf7662a47dc5720e7b6"
+dependencies = [
+ "memchr",
+ "thiserror",
+ "ucd-trie",
+]
+
+[[package]]
+name = "pest_derive"
+version = "2.8.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d725d9cfd79e87dccc9341a2ef39d1b6f6353d68c4b33c177febbe1a402c97c5"
+dependencies = [
+ "pest",
+ "pest_generator",
+]
+
+[[package]]
+name = "pest_generator"
+version = "2.8.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "db7d01726be8ab66ab32f9df467ae8b1148906685bbe75c82d1e65d7f5b3f841"
+dependencies = [
+ "pest",
+ "pest_meta",
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "pest_meta"
+version = "2.8.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7f9f832470494906d1fca5329f8ab5791cc60beb230c74815dff541cbd2b5ca0"
+dependencies = [
+ "once_cell",
+ "pest",
+ "sha2",
+]
+
+[[package]]
+name = "powerfmt"
+version = "0.2.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "439ee305def115ba05938db6eb1644ff94165c5ab5e9420d1c1bcedbba909391"
+
 [[package]]
 name = "ppv-lite86"
 version = "0.2.20"
@ -363,6 +725,12 @@ dependencies = [
 "syn",
 ]

+[[package]]
+name = "ryu"
+version = "1.0.20"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "28d3b2b1366ec20994f1fd18c3c594f05c5dd4bc44d8bb0c1c632c8d6829481f"
+
 [[package]]
 name = "safe_arch"
 version = "0.7.2"
@ -387,6 +755,90 @@ version = "1.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e1cf6437eb19a8f4a6cc0f7dca544973b0b78843adbfeb3683d1a94a0024a294"

+[[package]]
+name = "serde"
+version = "1.0.219"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5f0e2c6ed6606019b4e29e69dbaba95b11854410e5347d525002456dbbb786b6"
+dependencies = [
+ "serde_derive",
+]
+
+[[package]]
+name = "serde-wasm-bindgen"
+version = "0.6.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8302e169f0eddcc139c70f139d19d6467353af16f9fce27e8c30158036a1e16b"
+dependencies = [
+ "js-sys",
+ "serde",
+ "wasm-bindgen",
+]
+
+[[package]]
+name = "serde_derive"
+version = "1.0.219"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5b0276cf7f2c73365f7157c8123c21cd9a50fbbd844757af28ca1f5925fc2a00"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "serde_json"
+version = "1.0.140"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "20068b6e96dc6c9bd23e01df8827e6c7e1f2fddd43c21810382803c136b99373"
+dependencies = [
+ "itoa",
+ "memchr",
+ "ryu",
+ "serde",
+]
+
+[[package]]
+name = "serde_with"
+version = "3.12.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d6b6f7f2fcb69f747921f79f3926bd1e203fce4fef62c268dd3abfb6d86029aa"
+dependencies = [
+ "base64",
+ "chrono",
+ "hex",
+ "indexmap 1.9.3",
+ "indexmap 2.5.0",
+ "serde",
+ "serde_derive",
+ "serde_json",
+ "serde_with_macros",
+ "time",
+]
+
+[[package]]
+name = "serde_with_macros"
+version = "3.12.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8d00caa5193a3c8362ac2b73be6b9e768aa5a4b2f721d8f4b339600c3cb51f8e"
+dependencies = [
+ "darling",
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "sha2"
+version = "0.10.9"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a7507d819769d01a365ab707794a4084392c824f54a7a6a7862f8c3d0892b283"
+dependencies = [
+ "cfg-if",
+ "cpufeatures",
+ "digest",
+]
+
 [[package]]
 name = "shlex"
 version = "1.3.0"
@ -422,13 +874,19 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "3c5e1a9a646d36c3599cd173a41282daf47c44583ad367b8e6837255952e5c67"

 [[package]]
-name = "sycamore"
-version = "0.9.0-beta.3"
+name = "strsim"
+version = "0.11.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "dedaf7237c05913604a5b0b2536b613f6c8510c6b213d2583b1294869755cabd"
+checksum = "7da8b5736845d9f2fcb837ea5d9e2628564b3b043a70948a3f0b778838c5fb4f"
+
+[[package]]
+name = "sycamore"
+version = "0.9.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5f38201dcb10aa609e81ca6f7547758a7eb602240a5ff682e668909fd0f7b2cc"
 dependencies = [
- "hashbrown",
- "indexmap",
+ "hashbrown 0.14.5",
+ "indexmap 2.5.0",
 "paste",
 "sycamore-core",
 "sycamore-macro",
@ -440,20 +898,20 @@ dependencies = [

 [[package]]
 name = "sycamore-core"
-version = "0.9.0-beta.3"
+version = "0.9.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e5ddddc3d1bcb38c04ad55d2d1ab4f6a358e4daaeae0a0436892f1fade9fb31a"
+checksum = "41dc04bf0de321c6486356b2be751fac82fabb06c992d25b6748587561bba187"
 dependencies = [
- "hashbrown",
+ "hashbrown 0.14.5",
 "paste",
 "sycamore-reactive",
 ]

 [[package]]
 name = "sycamore-macro"
-version = "0.9.0-beta.3"
+version = "0.9.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "77181c27cb753e86065308901871ccc7456fb19527b6a4ffacad3b63175ed014"
+checksum = "a0c1d2eddc94db6d03e67eb832df5512b967e81053a573cd01bf3e1c3db00137"
 dependencies = [
 "once_cell",
 "proc-macro2",
@ -465,20 +923,21 @@ dependencies = [

 [[package]]
 name = "sycamore-reactive"
-version = "0.9.0-beta.3"
+version = "0.9.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7aa6870203507c07e850687c0ccf528eb0f04240e3596bac9137007ffb6c50b1"
+checksum = "f2bacf810535efc2701187a716a5652197ad241d620d5b00fb12caa6dfa23add"
 dependencies = [
 "paste",
 "slotmap",
 "smallvec",
+ "wasm-bindgen",
 ]

 [[package]]
 name = "sycamore-view-parser"
-version = "0.9.0-beta.3"
+version = "0.9.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "a6144640af2eafffc68a92f3aacbbfaa21f7fd31906e2336fe304fd100fe226b"
+checksum = "6c22875843db83cd4d49c0123a195e433bdc74e13ed0fff4ace0e77bb0a67033"
 dependencies = [
 "proc-macro2",
 "quote",
@ -487,9 +946,9 @@ dependencies = [

 [[package]]
 name = "sycamore-web"
-version = "0.9.0-beta.3"
+version = "0.9.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "bca93dcf1b1830bf1aac93508ed51babcda92c1d32d96067ab416d94e4b7c475"
+checksum = "4b17aa5875f59f541cdf6fb58751ec702a6ed9801f30dd2b4d5f2279025b98bd"
 dependencies = [
 "html-escape",
 "js-sys",
@ -505,21 +964,78 @@ dependencies = [

 [[package]]
 name = "syn"
-version = "2.0.77"
+version = "2.0.87"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9f35bcdf61fd8e7be6caf75f429fdca8beb3ed76584befb503b1569faee373ed"
+checksum = "25aa4ce346d03a6dcd68dd8b4010bcb74e54e62c90c573f394c46eae99aba32d"
 dependencies = [
 "proc-macro2",
 "quote",
 "unicode-ident",
 ]

+[[package]]
+name = "thiserror"
+version = "2.0.12"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "567b8a2dae586314f7be2a752ec7474332959c6460e02bde30d702a66d488708"
+dependencies = [
+ "thiserror-impl",
+]
+
+[[package]]
+name = "thiserror-impl"
+version = "2.0.12"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7f7cf42b4507d8ea322120659672cf1b9dbb93f8f2d4ecfd6e51350ff5b17a1d"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "time"
+version = "0.3.41"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8a7619e19bc266e0f9c5e6686659d394bc57973859340060a69221e57dbc0c40"
+dependencies = [
+ "deranged",
+ "itoa",
+ "num-conv",
+ "powerfmt",
+ "serde",
+ "time-core",
+ "time-macros",
+]
+
+[[package]]
+name = "time-core"
+version = "0.1.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c9e9a38711f559d9e3ce1cdb06dd7c5b8ea546bc90052da6d06bb76da74bb07c"
+
+[[package]]
+name = "time-macros"
+version = "0.2.22"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "3526739392ec93fd8b359c8e98514cb3e8e021beb4e5f597b00a0221f8ed8a49"
+dependencies = [
+ "num-conv",
+ "time-core",
+]
+
 [[package]]
 name = "typenum"
 version = "1.17.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "42ff0bf0c66b8238c6f3b578df37d0b7848e55df8577b3f74f92a69acceeb825"

+[[package]]
+name = "ucd-trie"
+version = "0.1.7"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "2896d95c02a80c6d6a5d6e953d479f5ddf2dfdb6a244441010e373ac0fb88971"
+
 [[package]]
 name = "unicode-ident"
 version = "1.0.13"
@ -676,6 +1192,65 @@ dependencies = [
 "windows-sys",
 ]

+[[package]]
+name = "windows-core"
+version = "0.61.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c0fdd3ddb90610c7638aa2b3a3ab2904fb9e5cdbecc643ddb3647212781c4ae3"
+dependencies = [
+ "windows-implement",
+ "windows-interface",
+ "windows-link",
+ "windows-result",
+ "windows-strings",
+]
+
+[[package]]
+name = "windows-implement"
+version = "0.60.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a47fddd13af08290e67f4acabf4b459f647552718f683a7b415d290ac744a836"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "windows-interface"
+version = "0.59.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "bd9211b69f8dcdfa817bfd14bf1c97c9188afa36f4750130fcdf3f400eca9fa8"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "windows-link"
+version = "0.1.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "76840935b766e1b0a05c0066835fb9ec80071d4c09a16f6bd5f7e655e3c14c38"
+
+[[package]]
+name = "windows-result"
+version = "0.3.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "56f42bd332cc6c8eac5af113fc0c1fd6a8fd2aa08a0119358686e5160d0586c6"
+dependencies = [
+ "windows-link",
+]
+
+[[package]]
+name = "windows-strings"
+version = "0.4.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "56e6c93f3a0c3b36176cb1327a4958a0353d5d166c2a35cb268ace15e91d3b57"
+dependencies = [
+ "windows-link",
+]
+
 [[package]]
 name = "windows-sys"
 version = "0.59.0"
--- a/app-proto/Cargo.toml
+++ b/app-proto/Cargo.toml
@ -10,12 +10,16 @@ default = ["console_error_panic_hook"]
 dev = []

 [dependencies]
+enum-iterator = "2.3.0"
 itertools = "0.13.0"
 js-sys = "0.3.70"
 lazy_static = "1.5.0"
 nalgebra = "0.33.0"
 readonly = "0.2.12"
-sycamore = "0.9.0-beta.3"
+sycamore = "0.9.1"
+
+# We use Charming to help display engine diagnostics
+charming = { version = "0.5.1", features = ["wasm"] }

 # The `console_error_panic_hook` crate provides better debugging of panics by
 # logging them with `console.error`. This is great for development, but requires
--- a/app-proto/examples/common/print.rs
+++ b/app-proto/examples/common/print.rs
@ -0,0 +1,36 @@
+#![allow(dead_code)]
+
+use nalgebra::DMatrix;
+
+use dyna3::engine::{Q, DescentHistory, Realization};
+
+pub fn title(title: &str) {
+    println!("─── {title} ───");
+}
+
+pub fn realization_diagnostics(realization: &Realization) {
+    let Realization { result, history } = realization;
+    println!();
+    if let Err(ref message) = result {
+        println!("❌️ {message}");
+    } else {
+        println!("✅️ Target accuracy achieved!");
+    }
+    println!("Steps: {}", history.scaled_loss.len() - 1);
+    println!("Loss: {}", history.scaled_loss.last().unwrap());
+}
+
+pub fn gram_matrix(config: &DMatrix<f64>) {
+    println!("\nCompleted Gram matrix:{}", (config.tr_mul(&*Q) * config).to_string().trim_end());
+}
+
+pub fn config(config: &DMatrix<f64>) {
+    println!("\nConfiguration:{}", config.to_string().trim_end());
+}
+
+pub fn loss_history(history: &DescentHistory) {
+    println!("\nStep │ Loss\n─────┼────────────────────────────────");
+    for (step, scaled_loss) in history.scaled_loss.iter().enumerate() {
+        println!("{:<4} │ {}", step, scaled_loss);
+    }
+}
--- a/app-proto/examples/irisawa-hexlet.rs
+++ b/app-proto/examples/irisawa-hexlet.rs
@ -1,25 +1,23 @@
-use dyna3::engine::{Q, examples::realize_irisawa_hexlet};
+#[path = "common/print.rs"]
+mod print;
+
+use dyna3::engine::{ConfigNeighborhood, examples::realize_irisawa_hexlet};

 fn main() {
    const SCALED_TOL: f64 = 1.0e-12;
-    let (config, _, success, history) = realize_irisawa_hexlet(SCALED_TOL);
-    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    if success {
-        println!("Target accuracy achieved!");
-    } else {
-        println!("Failed to reach target accuracy");
-    }
-    println!("Steps: {}", history.scaled_loss.len() - 1);
-    println!("Loss: {}", history.scaled_loss.last().unwrap());
-    if success {
+    let realization = realize_irisawa_hexlet(SCALED_TOL);
+    print::title("Irisawa hexlet");
+    print::realization_diagnostics(&realization);
+    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
+        // print the diameters of the chain spheres
        println!("\nChain diameters:");
        println!("  {} sun (given)", 1.0 / config[(3, 3)]);
        for k in 4..9 {
            println!("  {} sun", 1.0 / config[(3, k)]);
        }
+
+        // print the completed Gram matrix
+        print::gram_matrix(&config);
    }
-    println!("\nStep │ Loss\n─────┼────────────────────────────────");
-    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
-        println!("{:<4} │ {}", step, scaled_loss);
-    }
-}
+    print::loss_history(&realization.history);
+}
--- a/app-proto/examples/kaleidocycle.rs
+++ b/app-proto/examples/kaleidocycle.rs
@ -1,30 +1,32 @@
+#[path = "common/print.rs"]
+mod print;
+
 use nalgebra::{DMatrix, DVector};

-use dyna3::engine::{Q, examples::realize_kaleidocycle};
+use dyna3::engine::{ConfigNeighborhood, examples::realize_kaleidocycle};

 fn main() {
    const SCALED_TOL: f64 = 1.0e-12;
-    let (config, tangent, success, history) = realize_kaleidocycle(SCALED_TOL);
-    print!("Completed Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    print!("Configuration:{}", config);
-    if success {
-        println!("Target accuracy achieved!");
-    } else {
-        println!("Failed to reach target accuracy");
+    let realization = realize_kaleidocycle(SCALED_TOL);
+    print::title("Kaleidocycle");
+    print::realization_diagnostics(&realization);
+    if let Ok(ConfigNeighborhood { config, nbhd: tangent }) = realization.result {
+        // print the completed Gram matrix and the realized configuration
+        print::gram_matrix(&config);
+        print::config(&config);
+
+        // find the kaleidocycle's twist motion by projecting onto the tangent
+        // space
+        const N_POINTS: usize = 12;
+        let up = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
+        let down = -&up;
+        let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
+            |n| [
+                tangent.proj(&up.as_view(), n),
+                tangent.proj(&down.as_view(), n+1),
+            ]
+        ).sum();
+        let normalization = 5.0 / twist_motion[(2, 0)];
+        println!("\nTwist motion:{}", (normalization * twist_motion).to_string().trim_end());
    }
-    println!("Steps: {}", history.scaled_loss.len() - 1);
-    println!("Loss: {}\n", history.scaled_loss.last().unwrap());
-    
-    // find the kaleidocycle's twist motion by projecting onto the tangent space
-    const N_POINTS: usize = 12;
-    let up = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
-    let down = -&up;
-    let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
-        |n| [
-            tangent.proj(&up.as_view(), n),
-            tangent.proj(&down.as_view(), n+1)
-        ]
-    ).sum();
-    let normalization = 5.0 / twist_motion[(2, 0)];
-    print!("Twist motion:{}", normalization * twist_motion);
-}
+}
--- a/app-proto/examples/point-on-sphere.rs
+++ b/app-proto/examples/point-on-sphere.rs
@ -1,4 +1,13 @@
-use dyna3::engine::{Q, point, realize_gram, sphere, ConstraintProblem};
+#[path = "common/print.rs"]
+mod print;
+
+use dyna3::engine::{
+    point,
+    realize_gram,
+    sphere,
+    ConfigNeighborhood,
+    ConstraintProblem,
+};

 fn main() {
    let mut problem = ConstraintProblem::from_guess(&[
@ -11,21 +20,14 @@ fn main() {
        }
    }
    problem.frozen.push(3, 0, problem.guess[(3, 0)]);
-    println!();
-    let (config, _, success, history) = realize_gram(
+    let realization = realize_gram(
        &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
    );
-    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    print!("Configuration:{}", config);
-    if success {
-        println!("Target accuracy achieved!");
-    } else {
-        println!("Failed to reach target accuracy");
-    }
-    println!("Steps: {}", history.scaled_loss.len() - 1);
-    println!("Loss: {}", history.scaled_loss.last().unwrap());
-    println!("\nStep │ Loss\n─────┼────────────────────────────────");
-    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
-        println!("{:<4} │ {}", step, scaled_loss);
+    print::title("Point on a sphere");
+    print::realization_diagnostics(&realization);
+    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
+        print::gram_matrix(&config);
+        print::config(&config);
    }
+    print::loss_history(&realization.history);
 }
--- a/app-proto/examples/three-spheres.rs
+++ b/app-proto/examples/three-spheres.rs
@ -1,4 +1,12 @@
-use dyna3::engine::{Q, realize_gram, sphere, ConstraintProblem};
+#[path = "common/print.rs"]
+mod print;
+
+use dyna3::engine::{
+    realize_gram,
+    sphere,
+    ConfigNeighborhood,
+    ConstraintProblem,
+};

 fn main() {
    let mut problem = ConstraintProblem::from_guess({
@ -6,7 +14,7 @@ fn main() {
        &[
            sphere(1.0, 0.0, 0.0, 1.0),
            sphere(-0.5, a, 0.0, 1.0),
-            sphere(-0.5, -a, 0.0, 1.0)
+            sphere(-0.5, -a, 0.0, 1.0),
        ]
    });
    for j in 0..3 {
@ -14,20 +22,13 @@ fn main() {
            problem.gram.push_sym(j, k, if j == k { 1.0 } else { -1.0 });
        }
    }
-    println!();
-    let (config, _, success, history) = realize_gram(
+    let realization = realize_gram(
        &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
    );
-    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
-    if success {
-        println!("Target accuracy achieved!");
-    } else {
-        println!("Failed to reach target accuracy");
-    }
-    println!("Steps: {}", history.scaled_loss.len() - 1);
-    println!("Loss: {}", history.scaled_loss.last().unwrap());
-    println!("\nStep │ Loss\n─────┼────────────────────────────────");
-    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
-        println!("{:<4} │ {}", step, scaled_loss);
+    print::title("Three spheres");
+    print::realization_diagnostics(&realization);
+    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
+        print::gram_matrix(&config);
    }
+    print::loss_history(&realization.history);
 }
--- a/app-proto/index.html
+++ b/app-proto/index.html
@ -6,6 +6,12 @@
    <link data-trunk rel="css" href="main.css"/>
    <link href="https://fonts.bunny.net/css?family=fira-sans:ital,wght@0,400;1,400&display=swap" rel="stylesheet">
    <link href="https://fonts.bunny.net/css?family=noto-emoji:wght@400&text=%f0%9f%94%97%e2%9a%a0&display=swap" rel="stylesheet">
+
+    <!--
+      the Charming visualization crate, which we use to show engine diagnostics,
+      depends the ECharts JavaScript package
+    -->
+    <script src="https://cdn.jsdelivr.net/npm/echarts@5.5.1/dist/echarts.min.js"></script>
  </head>
  <body></body>
 </html>
--- a/app-proto/main.css
+++ b/app-proto/main.css
@ -18,6 +18,17 @@ body {
  font-family: 'Fira Sans', sans-serif;
 }

+.invalid {
+  color: var(--text-invalid);
+}
+
+.status {
+  width: 20px;
+  text-align: center;
+  font-family: 'Noto Emoji';
+  font-style: normal;
+}
+
 /* sidebar */

 #sidebar {
@ -138,6 +149,7 @@ details[open]:has(li) .element-switch::after {
 }

 .regulator-input {
+  margin-right: 4px;
  color: inherit;
  background-color: inherit;
  border: 1px solid var(--border);
@ -159,22 +171,65 @@ details[open]:has(li) .element-switch::after {
  border-color: var(--border-invalid);
 }

-.status {
-  width: 20px;
-  padding-left: 4px;
-  text-align: center;
-  font-family: 'Noto Emoji';
-  font-style: normal;
-}
-
 .regulator-input.invalid + .status::after, details:has(.invalid):not([open]) .status::after {
  content: '⚠';
  color: var(--text-invalid);
 }

+/* diagnostics */
+
+#diagnostics {
+  margin: 10px;
+}
+
+#diagnostics-bar {
+  display: flex;
+  gap: 8px;
+}
+
+#realization-status {
+  display: flex;
+  flex-grow: 1;
+}
+
+#realization-status .status {
+  margin-right: 4px;
+}
+
+#realization-status :not(.status) {
+  flex-grow: 1;
+}
+
+#realization-status .status::after {
+  content: '✓';
+}
+
+#realization-status.invalid .status::after {
+  content: '⚠';
+}
+
+#step-input > label {
+  padding-right: 4px;
+}
+
+#step-input > input {
+  width: 45px;
+}
+
+.diagnostics-panel {
+  margin-top: 10px;
+  min-height: 180px;
+}
+
+.diagnostics-chart {
+  background-color: var(--display-background);
+  border: 1px solid var(--border);
+  border-radius: 8px;
+}
+
 /* display */

-canvas {
+#display {
  float: left;
  margin-left: 20px;
  margin-top: 20px;
@ -183,7 +238,7 @@ canvas {
  border-radius: 16px;
 }

-canvas:focus {
+#display:focus {
  border-color: var(--border-focus-dark);
  outline: none;
 }
--- a/app-proto/run-examples
+++ b/app-proto/run-examples
@ -1,12 +0,0 @@
-#!/bin/sh
-
-# run all Cargo examples, as described here:
-#
-#   Karol Kuczmarski. "Add examples to your Rust libraries"
-#   http://xion.io/post/code/rust-examples.html
-#
-
-cargo run --example irisawa-hexlet
-cargo run --example three-spheres
-cargo run --example point-on-sphere
-cargo run --example kaleidocycle
--- a/app-proto/src/add_remove.rs
+++ b/app-proto/src/add_remove.rs
@ -1,513 +0,0 @@
-use itertools::izip;
-use nalgebra::Vector3;
-use std::{f64::consts::{FRAC_1_SQRT_2, PI}, rc::Rc};
-use sycamore::prelude::*;
-use web_sys::{console, wasm_bindgen::JsValue};
-
-use crate::{
-    engine,
-    AppState,
-    assembly::{
-        Assembly,
-        Element,
-        ElementColor,
-        InversiveDistanceRegulator,
-        Point,
-        Sphere
-    },
-    specified::SpecifiedValue
-};
-
-/* DEBUG */
-// load an example assembly for testing. this code will be removed once we've
-// built a more formal test assembly system
-fn load_gen_assemb(assembly: &Assembly) {
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            String::from("gemini_a"),
-            String::from("Castor"),
-            [1.00_f32, 0.25_f32, 0.00_f32],
-            engine::sphere(0.5, 0.5, 0.0, 1.0)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            String::from("gemini_b"),
-            String::from("Pollux"),
-            [0.00_f32, 0.25_f32, 1.00_f32],
-            engine::sphere(-0.5, -0.5, 0.0, 1.0)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            String::from("ursa_major"),
-            String::from("Ursa major"),
-            [0.25_f32, 0.00_f32, 1.00_f32],
-            engine::sphere(-0.5, 0.5, 0.0, 0.75)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            String::from("ursa_minor"),
-            String::from("Ursa minor"),
-            [0.25_f32, 1.00_f32, 0.00_f32],
-            engine::sphere(0.5, -0.5, 0.0, 0.5)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            String::from("moon_deimos"),
-            String::from("Deimos"),
-            [0.75_f32, 0.75_f32, 0.00_f32],
-            engine::sphere(0.0, 0.15, 1.0, 0.25)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            String::from("moon_phobos"),
-            String::from("Phobos"),
-            [0.00_f32, 0.75_f32, 0.50_f32],
-            engine::sphere(0.0, -0.15, -1.0, 0.25)
-        )
-    );
-}
-
-/* DEBUG */
-// load an example assembly for testing. this code will be removed once we've
-// built a more formal test assembly system
-fn load_low_curv_assemb(assembly: &Assembly) {
-    let a = 0.75_f64.sqrt();
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "central".to_string(),
-            "Central".to_string(),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(0.0, 0.0, 0.0, 1.0)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "assemb_plane".to_string(),
-            "Assembly plane".to_string(),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere_with_offset(0.0, 0.0, 1.0, 0.0, 0.0)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "side1".to_string(),
-            "Side 1".to_string(),
-            [1.00_f32, 0.00_f32, 0.25_f32],
-            engine::sphere_with_offset(1.0, 0.0, 0.0, 1.0, 0.0)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "side2".to_string(),
-            "Side 2".to_string(),
-            [0.25_f32, 1.00_f32, 0.00_f32],
-            engine::sphere_with_offset(-0.5, a, 0.0, 1.0, 0.0)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "side3".to_string(),
-            "Side 3".to_string(),
-            [0.00_f32, 0.25_f32, 1.00_f32],
-            engine::sphere_with_offset(-0.5, -a, 0.0, 1.0, 0.0)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "corner1".to_string(),
-            "Corner 1".to_string(),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(-4.0/3.0, 0.0, 0.0, 1.0/3.0)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            "corner2".to_string(),
-            "Corner 2".to_string(),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(2.0/3.0, -4.0/3.0 * a, 0.0, 1.0/3.0)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Sphere::new(
-            String::from("corner3"),
-            String::from("Corner 3"),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(2.0/3.0, 4.0/3.0 * a, 0.0, 1.0/3.0)
-        )
-    );
-}
-
-/* DEBUG */
-// load an example assembly for testing. this code will be removed once we've
-// built a more formal test assembly system
-fn load_pointed_assemb(assembly: &Assembly) {
-    let _ = assembly.try_insert_element(
-        Point::new(
-            "point_front".to_string(),
-            "Front point".to_string(),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::point(0.0, 0.0, FRAC_1_SQRT_2)
-        )
-    );
-    let _ = assembly.try_insert_element(
-        Point::new(
-            "point_back".to_string(),
-            "Back point".to_string(),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::point(0.0, 0.0, -FRAC_1_SQRT_2)
-        )
-    );
-    for index_x in 0..=1 {
-        for index_y in 0..=1 {
-            let x = index_x as f64 - 0.5;
-            let y = index_y as f64 - 0.5;
-            
-            let _ = assembly.try_insert_element(
-                Sphere::new(
-                    format!("sphere{index_x}{index_y}"),
-                    format!("Sphere {index_x}{index_y}"),
-                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
-                    engine::sphere(x, y, 0.0, 1.0)
-                )
-            );
-            
-            let _ = assembly.try_insert_element(
-                Point::new(
-                    format!("point{index_x}{index_y}"),
-                    format!("Point {index_x}{index_y}"),
-                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
-                    engine::point(x, y, 0.0)
-                )
-            );
-        }
-    }
-}
-
-// to finish setting up the problem, fix the following curvatures:
-//   sun      1
-//   moon     5/3 = 1.666666666666666...
-//   chain1   2
-// a tiny `x` or `z` nudge of the outer sphere reliably prevents realization
-// failures before they happen, or resolves them after they happen. the result
-// depends sensitively on the translation direction, suggesting that realization
-// is failing because the engine is having trouble breaking a symmetry
-// /* TO DO */
-// the engine's performance on this problem is scale-dependent! with the current
-// initial conditions, realization fails for any order of imposing the remaining
-// curvature constraints. scaling everything up by a factor of ten, as done in
-// the original problem, makes realization succeed reliably. one potentially
-// relevant difference is that a lot of the numbers in the current initial
-// conditions are exactly representable as floats, unlike the analogous numbers
-// in the scaled-up problem. the inexact representations might break the
-// symmetry that's getting the engine stuck
-fn load_irisawa_hexlet_assemb(assembly: &Assembly) {
-    let index_range = 1..=6;
-    let colors = [
-        [1.00_f32, 0.00_f32, 0.25_f32],
-        [1.00_f32, 0.25_f32, 0.00_f32],
-        [0.75_f32, 0.75_f32, 0.00_f32],
-        [0.25_f32, 1.00_f32, 0.00_f32],
-        [0.00_f32, 0.25_f32, 1.00_f32],
-        [0.25_f32, 0.00_f32, 1.00_f32]
-    ].into_iter();
-    
-    // create the spheres
-    let spheres = [
-        Sphere::new(
-            "outer".to_string(),
-            "Outer".to_string(),
-            [0.5_f32, 0.5_f32, 0.5_f32],
-            engine::sphere(0.0, 0.0, 0.0, 1.5)
-        ),
-        Sphere::new(
-            "sun".to_string(),
-            "Sun".to_string(),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            engine::sphere(0.0, -0.75, 0.0, 0.75)
-        ),
-        Sphere::new(
-            "moon".to_string(),
-            "Moon".to_string(),
-            [0.25_f32, 0.25_f32, 0.25_f32],
-            engine::sphere(0.0, 0.75, 0.0, 0.75)
-        ),
-    ].into_iter().chain(
-        index_range.clone().zip(colors).map(
-            |(k, color)| {
-                let ang = (k as f64) * PI/3.0;
-                Sphere::new(
-                    format!("chain{k}"),
-                    format!("Chain {k}"),
-                    color,
-                    engine::sphere(1.0 * ang.sin(), 0.0, 1.0 * ang.cos(), 0.5)
-                )
-            }
-        )
-    );
-    for sphere in spheres {
-        let _ = assembly.try_insert_element(sphere);
-    }
-    
-    // put the outer sphere in ghost mode and fix its curvature
-    let outer = assembly.elements_by_id.with_untracked(
-        |elts_by_id| elts_by_id["outer"].clone()
-    );
-    outer.ghost().set(true);
-    let outer_curvature_regulator = outer.regulators().with_untracked(
-        |regs| regs.first().unwrap().clone()
-    );
-    outer_curvature_regulator.set_point().set(
-        SpecifiedValue::try_from((1.0 / 3.0).to_string()).unwrap()
-    );
-    
-    // impose the desired tangencies
-    let [outer, sun, moon] = ["outer", "sun", "moon"].map(
-        |id| assembly.elements_by_id.with_untracked(
-            |elts_by_id| elts_by_id[id].clone()
-        )
-    );
-    let chain = index_range.map(
-        |k| assembly.elements_by_id.with_untracked(
-            |elts_by_id| elts_by_id[&format!("chain{k}")].clone()
-        )
-    );
-    for (chain_sphere, chain_sphere_next) in chain.clone().zip(chain.cycle().skip(1)) {
-        for (other_sphere, inversive_distance) in [
-            (outer.clone(), "1"),
-            (sun.clone(), "-1"),
-            (moon.clone(), "-1"),
-            (chain_sphere_next.clone(), "-1")
-        ] {
-            let tangency = InversiveDistanceRegulator::new([chain_sphere.clone(), other_sphere]);
-            tangency.set_point.set(SpecifiedValue::try_from(inversive_distance.to_string()).unwrap());
-            assembly.insert_regulator(Rc::new(tangency));
-        }
-    }
-    
-    let outer_sun_tangency = InversiveDistanceRegulator::new([outer.clone(), sun]);
-    outer_sun_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
-    assembly.insert_regulator(Rc::new(outer_sun_tangency));
-    
-    let outer_moon_tangency = InversiveDistanceRegulator::new([outer.clone(), moon]);
-    outer_moon_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
-    assembly.insert_regulator(Rc::new(outer_moon_tangency));
-}
-
-// setting the inversive distances between the vertices to -2 gives a regular
-// tetrahedron with side length 1, whose insphere and circumsphere have radii
-// sqrt(1/6) and sqrt(3/2), respectively. to measure those radii, set an
-// inversive distance of -1 between the insphere and each face, and then set an
-// inversive distance of 0 between the circumsphere and each vertex
-fn load_radius_ratio_assemb(assembly: &Assembly) {
-    let index_range = 1..=4;
-    
-    // create the spheres
-    const GRAY: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
-    let spheres = [
-        Sphere::new(
-            "sphere_faces".to_string(),
-            "Insphere".to_string(),
-            GRAY,
-            engine::sphere(0.0, 0.0, 0.0, 0.5)
-        ),
-        Sphere::new(
-            "sphere_vertices".to_string(),
-            "Circumsphere".to_string(),
-            GRAY,
-            engine::sphere(0.0, 0.0, 0.0, 0.25)
-        )
-    ];
-    for sphere in spheres {
-        let _ = assembly.try_insert_element(sphere);
-    }
-    
-    // create the vertices
-    let vertices = izip!(
-        index_range.clone(),
-        [
-            [1.00_f32, 0.50_f32, 0.75_f32],
-            [1.00_f32, 0.75_f32, 0.50_f32],
-            [1.00_f32, 1.00_f32, 0.50_f32],
-            [0.75_f32, 0.50_f32, 1.00_f32]
-        ].into_iter(),
-        [
-            engine::point(-0.6, -0.8, -0.6),
-            engine::point(-0.6, 0.8, 0.6),
-            engine::point(0.6, -0.8, 0.6),
-            engine::point(0.6, 0.8, -0.6)
-        ].into_iter()
-    ).map(
-        |(k, color, representation)| {
-            Point::new(
-                format!("v{k}"),
-                format!("Vertex {k}"),
-                color,
-                representation
-            )
-        }
-    );
-    for vertex in vertices {
-        let _ = assembly.try_insert_element(vertex);
-    }
-    
-    // create the faces
-    let base_dir = Vector3::new(1.0, 0.75, 1.0).normalize();
-    let offset = base_dir.dot(&Vector3::new(-0.6, 0.8, 0.6));
-    let faces = izip!(
-        index_range.clone(),
-        [
-            [1.00_f32, 0.00_f32, 0.25_f32],
-            [1.00_f32, 0.25_f32, 0.00_f32],
-            [0.75_f32, 0.75_f32, 0.00_f32],
-            [0.25_f32, 0.00_f32, 1.00_f32]
-        ].into_iter(),
-        [
-            engine::sphere_with_offset(base_dir[0], base_dir[1], base_dir[2], offset, 0.0),
-            engine::sphere_with_offset(base_dir[0], -base_dir[1], -base_dir[2], offset, 0.0),
-            engine::sphere_with_offset(-base_dir[0], base_dir[1], -base_dir[2], offset, 0.0),
-            engine::sphere_with_offset(-base_dir[0], -base_dir[1], base_dir[2], offset, 0.0)
-        ].into_iter()
-    ).map(
-        |(k, color, representation)| {
-            Sphere::new(
-                format!("f{k}"),
-                format!("Face {k}"),
-                color,
-                representation
-            )
-        }
-    );
-    for face in faces {
-        face.ghost().set(true);
-        let _ = assembly.try_insert_element(face);
-    }
-    
-    // impose the constraints
-    for j in index_range.clone() {
-        let [face_j, vertex_j] = [
-            format!("f{j}"),
-            format!("v{j}")
-        ].map(
-            |id| assembly.elements_by_id.with_untracked(
-                |elts_by_id| elts_by_id[&id].clone()
-            )
-        );
-        
-        // make the faces planar
-        let curvature_regulator = face_j.regulators().with_untracked(
-            |regs| regs.first().unwrap().clone()
-        );
-        curvature_regulator.set_point().set(
-            SpecifiedValue::try_from("0".to_string()).unwrap()
-        );
-        
-        for k in index_range.clone().filter(|&index| index != j) {
-            let vertex_k = assembly.elements_by_id.with_untracked(
-                |elts_by_id| elts_by_id[&format!("v{k}")].clone()
-            );
-            
-            // fix the distances between the vertices
-            if j < k {
-                let distance_regulator = InversiveDistanceRegulator::new(
-                    [vertex_j.clone(), vertex_k.clone()]
-                );
-                assembly.insert_regulator(Rc::new(distance_regulator));
-            }
-            
-            // put the vertices on the faces
-            let incidence_regulator = InversiveDistanceRegulator::new([face_j.clone(), vertex_k.clone()]);
-            incidence_regulator.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
-            assembly.insert_regulator(Rc::new(incidence_regulator));
-        }
-    }
-}
-
-#[component]
-pub fn AddRemove() -> View {
-    /* DEBUG */
-    let assembly_name = create_signal("general".to_string());
-    create_effect(move || {
-        // get name of chosen assembly
-        let name = assembly_name.get_clone();
-        console::log_1(
-            &JsValue::from(format!("Showing assembly \"{}\"", name.clone()))
-        );
-        
-        batch(|| {
-            let state = use_context::<AppState>();
-            let assembly = &state.assembly;
-            
-            // clear state
-            assembly.regulators.update(|regs| regs.clear());
-            assembly.elements.update(|elts| elts.clear());
-            assembly.elements_by_id.update(|elts_by_id| elts_by_id.clear());
-            state.selection.update(|sel| sel.clear());
-            
-            // load assembly
-            match name.as_str() {
-                "general" => load_gen_assemb(assembly),
-                "low-curv" => load_low_curv_assemb(assembly),
-                "pointed" => load_pointed_assemb(assembly),
-                "irisawa-hexlet" => load_irisawa_hexlet_assemb(assembly),
-                "radius-ratio" => load_radius_ratio_assemb(assembly),
-                _ => ()
-            };
-        });
-    });
-    
-    view! {
-        div(id="add-remove") {
-            button(
-                on:click=|_| {
-                    let state = use_context::<AppState>();
-                    state.assembly.insert_element_default::<Sphere>();
-                }
-            ) { "Add sphere" }
-            button(
-                on:click=|_| {
-                    let state = use_context::<AppState>();
-                    state.assembly.insert_element_default::<Point>();
-                }
-            ) { "Add point" }
-            button(
-                class="emoji", /* KLUDGE */ // for convenience, we're using an emoji as a temporary icon for this button
-                disabled={
-                    let state = use_context::<AppState>();
-                    state.selection.with(|sel| sel.len() != 2)
-                },
-                on:click=|_| {
-                    let state = use_context::<AppState>();
-                    let subjects: [_; 2] = state.selection.with(
-                        // the button is only enabled when two elements are
-                        // selected, so we know the cast to a two-element array
-                        // will succeed
-                        |sel| sel
-                            .clone()
-                            .into_iter()
-                            .collect::<Vec<_>>()
-                            .try_into()
-                            .unwrap()
-                    );
-                    state.assembly.insert_regulator(
-                        Rc::new(InversiveDistanceRegulator::new(subjects))
-                    );
-                    state.selection.update(|sel| sel.clear());
-                }
-            ) { "🔗" }
-            select(bind:value=assembly_name) { /* DEBUG */ // example assembly chooser
-                option(value="general") { "General" }
-                option(value="low-curv") { "Low-curvature" }
-                option(value="pointed") { "Pointed" }
-                option(value="irisawa-hexlet") { "Irisawa hexlet" }
-                option(value="radius-ratio") { "Radius ratio" }
-                option(value="empty") { "Empty" }
-            }
-        }
-    }
-}
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@ -1,33 +1,36 @@
+use enum_iterator::{all, Sequence};
 use nalgebra::{DMatrix, DVector, DVectorView};
 use std::{
    cell::Cell,
-    collections::{BTreeMap, BTreeSet},
    cmp::Ordering,
+    collections::{BTreeMap, BTreeSet},
    fmt,
-    fmt::{Debug, Formatter},
+    fmt::{Debug, Display, Formatter},
    hash::{Hash, Hasher},
    rc::Rc,
-    sync::{atomic, atomic::AtomicU64}
+    sync::{atomic, atomic::AtomicU64},
 };
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */

 use crate::{
-    display::DisplayItem,
+    components::{display::DisplayItem, outline::OutlineItem},
    engine::{
        Q,
-        change_half_curvature,
        local_unif_to_std,
        point,
        project_point_to_normalized,
        project_sphere_to_normalized,
        realize_gram,
        sphere,
+        ConfigNeighborhood,
        ConfigSubspace,
-        ConstraintProblem
+        ConstraintProblem,
+        DescentHistory,
+        MatrixEntry,
+        Realization,
    },
-    outline::OutlineItem,
-    specified::SpecifiedValue
+    specified::SpecifiedValue,
 };

 pub type ElementColor = [f32; 3];
@ -42,7 +45,7 @@ static NEXT_SERIAL: AtomicU64 = AtomicU64::new(0);
 pub trait Serial {
    // a serial number that uniquely identifies this element
    fn serial(&self) -> u64;
-    
+
    // take the next serial number, panicking if that was the last one left
    fn next_serial() -> u64 where Self: Sized {
        // the technique we use to panic on overflow is taken from _Rust Atomics
@ -83,6 +86,14 @@ impl Ord for dyn Serial {
    }
 }

+// Small helper function to generate consistent errors when there
+// are indexing issues in a ProblemPoser
+fn indexing_error(item: &str, name: &str, actor: &str) -> String {
+    format!(
+        "{item} \"{name}\" must be indexed before {actor} writes problem data"
+    )
+}
+
 pub trait ProblemPoser {
    fn pose(&self, problem: &mut ConstraintProblem);
 }
@ -90,33 +101,33 @@ pub trait ProblemPoser {
 pub trait Element: Serial + ProblemPoser + DisplayItem {
    // the default identifier for an element of this type
    fn default_id() -> String where Self: Sized;
-    
+
    // the default example of an element of this type
    fn default(id: String, id_num: u64) -> Self where Self: Sized;
-    
+
    // the default regulators that come with this element
    fn default_regulators(self: Rc<Self>) -> Vec<Rc<dyn Regulator>> {
        Vec::new()
    }
-    
+
    fn id(&self) -> &String;
    fn label(&self) -> &String;
    fn representation(&self) -> Signal<DVector<f64>>;
    fn ghost(&self) -> Signal<bool>;
-    
+
    // the regulators the element is subject to. the assembly that owns the
    // element is responsible for keeping this set up to date
    fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>>;
-    
+
    // project a representation vector for this kind of element onto its
    // normalization variety
    fn project_to_normalized(&self, rep: &mut DVector<f64>);
-    
+
    // the configuration matrix column index that was assigned to the element
    // last time the assembly was realized, or `None` if the element has never
    // been through a realization
    fn column_index(&self) -> Option<usize>;
-    
+
    // assign the element a configuration matrix column index. this method must
    // be used carefully to preserve invariant (1), described in the comment on
    // the `tangent` field of the `Assembly` structure
@ -124,8 +135,8 @@ pub trait Element: Serial + ProblemPoser + DisplayItem {
 }

 impl Debug for dyn Element {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), fmt::Error> {
-        self.id().fmt(f)
+    fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
+        Debug::fmt(&self.id(), f)
    }
 }

@ -163,27 +174,27 @@ pub struct Sphere {
    pub ghost: Signal<bool>,
    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
    serial: u64,
-    column_index: Cell<Option<usize>>
+    column_index: Cell<Option<usize>>,
 }

 impl Sphere {
    const CURVATURE_COMPONENT: usize = 3;
-    
+
    pub fn new(
        id: String,
        label: String,
        color: ElementColor,
-        representation: DVector<f64>
-    ) -> Sphere {
-        Sphere {
-            id: id,
-            label: label,
-            color: color,
+        representation: DVector<f64>,
+    ) -> Self {
+        Self {
+            id,
+            label,
+            color,
            representation: create_signal(representation),
            ghost: create_signal(false),
            regulators: create_signal(BTreeSet::new()),
            serial: Self::next_serial(),
-            column_index: None.into()
+            column_index: None.into(),
        }
    }
 }
@ -192,48 +203,48 @@ impl Element for Sphere {
    fn default_id() -> String {
        "sphere".to_string()
    }
-    
-    fn default(id: String, id_num: u64) -> Sphere {
-        Sphere::new(
+
+    fn default(id: String, id_num: u64) -> Self {
+        Self::new(
            id,
            format!("Sphere {id_num}"),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            sphere(0.0, 0.0, 0.0, 1.0)
+            sphere(0.0, 0.0, 0.0, 1.0),
        )
    }
-    
+
    fn default_regulators(self: Rc<Self>) -> Vec<Rc<dyn Regulator>> {
        vec![Rc::new(HalfCurvatureRegulator::new(self))]
    }
-    
+
    fn id(&self) -> &String {
        &self.id
    }
-    
+
    fn label(&self) -> &String {
        &self.label
    }
-    
+
    fn representation(&self) -> Signal<DVector<f64>> {
        self.representation
    }
-    
+
    fn ghost(&self) -> Signal<bool> {
        self.ghost
    }
-    
+
    fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>> {
        self.regulators
    }
-    
+
    fn project_to_normalized(&self, rep: &mut DVector<f64>) {
        project_sphere_to_normalized(rep);
    }
-    
+
    fn column_index(&self) -> Option<usize> {
        self.column_index.get()
    }
-    
+
    fn set_column_index(&self, index: usize) {
        self.column_index.set(Some(index));
    }
@ -248,8 +259,7 @@ impl Serial for Sphere {
 impl ProblemPoser for Sphere {
    fn pose(&self, problem: &mut ConstraintProblem) {
        let index = self.column_index().expect(
-            format!("Sphere \"{}\" should be indexed before writing problem data", self.id).as_str()
-        );
+            indexing_error("Sphere", &self.id, "it").as_str());
        problem.gram.push_sym(index, index, 1.0);
        problem.guess.set_column(index, &self.representation.get_clone_untracked());
    }
@ -263,19 +273,20 @@ pub struct Point {
    pub ghost: Signal<bool>,
    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
    serial: u64,
-    column_index: Cell<Option<usize>>
+    column_index: Cell<Option<usize>>,
 }

 impl Point {
    const WEIGHT_COMPONENT: usize = 3;
-    
+    const NORM_COMPONENT: usize = 4;
+
    pub fn new(
        id: String,
        label: String,
        color: ElementColor,
-        representation: DVector<f64>
-    ) -> Point {
-        Point {
+        representation: DVector<f64>,
+    ) -> Self {
+        Self {
            id,
            label,
            color,
@ -283,7 +294,7 @@ impl Point {
            ghost: create_signal(false),
            regulators: create_signal(BTreeSet::new()),
            serial: Self::next_serial(),
-            column_index: None.into()
+            column_index: None.into(),
        }
    }
 }
@ -292,44 +303,53 @@ impl Element for Point {
    fn default_id() -> String {
        "point".to_string()
    }
-    
-    fn default(id: String, id_num: u64) -> Point {
-        Point::new(
+
+    fn default(id: String, id_num: u64) -> Self {
+        Self::new(
            id,
            format!("Point {id_num}"),
            [0.75_f32, 0.75_f32, 0.75_f32],
-            point(0.0, 0.0, 0.0)
+            point(0.0, 0.0, 0.0),
        )
    }
-    
+
+    fn default_regulators(self: Rc<Self>) -> Vec<Rc<dyn Regulator>> {
+        all::<Axis>()
+            .map(|axis| {
+                Rc::new(PointCoordinateRegulator::new(self.clone(), axis))
+                    as Rc::<dyn Regulator>
+            })
+            .collect()
+    }
+
    fn id(&self) -> &String {
        &self.id
    }
-    
+
    fn label(&self) -> &String {
        &self.label
    }
-    
+
    fn representation(&self) -> Signal<DVector<f64>> {
        self.representation
    }
-    
+
    fn ghost(&self) -> Signal<bool> {
        self.ghost
    }
-    
+
    fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>> {
        self.regulators
    }
-    
+
    fn project_to_normalized(&self, rep: &mut DVector<f64>) {
        project_point_to_normalized(rep);
    }
-    
+
    fn column_index(&self) -> Option<usize> {
        self.column_index.get()
    }
-    
+
    fn set_column_index(&self, index: usize) {
        self.column_index.set(Some(index));
    }
@ -344,10 +364,9 @@ impl Serial for Point {
 impl ProblemPoser for Point {
    fn pose(&self, problem: &mut ConstraintProblem) {
        let index = self.column_index().expect(
-            format!("Point \"{}\" should be indexed before writing problem data", self.id).as_str()
-        );
+            indexing_error("Point", &self.id, "it").as_str());
        problem.gram.push_sym(index, index, 0.0);
-        problem.frozen.push(Point::WEIGHT_COMPONENT, index, 0.5);
+        problem.frozen.push(Self::WEIGHT_COMPONENT, index, 0.5);
        problem.guess.set_column(index, &self.representation.get_clone_untracked());
    }
 }
@ -356,16 +375,6 @@ pub trait Regulator: Serial + ProblemPoser + OutlineItem {
    fn subjects(&self) -> Vec<Rc<dyn Element>>;
    fn measurement(&self) -> ReadSignal<f64>;
    fn set_point(&self) -> Signal<SpecifiedValue>;
-    
-    // this method is used to responsively precondition the assembly for
-    // realization when the regulator becomes a constraint, or is edited while
-    // acting as a constraint. it should track the set point, do any desired
-    // preconditioning when the set point is present, and use its return value
-    // to report whether the set is present. the default implementation does no
-    // preconditioning
-    fn try_activate(&self) -> bool {
-        self.set_point().with(|set_pt| set_pt.is_present())
-    }
 }

 impl Hash for dyn Regulator {
@ -398,11 +407,11 @@ pub struct InversiveDistanceRegulator {
    pub subjects: [Rc<dyn Element>; 2],
    pub measurement: ReadSignal<f64>,
    pub set_point: Signal<SpecifiedValue>,
-    serial: u64
+    serial: u64,
 }

 impl InversiveDistanceRegulator {
-    pub fn new(subjects: [Rc<dyn Element>; 2]) -> InversiveDistanceRegulator {
+    pub fn new(subjects: [Rc<dyn Element>; 2]) -> Self {
        let representations = subjects.each_ref().map(|subj| subj.representation());
        let measurement = create_memo(move || {
            representations[0].with(|rep_0|
@ -411,11 +420,11 @@ impl InversiveDistanceRegulator {
                )
            )
        });
-        
+
        let set_point = create_signal(SpecifiedValue::from_empty_spec());
        let serial = Self::next_serial();
-        
-        InversiveDistanceRegulator { subjects, measurement, set_point, serial }
+
+        Self { subjects, measurement, set_point, serial }
    }
 }

@ -423,11 +432,11 @@ impl Regulator for InversiveDistanceRegulator {
    fn subjects(&self) -> Vec<Rc<dyn Element>> {
        self.subjects.clone().into()
    }
-    
+
    fn measurement(&self) -> ReadSignal<f64> {
        self.measurement
    }
-    
+
    fn set_point(&self) -> Signal<SpecifiedValue> {
        self.set_point
    }
@ -445,8 +454,8 @@ impl ProblemPoser for InversiveDistanceRegulator {
            if let Some(val) = set_pt.value {
                let [row, col] = self.subjects.each_ref().map(
                    |subj| subj.column_index().expect(
-                        "Subjects should be indexed before inversive distance regulator writes problem data"
-                    )
+                        indexing_error("Subject", subj.id(),
+                            "inversive distance regulator").as_str())
                );
                problem.gram.push_sym(row, col, val);
            }
@ -455,22 +464,22 @@ impl ProblemPoser for InversiveDistanceRegulator {
 }

 pub struct HalfCurvatureRegulator {
-    pub subject: Rc<dyn Element>,
+    pub subject: Rc<Sphere>,
    pub measurement: ReadSignal<f64>,
    pub set_point: Signal<SpecifiedValue>,
-    serial: u64
+    serial: u64,
 }

 impl HalfCurvatureRegulator {
-    pub fn new(subject: Rc<dyn Element>) -> HalfCurvatureRegulator {
+    pub fn new(subject: Rc<Sphere>) -> Self {
        let measurement = subject.representation().map(
            |rep| rep[Sphere::CURVATURE_COMPONENT]
        );
-        
+
        let set_point = create_signal(SpecifiedValue::from_empty_spec());
        let serial = Self::next_serial();
-        
-        HalfCurvatureRegulator { subject, measurement, set_point, serial }
+
+        Self { subject, measurement, set_point, serial }
    }
 }

@ -478,26 +487,14 @@ impl Regulator for HalfCurvatureRegulator {
    fn subjects(&self) -> Vec<Rc<dyn Element>> {
        vec![self.subject.clone()]
    }
-    
+
    fn measurement(&self) -> ReadSignal<f64> {
        self.measurement
    }
-    
+
    fn set_point(&self) -> Signal<SpecifiedValue> {
        self.set_point
    }
-    
-    fn try_activate(&self) -> bool {
-        match self.set_point.with(|set_pt| set_pt.value) {
-            Some(half_curv) => {
-                self.subject.representation().update(
-                    |rep| change_half_curvature(rep, half_curv)
-                );
-                true
-            }
-            None => false
-        }
-    }
 }

 impl Serial for HalfCurvatureRegulator {
@ -511,18 +508,88 @@ impl ProblemPoser for HalfCurvatureRegulator {
        self.set_point.with_untracked(|set_pt| {
            if let Some(val) = set_pt.value {
                let col = self.subject.column_index().expect(
-                    "Subject should be indexed before half-curvature regulator writes problem data"
-                );
+                    indexing_error("Subject", &self.subject.id,
+                        "half-curvature regulator").as_str());
                problem.frozen.push(Sphere::CURVATURE_COMPONENT, col, val);
            }
        });
    }
 }

+#[derive(Clone, Copy, Sequence)]
+pub enum Axis { X = 0, Y = 1, Z = 2 }
+impl Axis {
+    fn name(&self) -> &'static str {
+        match self { Axis::X => "X", Axis::Y => "Y", Axis::Z => "Z" }
+    }
+}
+
+impl Display for Axis {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.write_str(self.name())
+    }
+}
+
+pub struct PointCoordinateRegulator {
+    pub subject: Rc<Point>,
+    pub axis: Axis,
+    pub measurement: ReadSignal<f64>,
+    pub set_point: Signal<SpecifiedValue>,
+    serial: u64
+}
+
+impl PointCoordinateRegulator {
+    pub fn new(subject: Rc<Point>, axis: Axis) -> Self {
+        let measurement = subject.representation().map(
+            move |rep| rep[axis as usize]
+        );
+        let set_point = create_signal(SpecifiedValue::from_empty_spec());
+        Self { subject, axis, measurement, set_point, serial: Self::next_serial() }
+    }
+}
+
+impl Serial for PointCoordinateRegulator {
+    fn serial(&self) -> u64 { self.serial }
+}
+
+impl Regulator for PointCoordinateRegulator {
+    fn subjects(&self) -> Vec<Rc<dyn Element>> { vec![self.subject.clone()] }
+    fn measurement(&self) -> ReadSignal<f64> { self.measurement }
+    fn set_point(&self) -> Signal<SpecifiedValue> { self.set_point }
+}
+
+impl ProblemPoser for PointCoordinateRegulator {
+    fn pose(&self, problem: &mut ConstraintProblem) {
+        self.set_point.with_untracked(|set_pt| {
+            if let Some(val) = set_pt.value {
+                let col = self.subject.column_index().expect(
+                    indexing_error("Subject", &self.subject.id,
+                        "point-coordinate regulator").as_str());
+                problem.frozen.push(self.axis as usize, col, val);
+                // If all three of the subject's spatial coordinates have been
+                // frozen, then freeze its norm component:
+                let mut coords = [0.0; Axis::CARDINALITY];
+                let mut nset: usize = 0;
+                for &MatrixEntry {index, value} in &(problem.frozen) {
+                    if index.1 == col && index.0 < Axis::CARDINALITY {
+                        nset += 1;
+                        coords[index.0] = value
+                    }
+                }
+                if nset == Axis::CARDINALITY {
+                    let [x, y, z] = coords;
+                    problem.frozen.push(
+                        Point::NORM_COMPONENT, col, point(x,y,z)[Point::NORM_COMPONENT]);
+                }
+            }
+        });
+    }
+}
+
 // the velocity is expressed in uniform coordinates
 pub struct ElementMotion<'a> {
    pub element: Rc<dyn Element>,
-    pub velocity: DVectorView<'a, f64>
+    pub velocity: DVectorView<'a, f64>,
 }

 type AssemblyMotion<'a> = Vec<ElementMotion<'a>>;
@ -533,10 +600,7 @@ pub struct Assembly {
    // elements and regulators
    pub elements: Signal<BTreeSet<Rc<dyn Element>>>,
    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
-    
-    // a flag that tells us whether the assembly is realized
-    pub realized: Signal<bool>,
-    
+
    // solution variety tangent space. the basis vectors are stored in
    // configuration matrix format, ordered according to the elements' column
    // indices. when you realize the assembly, every element that's present
@ -548,9 +612,17 @@ pub struct Assembly {
    //      in that column of the tangent space basis matrices
    //
    pub tangent: Signal<ConfigSubspace>,
-    
+
    // indexing
-    pub elements_by_id: Signal<BTreeMap<String, Rc<dyn Element>>>
+    pub elements_by_id: Signal<BTreeMap<String, Rc<dyn Element>>>,
+
+    // realization control
+    pub realization_trigger: Signal<()>,
+
+    // realization diagnostics
+    pub realization_status: Signal<Result<(), String>>,
+    pub descent_history: Signal<DescentHistory>,
+    pub step: Signal<SpecifiedValue>,
 }

 impl Assembly {
@ -559,24 +631,45 @@ impl Assembly {
        let assembly = Assembly {
            elements: create_signal(BTreeSet::new()),
            regulators: create_signal(BTreeSet::new()),
-            realized: create_signal(true),
            tangent: create_signal(ConfigSubspace::zero(0)),
-            elements_by_id: create_signal(BTreeMap::default())
+            elements_by_id: create_signal(BTreeMap::default()),
+            realization_trigger: create_signal(()),
+            realization_status: create_signal(Ok(())),
+            descent_history: create_signal(DescentHistory::new()),
+            step: create_signal(SpecifiedValue::from_empty_spec()),
        };
-        
-        // realize the assembly whenever the `realized` flag is set to `false`
-        let assembly_for_effect = assembly.clone();
-        create_memo(move || {
-            if !assembly_for_effect.realized.get() {
-                assembly_for_effect.realize();
+
+        // realize the assembly whenever the element list, the regulator list,
+        // a regulator's set point, or the realization trigger is updated
+        let assembly_for_realization = assembly.clone();
+        create_effect(move || {
+            assembly_for_realization.elements.track();
+            assembly_for_realization.regulators.with(
+                |regs| for reg in regs {
+                    reg.set_point().track();
+                }
+            );
+            assembly_for_realization.realization_trigger.track();
+            assembly_for_realization.realize();
+        });
+
+        // load a configuration from the descent history whenever the active
+        // step is updated
+        let assembly_for_step_selection = assembly.clone();
+        create_effect(move || {
+            if let Some(step) = assembly.step.with(|n| n.value) {
+                let config = assembly.descent_history.with_untracked(
+                    |history| history.config[step as usize].clone()
+                );
+                assembly_for_step_selection.load_config(&config)
            }
        });
-        
+
        assembly
    }
-    
+
    // --- inserting elements and regulators ---
-    
+
    // insert an element into the assembly without checking whether we already
    // have an element with the same identifier. any element that does have the
    // same identifier will get kicked out of the `elements_by_id` index
@ -586,13 +679,13 @@ impl Assembly {
        let elt_rc = Rc::new(elt);
        self.elements.update(|elts| elts.insert(elt_rc.clone()));
        self.elements_by_id.update(|elts_by_id| elts_by_id.insert(id, elt_rc.clone()));
-        
+
        // create and insert the element's default regulators
        for reg in elt_rc.default_regulators() {
            self.insert_regulator(reg);
        }
    }
-    
+
    pub fn try_insert_element(&self, elt: impl Element + 'static) -> bool {
        let can_insert = self.elements_by_id.with_untracked(
            |elts_by_id| !elts_by_id.contains_key(elt.id())
@ -602,7 +695,7 @@ impl Assembly {
        }
        can_insert
    }
-    
+
    pub fn insert_element_default<T: Element + 'static>(&self) {
        // find the next unused identifier in the default sequence
        let default_id = T::default_id();
@ -614,17 +707,17 @@ impl Assembly {
            id_num += 1;
            id = format!("{default_id}{id_num}");
        }
-        
+
        // create and insert the default example of `T`
        let _ = self.insert_element_unchecked(T::default(id, id_num));
    }
-    
+
    pub fn insert_regulator(&self, regulator: Rc<dyn Regulator>) {
        // add the regulator to the assembly's regulator list
        self.regulators.update(
            |regs| regs.insert(regulator.clone())
        );
-        
+
        // add the regulator to each subject's regulator list
        let subject_regulators: Vec<_> = regulator.subjects().into_iter().map(
            |subj| subj.regulators()
@ -632,20 +725,7 @@ impl Assembly {
        for regulators in subject_regulators {
            regulators.update(|regs| regs.insert(regulator.clone()));
        }
-        
-        // update the realization when the regulator becomes a constraint, or is
-        // edited while acting as a constraint
-        let self_for_effect = self.clone();
-        create_effect(move || {
-            /* DEBUG */
-            // log the regulator update
-            console_log!("Updated regulator with subjects {:?}", regulator.subjects());
-            
-            if regulator.try_activate() {
-                self_for_effect.realized.set(false);
-            }
-        });
-        
+
        /* DEBUG */
        // print an updated list of regulators
        console_log!("Regulators:");
@ -668,9 +748,19 @@ impl Assembly {
            }
        });
    }
-    
+
+    // --- updating the configuration ---
+
+    pub fn load_config(&self, config: &DMatrix<f64>) {
+        for elt in self.elements.get_clone_untracked() {
+            elt.representation().update(
+                |rep| rep.set_column(0, &config.column(elt.column_index().unwrap()))
+            );
+        }
+    }
+
    // --- realization ---
-    
+
    pub fn realize(&self) {
        // index the elements
        self.elements.update_silent(|elts| {
@ -678,7 +768,7 @@ impl Assembly {
                elt.set_column_index(index);
            }
        });
-        
+
        // set up the constraint problem
        let problem = self.elements.with_untracked(|elts| {
            let mut problem = ConstraintProblem::new(elts.len());
@ -692,49 +782,74 @@ impl Assembly {
            });
            problem
        });
-        
+
        /* DEBUG */
        // log the Gram matrix
        console_log!("Gram matrix:\n{}", problem.gram);
-        
+        console_log!("Frozen entries:\n{}", problem.frozen);
+
        /* DEBUG */
        // log the initial configuration matrix
        console_log!("Old configuration:{:>8.3}", problem.guess);
-        
+
        // look for a configuration with the given Gram matrix
-        let (config, tangent, success, history) = realize_gram(
+        let Realization { result, history } = realize_gram(
            &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
        );
-        
+
        /* DEBUG */
-        // report the outcome of the search
-        if success {
-            console_log!("Target accuracy achieved!")
+        // report the outcome of the search in the browser console
+        if let Err(ref message) = result {
+            console_log!("❌️ {message}");
        } else {
-            console_log!("Failed to reach target accuracy")
+            console_log!("✅️ Target accuracy achieved!");
        }
-        console_log!("Steps: {}", history.scaled_loss.len() - 1);
-        console_log!("Loss: {}", *history.scaled_loss.last().unwrap());
-        console_log!("Tangent dimension: {}", tangent.dim());
-        
-        if success {
-            // read out the solution
-            for elt in self.elements.get_clone_untracked() {
-                elt.representation().update(
-                    |rep| rep.set_column(0, &config.column(elt.column_index().unwrap()))
+        if history.scaled_loss.len() > 0 {
+            console_log!("Steps: {}", history.scaled_loss.len() - 1);
+            console_log!("Loss: {}", history.scaled_loss.last().unwrap());
+        }
+
+        // report the descent history
+        let step_cnt = history.config.len();
+        self.descent_history.set(history);
+
+        match result {
+            Ok(ConfigNeighborhood { nbhd: tangent, .. }) => {
+                /* DEBUG */
+                // report the tangent dimension
+                console_log!("Tangent dimension: {}", tangent.dim());
+
+                // report the realization status
+                self.realization_status.set(Ok(()));
+
+                // display the last realization step
+                self.step.set(
+                    if step_cnt > 0 {
+                        let last_step = step_cnt - 1;
+                        SpecifiedValue::try_from(last_step.to_string()).unwrap()
+                    } else {
+                        SpecifiedValue::from_empty_spec()
+                    }
                );
-            }
-            
-            // update the realization flag
-            self.realized.set(true);
-            
-            // save the tangent space
-            self.tangent.set_silent(tangent);
+
+                // save the tangent space
+                self.tangent.set_silent(tangent);
+            },
+            Err(message) => {
+                // report the realization status. the `Err(message)` we're
+                // setting the status to has a different type than the
+                // `Err(message)` we received from the match: we're changing the
+                // `Ok` type from `Realization` to `()`
+                self.realization_status.set(Err(message));
+
+                // display the initial guess
+                self.step.set(SpecifiedValue::from(Some(0.0)));
+            },
        }
    }
-    
+
    // --- deformation ---
-    
+
    // project the given motion to the tangent space of the solution variety and
    // move the assembly along it. the implementation is based on invariant (1)
    // from above and the following additional invariant:
@ -751,7 +866,7 @@ impl Assembly {
        if self.tangent.with(|tan| tan.dim() <= 0 && tan.assembly_dim() > 0) {
            console::log_1(&JsValue::from("The assembly is rigid"));
        }
-        
+
        // give a column index to each moving element that doesn't have one yet.
        // this temporarily breaks invariant (1), but the invariant will be
        // restored when we realize the assembly at the end of the deformation.
@ -769,7 +884,7 @@ impl Assembly {
            }
            next_column_index
        };
-        
+
        // project the element motions onto the tangent space of the solution
        // variety and sum them to get a deformation of the whole assembly. the
        // matrix `motion_proj` that holds the deformation has extra columns for
@ -780,7 +895,7 @@ impl Assembly {
            // we can unwrap the column index because we know that every moving
            // element has one at this point
            let column_index = elt_motion.element.column_index().unwrap();
-            
+
            if column_index < realized_dim {
                // this element had a column index when we started, so by
                // invariant (1), it's reflected in the tangent space
@ -798,7 +913,7 @@ impl Assembly {
                target_column += unif_to_std * elt_motion.velocity;
            }
        }
-        
+
        // step the assembly along the deformation. this changes the elements'
        // normalizations, so we restore those afterward
        for elt in self.elements.get_clone_untracked() {
@ -812,35 +927,37 @@ impl Assembly {
                    },
                    None => {
                        console_log!("No velocity to unpack for fresh element \"{}\"", elt.id())
-                    }
+                    },
                };
            });
        }
-        
-        // bring the configuration back onto the solution variety. this also
-        // gets the elements' column indices and the saved tangent space back in
-        // sync
-        self.realized.set(false);
+
+        // trigger a realization to bring the configuration back onto the
+        // solution variety. this also gets the elements' column indices and the
+        // saved tangent space back in sync
+        self.realization_trigger.set(());
    }
 }

 #[cfg(test)]
 mod tests {
    use super::*;
-    
+
    use crate::engine;
-    
+
    #[test]
-    #[should_panic(expected = "Sphere \"sphere\" should be indexed before writing problem data")]
+    #[should_panic(expected =
+        "Sphere \"sphere\" must be indexed before it writes problem data")]
    fn unindexed_element_test() {
        let _ = create_root(|| {
            let elt = Sphere::default("sphere".to_string(), 0);
            elt.pose(&mut ConstraintProblem::new(1));
        });
    }
-    
+
    #[test]
-    #[should_panic(expected = "Subjects should be indexed before inversive distance regulator writes problem data")]
+    #[should_panic(expected = "Subject \"sphere1\" must be indexed before \
+        inversive distance regulator writes problem data")]
    fn unindexed_subject_test_inversive_distance() {
        let _ = create_root(|| {
            let subjects = [0, 1].map(
@ -855,7 +972,7 @@ mod tests {
            }.pose(&mut ConstraintProblem::new(2));
        });
    }
-    
+
    #[test]
    fn curvature_drift_test() {
        const INITIAL_RADIUS: f64 = 0.25;
@ -872,10 +989,10 @@ mod tests {
                    String::from(sphere_id),
                    String::from("Sphere 0"),
                    [0.75_f32, 0.75_f32, 0.75_f32],
-                    engine::sphere(0.0, 0.0, 0.0, INITIAL_RADIUS)
+                    engine::sphere(0.0, 0.0, 0.0, INITIAL_RADIUS),
                )
            );
-            
+
            // nudge the sphere repeatedly along the `z` axis
            const STEP_SIZE: f64 = 0.0025;
            const STEP_CNT: usize = 400;
@ -886,12 +1003,12 @@ mod tests {
                    vec![
                        ElementMotion {
                            element: sphere.clone(),
-                            velocity: velocity.as_view()
+                            velocity: velocity.as_view(),
                        }
                    ]
                );
            }
-            
+
            // check how much the sphere's curvature has drifted
            const INITIAL_HALF_CURV: f64 = 0.5 / INITIAL_RADIUS;
            const DRIFT_TOL: f64 = 0.015;
@ -901,4 +1018,4 @@ mod tests {
            assert!((final_half_curv / INITIAL_HALF_CURV - 1.0).abs() < DRIFT_TOL);
        });
    }
-}
+}
--- a/app-proto/src/components.rs
+++ b/app-proto/src/components.rs
@ -0,0 +1,5 @@
+pub mod add_remove;
+pub mod diagnostics;
+pub mod display;
+pub mod outline;
+pub mod test_assembly_chooser;
--- a/app-proto/src/components/add_remove.rs
+++ b/app-proto/src/components/add_remove.rs
@ -0,0 +1,69 @@
+use std::rc::Rc;
+use sycamore::prelude::*;
+
+use super::test_assembly_chooser::TestAssemblyChooser;
+use crate::{
+    AppState,
+    assembly::{InversiveDistanceRegulator, Point, Sphere},
+};
+
+#[component]
+pub fn AddRemove() -> View {
+    view! {
+        div(id = "add-remove") {
+            button(
+                on:click = |_| {
+                    let state = use_context::<AppState>();
+                    batch(|| {
+                        // this call is batched to avoid redundant realizations.
+                        // it updates the element list and the regulator list,
+                        // which are both tracked by the realization effect
+                        /* TO DO */
+                        // it would make more to do the batching inside
+                        // `insert_element_default`, but that will have to wait
+                        // until Sycamore handles nested batches correctly.
+                        //
+                        //   https://github.com/sycamore-rs/sycamore/issues/802
+                        //
+                        // the nested batch issue is relevant here because the
+                        // assembly loaders in the test assembly chooser use
+                        // `insert_element_default` within larger batches
+                        state.assembly.insert_element_default::<Sphere>();
+                    });
+                }
+            ) { "Add sphere" }
+            button(
+                on:click = |_| {
+                    let state = use_context::<AppState>();
+                    state.assembly.insert_element_default::<Point>();
+                }
+            ) { "Add point" }
+            button(
+                class = "emoji", /* KLUDGE */ // for convenience, we're using an emoji as a temporary icon for this button
+                disabled = {
+                    let state = use_context::<AppState>();
+                    state.selection.with(|sel| sel.len() != 2)
+                },
+                on:click = |_| {
+                    let state = use_context::<AppState>();
+                    let subjects: [_; 2] = state.selection.with(
+                        // the button is only enabled when two elements are
+                        // selected, so we know the cast to a two-element array
+                        // will succeed
+                        |sel| sel
+                            .clone()
+                            .into_iter()
+                            .collect::<Vec<_>>()
+                            .try_into()
+                            .unwrap()
+                    );
+                    state.assembly.insert_regulator(
+                        Rc::new(InversiveDistanceRegulator::new(subjects))
+                    );
+                    state.selection.update(|sel| sel.clear());
+                }
+            ) { "🔗" }
+            TestAssemblyChooser {}
+        }
+    }
+}
--- a/app-proto/src/components/diagnostics.rs
+++ b/app-proto/src/components/diagnostics.rs
@ -0,0 +1,320 @@
+use charming::{
+    Chart,
+    WasmRenderer,
+    component::{Axis, DataZoom, Grid},
+    element::{AxisType, Symbol},
+    series::{Line, Scatter},
+};
+use sycamore::prelude::*;
+
+use crate::{AppState, specified::SpecifiedValue};
+
+#[derive(Clone)]
+struct DiagnosticsState {
+    active_tab: Signal<String>,
+}
+
+impl DiagnosticsState {
+    fn new(initial_tab: String) -> Self {
+        Self { active_tab: create_signal(initial_tab) }
+    }
+}
+
+// a realization status indicator
+#[component]
+fn RealizationStatus() -> View {
+    let state = use_context::<AppState>();
+    let realization_status = state.assembly.realization_status;
+    view! {
+        div(
+            id = "realization-status",
+            class = realization_status.with(
+                |status| match status {
+                    Ok(_) => "",
+                    Err(_) => "invalid",
+                }
+            )
+        ) {
+            div(class = "status")
+            div {
+                (realization_status.with(
+                    |status| match status {
+                        Ok(_) => "Target accuracy achieved".to_string(),
+                        Err(message) => message.clone(),
+                    }
+                ))
+            }
+        }
+    }
+}
+
+// history step input
+#[component]
+fn StepInput() -> View {
+    // get the assembly
+    let state = use_context::<AppState>();
+    let assembly = state.assembly;
+
+    // the `last_step` signal holds the index of the last step
+    let last_step = assembly.descent_history.map(
+        |history| match history.config.len() {
+            0 => None,
+            n => Some(n - 1),
+        }
+    );
+    let input_max = last_step.map(|last| last.unwrap_or(0));
+
+    // these signals hold the entered step number
+    let value = create_signal(String::new());
+    let value_as_number = create_signal(0.0);
+
+    create_effect(move || {
+        value.set(assembly.step.with(|n| n.spec.clone()));
+    });
+
+    view! {
+        div(id = "step-input") {
+            label { "Step" }
+            input(
+                r#type = "number",
+                min = "0",
+                max = input_max.with(|max| max.to_string()),
+                bind:value = value,
+                bind:valueAsNumber = value_as_number,
+                on:change = move |_| {
+                    if last_step.with(|last| last.is_some()) {
+                        // clamp the step within its allowed range. the lower
+                        // bound is redundant on browsers that make it
+                        // impossible to type negative values into a number
+                        // input with a non-negative `min`, but there's no harm
+                        // in being careful
+                        let step_raw = value.with(
+                            |val| SpecifiedValue::try_from(val.clone())
+                                .unwrap_or(SpecifiedValue::from_empty_spec()
+                            )
+                        );
+                        let step = SpecifiedValue::from(
+                            step_raw.value.map(
+                                |val| val.clamp(0.0, input_max.get() as f64)
+                            )
+                        );
+
+                        // set the input string and the assembly's active step
+                        value.set(step.spec.clone());
+                        assembly.step.set(step);
+                    } else {
+                        value.set(String::new());
+                    }
+                },
+            )
+        }
+    }
+}
+
+fn into_log10_time_point((step, value): (usize, f64)) -> Vec<Option<f64>> {
+    vec![
+        Some(step as f64),
+        if value == 0.0 { None } else { Some(value.abs().log10()) },
+    ]
+}
+
+// the loss history from the last realization
+#[component]
+fn LossHistory() -> View {
+    const CONTAINER_ID: &str = "loss-history";
+    let state = use_context::<AppState>();
+    let renderer = WasmRenderer::new_opt(None, Some(178));
+
+    on_mount(move || {
+        create_effect(move || {
+            // get the loss history
+            let scaled_loss: Vec<_> = state.assembly.descent_history.with(
+                |history| history.scaled_loss
+                    .iter()
+                    .enumerate()
+                    .map(|(step, &loss)| (step, loss))
+                    .map(into_log10_time_point)
+                    .collect()
+            );
+
+            // initialize the chart axes
+            let step_axis = Axis::new()
+                .type_(AxisType::Category)
+                .boundary_gap(false);
+            let scaled_loss_axis = Axis::new();
+
+            // load the chart data. when there's no history, we load the data
+            // point (0, None) to clear the chart. it would feel more natural to
+            // load empty data vectors, but that turns out not to clear the
+            // chart: it instead leads to previous data being re-used
+            let scaled_loss_series = Line::new().data(
+                if scaled_loss.len() > 0 {
+                    scaled_loss
+                } else {
+                    vec![vec![Some(0.0), None::<f64>]]
+                }
+            );
+            let chart = Chart::new()
+                .animation(false)
+                .data_zoom(DataZoom::new().y_axis_index(0).right(40))
+                .x_axis(step_axis)
+                .y_axis(scaled_loss_axis)
+                .grid(Grid::new().top(20).right(80).bottom(30).left(60))
+                .series(scaled_loss_series);
+            renderer.render(CONTAINER_ID, &chart).unwrap();
+        });
+    });
+
+    view! {
+        div(id = CONTAINER_ID, class = "diagnostics-chart")
+    }
+}
+
+// the spectrum of the Hessian during the last realization
+#[component]
+fn SpectrumHistory() -> View {
+    const CONTAINER_ID: &str = "spectrum-history";
+    let state = use_context::<AppState>();
+    let renderer = WasmRenderer::new(478, 178);
+
+    on_mount(move || {
+        create_effect(move || {
+            // get the spectrum of the Hessian at each step, split into its
+            // positive, negative, and strictly-zero parts
+            let (
+                hess_eigvals_zero,
+                hess_eigvals_nonzero,
+            ): (Vec<_>, Vec<_>) = state.assembly.descent_history.with(
+                |history| history.hess_eigvals
+                    .iter()
+                    .enumerate()
+                    .map(
+                        |(step, eigvals)| eigvals.iter().map(
+                            move |&val| (step, val)
+                        )
+                    )
+                    .flatten()
+                    .partition(|&(_, val)| val == 0.0)
+            );
+            let zero_level = hess_eigvals_nonzero
+                .iter()
+                .map(|(_, val)| val.abs())
+                .reduce(f64::min)
+                .map(|val| 0.1 * val)
+                .unwrap_or(1.0);
+            let (
+                hess_eigvals_pos,
+                hess_eigvals_neg,
+            ): (Vec<_>, Vec<_>) = hess_eigvals_nonzero
+                .into_iter()
+                .partition(|&(_, val)| val > 0.0);
+
+            // initialize the chart axes
+            let step_axis = Axis::new()
+                .type_(AxisType::Category)
+                .boundary_gap(false);
+            let eigval_axis = Axis::new();
+
+            // load the chart data. when there's no history, we load the data
+            // point (0, None) to clear the chart. it would feel more natural to
+            // load empty data vectors, but that turns out not to clear the
+            // chart: it instead leads to previous data being re-used
+            let eigval_series_pos = Scatter::new()
+                .symbol_size(4.5)
+                .data(
+                    if hess_eigvals_pos.len() > 0 {
+                        hess_eigvals_pos
+                            .into_iter()
+                            .map(into_log10_time_point)
+                            .collect()
+                    } else {
+                        vec![vec![Some(0.0), None::<f64>]]
+                    }
+                );
+            let eigval_series_neg = Scatter::new()
+                .symbol(Symbol::Diamond)
+                .symbol_size(6.0)
+                .data(
+                    if hess_eigvals_neg.len() > 0 {
+                        hess_eigvals_neg
+                            .into_iter()
+                            .map(into_log10_time_point)
+                            .collect()
+                    } else {
+                        vec![vec![Some(0.0), None::<f64>]]
+                    }
+                );
+            let eigval_series_zero = Scatter::new()
+                .symbol(Symbol::Triangle)
+                .symbol_size(5.0)
+                .data(
+                    if hess_eigvals_zero.len() > 0 {
+                        hess_eigvals_zero
+                            .into_iter()
+                            .map(|(step, _)| (step, zero_level))
+                            .map(into_log10_time_point)
+                            .collect()
+                    } else {
+                        vec![vec![Some(0.0), None::<f64>]]
+                    }
+                );
+            let chart = Chart::new()
+                .animation(false)
+                .data_zoom(DataZoom::new().y_axis_index(0).right(40))
+                .x_axis(step_axis)
+                .y_axis(eigval_axis)
+                .grid(Grid::new().top(20).right(80).bottom(30).left(60))
+                .series(eigval_series_pos)
+                .series(eigval_series_neg)
+                .series(eigval_series_zero);
+            renderer.render(CONTAINER_ID, &chart).unwrap();
+        });
+    });
+
+    view! {
+        div(id = CONTAINER_ID, class = "diagnostics-chart")
+    }
+}
+
+#[component(inline_props)]
+fn DiagnosticsPanel(name: &'static str, children: Children) -> View {
+    let diagnostics_state = use_context::<DiagnosticsState>();
+    view! {
+        div(
+            class = "diagnostics-panel",
+            "hidden" = diagnostics_state.active_tab.with(
+                |active_tab| {
+                    if active_tab == name {
+                        None
+                    } else {
+                        Some("")
+                    }
+                }
+            )
+        ) {
+            (children)
+        }
+    }
+}
+
+#[component]
+pub fn Diagnostics() -> View {
+    let diagnostics_state = DiagnosticsState::new("loss".to_string());
+    let active_tab = diagnostics_state.active_tab.clone();
+    provide_context(diagnostics_state);
+
+    view! {
+        div(id = "diagnostics") {
+            div(id = "diagnostics-bar") {
+                RealizationStatus {}
+                select(bind:value = active_tab) {
+                    option(value = "loss") { "Loss" }
+                    option(value = "spectrum") { "Spectrum" }
+                }
+                StepInput {}
+            }
+            DiagnosticsPanel(name = "loss") { LossHistory {} }
+            DiagnosticsPanel(name = "spectrum") { SpectrumHistory {} }
+        }
+    }
+}
--- a/app-proto/src/components/display.rs
+++ b/app-proto/src/components/display.rs
@ -12,12 +12,12 @@ use web_sys::{
    WebGlProgram,
    WebGlShader,
    WebGlUniformLocation,
-    wasm_bindgen::{JsCast, JsValue}
+    wasm_bindgen::{JsCast, JsValue},
 };

 use crate::{
    AppState,
-    assembly::{Element, ElementColor, ElementMotion, Point, Sphere}
+    assembly::{Element, ElementColor, ElementMotion, Point, Sphere},
 };

 // --- color ---
@ -37,23 +37,26 @@ fn combine_channels(color: ElementColor, opacity: f32) -> ColorWithOpacity {
 struct SceneSpheres {
    representations: Vec<DVector<f64>>,
    colors_with_opacity: Vec<ColorWithOpacity>,
-    highlights: Vec<f32>
+    highlights: Vec<f32>,
 }

 impl SceneSpheres {
-    fn new() -> SceneSpheres{
-        SceneSpheres {
+    fn new() -> Self {
+        Self {
            representations: Vec::new(),
            colors_with_opacity: Vec::new(),
-            highlights: Vec::new()
+            highlights: Vec::new(),
        }
    }
-    
+
    fn len_i32(&self) -> i32 {
        self.representations.len().try_into().expect("Number of spheres must fit in a 32-bit integer")
    }
-    
-    fn push(&mut self, representation: DVector<f64>, color: ElementColor, opacity: f32, highlight: f32) {
+
+    fn push(
+        &mut self, representation: DVector<f64>,
+        color: ElementColor, opacity: f32, highlight: f32,
+    ) {
        self.representations.push(representation);
        self.colors_with_opacity.push(combine_channels(color, opacity));
        self.highlights.push(highlight);
@ -64,20 +67,23 @@ struct ScenePoints {
    representations: Vec<DVector<f64>>,
    colors_with_opacity: Vec<ColorWithOpacity>,
    highlights: Vec<f32>,
-    selections: Vec<f32>
+    selections: Vec<f32>,
 }

 impl ScenePoints {
-    fn new() -> ScenePoints {
-        ScenePoints {
+    fn new() -> Self {
+        Self {
            representations: Vec::new(),
            colors_with_opacity: Vec::new(),
            highlights: Vec::new(),
-            selections: Vec::new()
+            selections: Vec::new(),
        }
    }
-    
-    fn push(&mut self, representation: DVector<f64>, color: ElementColor, opacity: f32, highlight: f32, selected: bool) {
+
+    fn push(
+        &mut self, representation: DVector<f64>,
+        color: ElementColor, opacity: f32, highlight: f32, selected: bool,
+    ) {
        self.representations.push(representation);
        self.colors_with_opacity.push(combine_channels(color, opacity));
        self.highlights.push(highlight);
@ -87,25 +93,30 @@ impl ScenePoints {

 pub struct Scene {
    spheres: SceneSpheres,
-    points: ScenePoints
+    points: ScenePoints,
 }

 impl Scene {
-    fn new() -> Scene {
-        Scene {
+    fn new() -> Self {
+        Self {
            spheres: SceneSpheres::new(),
-            points: ScenePoints::new()
+            points: ScenePoints::new(),
        }
    }
 }

 pub trait DisplayItem {
    fn show(&self, scene: &mut Scene, selected: bool);
-    
+
    // the smallest positive depth, represented as a multiple of `dir`, where
    // the line generated by `dir` hits the element. returns `None` if the line
    // misses the element
-    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>, pixel_size: f64) -> Option<f64>;
+    fn cast(
+        &self,
+        dir: Vector3<f64>,
+        assembly_to_world: &DMatrix<f64>,
+        pixel_size: f64,
+    ) -> Option<f64>;
 }

 impl DisplayItem for Sphere {
@ -114,26 +125,31 @@ impl DisplayItem for Sphere {
        const DEFAULT_OPACITY: f32 = 0.5;
        const GHOST_OPACITY: f32 = 0.2;
        const HIGHLIGHT: f32 = 0.2;
-        
+
        let representation = self.representation.get_clone_untracked();
        let color = if selected { self.color.map(|channel| 0.2 + 0.8*channel) } else { self.color };
        let opacity = if self.ghost.get() { GHOST_OPACITY } else { DEFAULT_OPACITY };
        let highlight = if selected { 1.0 } else { HIGHLIGHT };
        scene.spheres.push(representation, color, opacity, highlight);
    }
-    
+
    // this method should be kept synchronized with `sphere_cast` in
    // `spheres.frag`, which does essentially the same thing on the GPU side
-    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>, _pixel_size: f64) -> Option<f64> {
+    fn cast(
+        &self,
+        dir: Vector3<f64>,
+        assembly_to_world: &DMatrix<f64>,
+        _pixel_size: f64,
+    ) -> Option<f64> {
        // if `a/b` is less than this threshold, we approximate
        // `a*u^2 + b*u + c` by the linear function `b*u + c`
        const DEG_THRESHOLD: f64 = 1e-9;
-        
+
        let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
        let a = -rep[3] * dir.norm_squared();
        let b = rep.rows_range(..3).dot(&dir);
        let c = -rep[4];
-        
+
        let adjust = 4.0*a*c/(b*b);
        if adjust < 1.0 {
            // as long as `b` is non-zero, the linear approximation of
@ -168,30 +184,35 @@ impl DisplayItem for Point {
        /* SCAFFOLDING */
        const GHOST_OPACITY: f32 = 0.4;
        const HIGHLIGHT: f32 = 0.5;
-        
+
        let representation = self.representation.get_clone_untracked();
        let color = if selected { self.color.map(|channel| 0.2 + 0.8*channel) } else { self.color };
        let opacity = if self.ghost.get() { GHOST_OPACITY } else { 1.0 };
        let highlight = if selected { 1.0 } else { HIGHLIGHT };
        scene.points.push(representation, color, opacity, highlight, selected);
    }
-    
+
    /* SCAFFOLDING */
-    fn cast(&self, dir: Vector3<f64>, assembly_to_world: &DMatrix<f64>, pixel_size: f64) -> Option<f64> {
+    fn cast(
+        &self,
+        dir: Vector3<f64>,
+        assembly_to_world: &DMatrix<f64>,
+        pixel_size: f64,
+    ) -> Option<f64> {
        let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
        if rep[2] < 0.0 {
            // this constant should be kept synchronized with `point.frag`
            const POINT_RADIUS_PX: f64 = 4.0;
-            
+
            // find the radius of the point in screen projection units
            let point_radius_proj = POINT_RADIUS_PX * pixel_size;
-            
+
            // find the squared distance between the screen projections of the
            // ray and the point
            let dir_proj = -dir.fixed_rows::<2>(0) / dir[2];
            let rep_proj = -rep.fixed_rows::<2>(0) / rep[2];
            let dist_sq = (dir_proj - rep_proj).norm_squared();
-            
+
            // if the ray hits the point, return its depth
            if dist_sq < point_radius_proj * point_radius_proj {
                Some(rep[2] / dir[2])
@ -220,7 +241,7 @@ fn compile_shader(
 fn set_up_program(
    context: &WebGl2RenderingContext,
    vertex_shader_source: &str,
-    fragment_shader_source: &str
+    fragment_shader_source: &str,
 ) -> WebGlProgram {
    // compile the shaders
    let vertex_shader = compile_shader(
@ -233,13 +254,13 @@ fn set_up_program(
        WebGl2RenderingContext::FRAGMENT_SHADER,
        fragment_shader_source,
    );
-    
+
    // create the program and attach the shaders
    let program = context.create_program().unwrap();
    context.attach_shader(&program, &vertex_shader);
    context.attach_shader(&program, &fragment_shader);
    context.link_program(&program);
-    
+
    /* DEBUG */
    // report whether linking succeeded
    let link_status = context
@ -252,7 +273,7 @@ fn set_up_program(
        "Linking failed"
    };
    console::log_1(&JsValue::from(link_msg));
-    
+
    program
 }

@ -260,12 +281,12 @@ fn get_uniform_array_locations<const N: usize>(
    context: &WebGl2RenderingContext,
    program: &WebGlProgram,
    var_name: &str,
-    member_name_opt: Option<&str>
+    member_name_opt: Option<&str>,
 ) -> [Option<WebGlUniformLocation>; N] {
    array::from_fn(|n| {
        let name = match member_name_opt {
            Some(member_name) => format!("{var_name}[{n}].{member_name}"),
-            None => format!("{var_name}[{n}]")
+            None => format!("{var_name}[{n}]"),
        };
        context.get_uniform_location(&program, name.as_str())
    })
@ -276,7 +297,7 @@ fn bind_to_attribute(
    context: &WebGl2RenderingContext,
    attr_index: u32,
    attr_size: i32,
-    buffer: &Option<WebGlBuffer>
+    buffer: &Option<WebGlBuffer>,
 ) {
    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, buffer.as_ref());
    context.vertex_attrib_pointer_with_i32(
@ -292,12 +313,12 @@ fn bind_to_attribute(
 // load the given data into a new vertex buffer object
 fn load_new_buffer(
    context: &WebGl2RenderingContext,
-    data: &[f32]
+    data: &[f32],
 ) -> Option<WebGlBuffer> {
    // create a buffer and bind it to ARRAY_BUFFER
    let buffer = context.create_buffer();
    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, buffer.as_ref());
-    
+
    // load the given data into the buffer. this block is unsafe because
    // `Float32Array::view` creates a raw view into our module's
    // `WebAssembly.Memory` buffer. allocating more memory will change the
@ -311,7 +332,7 @@ fn load_new_buffer(
            WebGl2RenderingContext::STATIC_DRAW,
        );
    }
-    
+
    buffer
 }

@ -319,7 +340,7 @@ fn bind_new_buffer_to_attribute(
    context: &WebGl2RenderingContext,
    attr_index: u32,
    attr_size: i32,
-    data: &[f32]
+    data: &[f32],
 ) {
    let buffer = load_new_buffer(context, data);
    bind_to_attribute(context, attr_index, attr_size, &buffer);
@ -332,18 +353,18 @@ fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
    let width = rect.width();
    let height = rect.height();
    let shortdim = width.min(height);
-    
+
    // this constant should be kept synchronized with `spheres.frag` and
    // `point.vert`
    const FOCAL_SLOPE: f64 = 0.3;
-    
+
    (
        Vector3::new(
            FOCAL_SLOPE * (2.0*(f64::from(event.client_x()) - rect.left()) - width) / shortdim,
            FOCAL_SLOPE * (2.0*(rect.bottom() - f64::from(event.client_y())) - height) / shortdim,
-            -1.0
+            -1.0,
        ),
-        FOCAL_SLOPE * 2.0 / shortdim
+        FOCAL_SLOPE * 2.0 / shortdim,
    )
 }

@ -352,13 +373,13 @@ fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
 #[component]
 pub fn Display() -> View {
    let state = use_context::<AppState>();
-    
+
    // canvas
    let display = create_node_ref();
-    
+
    // viewpoint
    let assembly_to_world = create_signal(DMatrix::<f64>::identity(5, 5));
-    
+
    // navigation
    let pitch_up = create_signal(0.0);
    let pitch_down = create_signal(0.0);
@ -369,7 +390,7 @@ pub fn Display() -> View {
    let zoom_in = create_signal(0.0);
    let zoom_out = create_signal(0.0);
    let turntable = create_signal(false); /* BENCHMARKING */
-    
+
    // manipulation
    let translate_neg_x = create_signal(0.0);
    let translate_pos_x = create_signal(0.0);
@ -379,7 +400,7 @@ pub fn Display() -> View {
    let translate_pos_z = create_signal(0.0);
    let shrink_neg = create_signal(0.0);
    let shrink_pos = create_signal(0.0);
-    
+
    // change listener
    let scene_changed = create_signal(true);
    create_effect(move || {
@ -392,18 +413,18 @@ pub fn Display() -> View {
        state.selection.track();
        scene_changed.set(true);
    });
-    
+
    /* INSTRUMENTS */
    const SAMPLE_PERIOD: i32 = 60;
    let mut last_sample_time = 0.0;
    let mut frames_since_last_sample = 0;
    let mean_frame_interval = create_signal(0.0);
-    
+
    let assembly_for_raf = state.assembly.clone();
    on_mount(move || {
        // timing
        let mut last_time = 0.0;
-        
+
        // viewpoint
        const ROT_SPEED: f64 = 0.4; // in radians per second
        const ZOOM_SPEED: f64 = 0.15; // multiplicative rate per second
@ -411,18 +432,18 @@ pub fn Display() -> View {
        let mut orientation = DMatrix::<f64>::identity(5, 5);
        let mut rotation = DMatrix::<f64>::identity(5, 5);
        let mut location_z: f64 = 5.0;
-        
+
        // manipulation
        const TRANSLATION_SPEED: f64 = 0.15; // in length units per second
        const SHRINKING_SPEED: f64 = 0.15; // in length units per second
-        
+
        // display parameters
        const LAYER_THRESHOLD: i32 = 0; /* DEBUG */
        const DEBUG_MODE: i32 = 0; /* DEBUG */
-        
+
        /* INSTRUMENTS */
        let performance = window().unwrap().performance().unwrap();
-        
+
        // get the display canvas
        let canvas = display.get().unchecked_into::<web_sys::HtmlCanvasElement>();
        let ctx = canvas
@ -431,28 +452,28 @@ pub fn Display() -> View {
            .unwrap()
            .dyn_into::<WebGl2RenderingContext>()
            .unwrap();
-        
+
        // disable depth testing
        ctx.disable(WebGl2RenderingContext::DEPTH_TEST);
-        
+
        // set blend mode
        ctx.enable(WebGl2RenderingContext::BLEND);
        ctx.blend_func(WebGl2RenderingContext::SRC_ALPHA, WebGl2RenderingContext::ONE_MINUS_SRC_ALPHA);
-        
+
        // set up the sphere rendering program
        let sphere_program = set_up_program(
            &ctx,
            include_str!("identity.vert"),
-            include_str!("spheres.frag")
+            include_str!("spheres.frag"),
        );
-        
+
        // set up the point rendering program
        let point_program = set_up_program(
            &ctx,
            include_str!("point.vert"),
-            include_str!("point.frag")
+            include_str!("point.frag"),
        );
-        
+
        /* DEBUG */
        // print the maximum number of vectors that can be passed as
        // uniforms to a fragment shader. the OpenGL ES 3.0 standard
@ -467,12 +488,12 @@ pub fn Display() -> View {
        // capped at 1024 elements
        console::log_2(
            &ctx.get_parameter(WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
-            &JsValue::from("uniform vectors available")
+            &JsValue::from("uniform vectors available"),
        );
-        
+
        // find the sphere program's vertex attribute
        let viewport_position_attr = ctx.get_attrib_location(&sphere_program, "position") as u32;
-        
+
        // find the sphere program's uniforms
        const SPHERE_MAX: usize = 200;
        let sphere_cnt_loc = ctx.get_uniform_location(&sphere_program, "sphere_cnt");
@ -492,7 +513,7 @@ pub fn Display() -> View {
        let shortdim_loc = ctx.get_uniform_location(&sphere_program, "shortdim");
        let layer_threshold_loc = ctx.get_uniform_location(&sphere_program, "layer_threshold");
        let debug_mode_loc = ctx.get_uniform_location(&sphere_program, "debug_mode");
-        
+
        // load the viewport vertex positions into a new vertex buffer object
        const VERTEX_CNT: usize = 6;
        let viewport_positions: [f32; 3*VERTEX_CNT] = [
@ -503,23 +524,23 @@ pub fn Display() -> View {
            // southeast triangle
            -1.0, -1.0, 0.0,
             1.0,  1.0, 0.0,
-             1.0, -1.0, 0.0
+             1.0, -1.0, 0.0,
        ];
        let viewport_position_buffer = load_new_buffer(&ctx, &viewport_positions);
-        
+
        // find the point program's vertex attributes
        let point_position_attr = ctx.get_attrib_location(&point_program, "position") as u32;
        let point_color_attr = ctx.get_attrib_location(&point_program, "color") as u32;
        let point_highlight_attr = ctx.get_attrib_location(&point_program, "highlight") as u32;
        let point_selection_attr = ctx.get_attrib_location(&point_program, "selected") as u32;
-        
+
        // set up a repainting routine
        let (_, start_animation_loop, _) = create_raf(move || {
            // get the time step
            let time = performance.now();
            let time_step = 0.001*(time - last_time);
            last_time = time;
-            
+
            // get the navigation state
            let pitch_up_val = pitch_up.get();
            let pitch_down_val = pitch_down.get();
@ -530,7 +551,7 @@ pub fn Display() -> View {
            let zoom_in_val = zoom_in.get();
            let zoom_out_val = zoom_out.get();
            let turntable_val = turntable.get(); /* BENCHMARKING */
-            
+
            // get the manipulation state
            let translate_neg_x_val = translate_neg_x.get();
            let translate_pos_x_val = translate_pos_x.get();
@ -540,7 +561,7 @@ pub fn Display() -> View {
            let translate_pos_z_val = translate_pos_z.get();
            let shrink_neg_val = shrink_neg.get();
            let shrink_pos_val = shrink_pos.get();
-            
+
            // update the assembly's orientation
            let ang_vel = {
                let pitch = pitch_up_val - pitch_down_val;
@ -561,13 +582,31 @@ pub fn Display() -> View {
                Rotation3::from_scaled_axis(time_step * ang_vel).matrix()
            );
            orientation = &rotation * &orientation;
-            
+
            // update the assembly's location
            let zoom = zoom_out_val - zoom_in_val;
            location_z *= (time_step * ZOOM_SPEED * zoom).exp();
-            
+
            // manipulate the assembly
-            if state.selection.with(|sel| sel.len() == 1) {
+            /* KLUDGE */
+            // to avoid the complexity of making tangent space projection
+            // conditional and dealing with unnormalized representation vectors,
+            // we only allow manipulation when we're looking at the last step of
+            // a successful realization
+            let realization_successful = state.assembly.realization_status.with(
+                |status| status.is_ok()
+            );
+            let step_val = state.assembly.step.with_untracked(|step| step.value);
+            let on_init_step = step_val.is_some_and(|n| n == 0.0);
+            let on_last_step = step_val.is_some_and(
+                |n| state.assembly.descent_history.with_untracked(
+                    |history| n as usize + 1 == history.config.len().max(1)
+                )
+            );
+            let on_manipulable_step =
+                !realization_successful && on_init_step
+                || realization_successful && on_last_step;
+            if on_manipulable_step && state.selection.with(|sel| sel.len() == 1) {
                let sel = state.selection.with(
                    |sel| sel.into_iter().next().unwrap().clone()
                );
@ -596,18 +635,18 @@ pub fn Display() -> View {
                        vec![
                            ElementMotion {
                                element: sel,
-                                velocity: elt_motion.as_view()
+                                velocity: elt_motion.as_view(),
                            }
                        ]
                    );
                    scene_changed.set(true);
                }
            }
-            
+
            if scene_changed.get() {
                const SPACE_DIM: usize = 3;
                const COLOR_SIZE: usize = 3;
-                
+
                /* INSTRUMENTS */
                // measure mean frame interval
                frames_since_last_sample += 1;
@ -616,11 +655,11 @@ pub fn Display() -> View {
                    last_sample_time = time;
                    frames_since_last_sample = 0;
                }
-                
+
                // --- get the assembly ---
-                
+
                let mut scene = Scene::new();
-                
+
                // find the map from assembly space to world space
                let location = {
                    let u = -location_z;
@ -629,11 +668,11 @@ pub fn Display() -> View {
                        0.0, 1.0,   0.0, 0.0, 0.0,
                        0.0, 0.0,   1.0, 0.0,   u,
                        0.0, 0.0, 2.0*u, 1.0, u*u,
-                        0.0, 0.0,   0.0, 0.0, 1.0
+                        0.0, 0.0,   0.0, 0.0, 1.0,
                    ])
                };
                let asm_to_world = &location * &orientation;
-                
+
                // set up the scene
                state.assembly.elements.with_untracked(
                    |elts| for elt in elts {
@ -642,74 +681,74 @@ pub fn Display() -> View {
                    }
                );
                let sphere_cnt = scene.spheres.len_i32();
-                
+
                // --- draw the spheres ---
-                
+
                // use the sphere rendering program
                ctx.use_program(Some(&sphere_program));
-                
+
                // enable the sphere program's vertex attribute
                ctx.enable_vertex_attrib_array(viewport_position_attr);
-                
+
                // write the spheres in world coordinates
                let sphere_reps_world: Vec<_> = scene.spheres.representations.into_iter().map(
                    |rep| (&asm_to_world * rep).cast::<f32>()
                ).collect();
-                
+
                // set the resolution
                let width = canvas.width() as f32;
                let height = canvas.height() as f32;
                ctx.uniform2f(resolution_loc.as_ref(), width, height);
                ctx.uniform1f(shortdim_loc.as_ref(), width.min(height));
-                
+
                // pass the scene data
                ctx.uniform1i(sphere_cnt_loc.as_ref(), sphere_cnt);
                for n in 0..sphere_reps_world.len() {
                    let v = &sphere_reps_world[n];
                    ctx.uniform3fv_with_f32_array(
                        sphere_sp_locs[n].as_ref(),
-                        v.rows(0, 3).as_slice()
+                        v.rows(0, 3).as_slice(),
                    );
                    ctx.uniform2fv_with_f32_array(
                        sphere_lt_locs[n].as_ref(),
-                        v.rows(3, 2).as_slice()
+                        v.rows(3, 2).as_slice(),
                    );
                    ctx.uniform4fv_with_f32_array(
                        sphere_color_locs[n].as_ref(),
-                        &scene.spheres.colors_with_opacity[n]
+                        &scene.spheres.colors_with_opacity[n],
                    );
                    ctx.uniform1f(
                        sphere_highlight_locs[n].as_ref(),
-                        scene.spheres.highlights[n]
+                        scene.spheres.highlights[n],
                    );
                }
-                
+
                // pass the display parameters
                ctx.uniform1i(layer_threshold_loc.as_ref(), LAYER_THRESHOLD);
                ctx.uniform1i(debug_mode_loc.as_ref(), DEBUG_MODE);
-                
+
                // bind the viewport vertex position buffer to the position
                // attribute in the vertex shader
                bind_to_attribute(&ctx, viewport_position_attr, SPACE_DIM as i32, &viewport_position_buffer);
-                
+
                // draw the scene
                ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
-                
+
                // disable the sphere program's vertex attribute
                ctx.disable_vertex_attrib_array(viewport_position_attr);
-                
+
                // --- draw the points ---
-                
+
                if !scene.points.representations.is_empty() {
                    // use the point rendering program
                    ctx.use_program(Some(&point_program));
-                    
+
                    // enable the point program's vertex attributes
                    ctx.enable_vertex_attrib_array(point_position_attr);
                    ctx.enable_vertex_attrib_array(point_color_attr);
                    ctx.enable_vertex_attrib_array(point_highlight_attr);
                    ctx.enable_vertex_attrib_array(point_selection_attr);
-                    
+
                    // write the points in world coordinates
                    let asm_to_world_sp = asm_to_world.rows(0, SPACE_DIM);
                    let point_positions = DMatrix::from_columns(
@ -717,7 +756,7 @@ pub fn Display() -> View {
                            |rep| &asm_to_world_sp * rep
                        ).collect::<Vec<_>>().as_slice()
                    ).cast::<f32>();
-                    
+
                    // load the point positions and colors into new buffers and
                    // bind them to the corresponding attributes in the vertex
                    // shader
@ -725,22 +764,22 @@ pub fn Display() -> View {
                    bind_new_buffer_to_attribute(&ctx, point_color_attr, (COLOR_SIZE + 1) as i32, scene.points.colors_with_opacity.concat().as_slice());
                    bind_new_buffer_to_attribute(&ctx, point_highlight_attr, 1 as i32, scene.points.highlights.as_slice());
                    bind_new_buffer_to_attribute(&ctx, point_selection_attr, 1 as i32, scene.points.selections.as_slice());
-                    
+
                    // draw the scene
                    ctx.draw_arrays(WebGl2RenderingContext::POINTS, 0, point_positions.ncols() as i32);
-                    
+
                    // disable the point program's vertex attributes
                    ctx.disable_vertex_attrib_array(point_position_attr);
                    ctx.disable_vertex_attrib_array(point_color_attr);
                    ctx.disable_vertex_attrib_array(point_highlight_attr);
                    ctx.disable_vertex_attrib_array(point_selection_attr);
                }
-                
+
                // --- update the display state ---
-                
+
                // update the viewpoint
                assembly_to_world.set(asm_to_world);
-                
+
                // clear the scene change flag
                scene_changed.set(
                    pitch_up_val != 0.0
@ -760,7 +799,7 @@ pub fn Display() -> View {
        });
        start_animation_loop();
    });
-    
+
    let set_nav_signal = move |event: &KeyboardEvent, value: f64| {
        let mut navigating = true;
        let shift = event.shift_key();
@ -773,14 +812,14 @@ pub fn Display() -> View {
            "ArrowLeft" if shift => roll_ccw.set(value),
            "ArrowRight" => yaw_right.set(value),
            "ArrowLeft" => yaw_left.set(value),
-            _ => navigating = false
+            _ => navigating = false,
        };
        if navigating {
            scene_changed.set(true);
            event.prevent_default();
        }
    };
-    
+
    let set_manip_signal = move |event: &KeyboardEvent, value: f64| {
        let mut manipulating = true;
        let shift = event.shift_key();
@ -793,23 +832,24 @@ pub fn Display() -> View {
            "s" | "S" => translate_neg_y.set(value),
            "]" | "}" => shrink_neg.set(value),
            "[" | "{" => shrink_pos.set(value),
-            _ => manipulating = false
+            _ => manipulating = false,
        };
        if manipulating {
            event.prevent_default();
        }
    };
-    
+
    view! {
        /* TO DO */
        // switch back to integer-valued parameters when that becomes possible
        // again
        canvas(
-            ref=display,
-            width="600",
-            height="600",
-            tabindex="0",
-            on:keydown=move |event: KeyboardEvent| {
+            ref = display,
+            id = "display",
+            width = "600",
+            height = "600",
+            tabindex = "0",
+            on:keydown = move |event: KeyboardEvent| {
                if event.key() == "Shift" {
                    // swap navigation inputs
                    roll_cw.set(yaw_right.get());
@ -820,7 +860,7 @@ pub fn Display() -> View {
                    yaw_left.set(0.0);
                    pitch_up.set(0.0);
                    pitch_down.set(0.0);
-                    
+
                    // swap manipulation inputs
                    translate_pos_z.set(translate_neg_y.get());
                    translate_neg_z.set(translate_pos_y.get());
@ -835,7 +875,7 @@ pub fn Display() -> View {
                    set_manip_signal(&event, 1.0);
                }
            },
-            on:keyup=move |event: KeyboardEvent| {
+            on:keyup = move |event: KeyboardEvent| {
                if event.key() == "Shift" {
                    // swap navigation inputs
                    yaw_right.set(roll_cw.get());
@ -846,7 +886,7 @@ pub fn Display() -> View {
                    roll_ccw.set(0.0);
                    zoom_in.set(0.0);
                    zoom_out.set(0.0);
-                    
+
                    // swap manipulation inputs
                    translate_pos_y.set(translate_neg_z.get());
                    translate_neg_y.set(translate_pos_z.get());
@ -857,7 +897,7 @@ pub fn Display() -> View {
                    set_manip_signal(&event, 0.0);
                }
            },
-            on:blur=move |_| {
+            on:blur = move |_| {
                pitch_up.set(0.0);
                pitch_down.set(0.0);
                yaw_right.set(0.0);
@ -865,7 +905,7 @@ pub fn Display() -> View {
                roll_ccw.set(0.0);
                roll_cw.set(0.0);
            },
-            on:click=move |event: MouseEvent| {
+            on:click = move |event: MouseEvent| {
                // find the nearest element along the pointer direction
                let (dir, pixel_size) = event_dir(&event);
                console::log_1(&JsValue::from(dir.to_string()));
@ -882,18 +922,18 @@ pub fn Display() -> View {
                                    clicked = Some((elt, depth))
                                }
                            },
-                            None => clicked = Some((elt, depth))
-                        }
-                        None => ()
+                            None => clicked = Some((elt, depth)),
+                        },
+                        None => (),
                    };
                }
-                
+
                // if we clicked something, select it
                match clicked {
                    Some((elt, _)) => state.select(&elt, event.shift_key()),
-                    None => state.selection.update(|sel| sel.clear())
+                    None => state.selection.update(|sel| sel.clear()),
                };
-            }
+            },
        )
    }
-}
+}
--- a/app-proto/src/components/identity.vert
+++ b/app-proto/src/components/identity.vert
--- a/app-proto/src/components/outline.rs
+++ b/app-proto/src/components/outline.rs
@ -1,11 +1,7 @@
 use itertools::Itertools;
 use std::rc::Rc;
 use sycamore::prelude::*;
-use web_sys::{
-    KeyboardEvent,
-    MouseEvent,
-    wasm_bindgen::JsCast
-};
+use web_sys::{KeyboardEvent, MouseEvent, wasm_bindgen::JsCast};

 use crate::{
    AppState,
@ -13,7 +9,8 @@ use crate::{
        Element,
        HalfCurvatureRegulator,
        InversiveDistanceRegulator,
-        Regulator
+        PointCoordinateRegulator,
+        Regulator,
    },
    specified::SpecifiedValue
 };
@ -24,16 +21,16 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
    // get the regulator's measurement and set point signals
    let measurement = regulator.measurement();
    let set_point = regulator.set_point();
-    
+
    // the `valid` signal tracks whether the last entered value is a valid set
    // point specification
    let valid = create_signal(true);
-    
+
    // the `value` signal holds the current set point specification
    let value = create_signal(
        set_point.with_untracked(|set_pt| set_pt.spec.clone())
    );
-    
+
    // this `reset_value` closure resets the input value to the regulator's set
    // point specification
    let reset_value = move || {
@ -42,15 +39,15 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
            value.set(set_point.with(|set_pt| set_pt.spec.clone()));
        })
    };
-    
+
    // reset the input value whenever the regulator's set point specification
    // is updated
    create_effect(reset_value);
-    
+
    view! {
        input(
-            r#type="text",
-            class=move || {
+            r#type = "text",
+            class = move || {
                if valid.get() {
                    set_point.with(|set_pt| {
                        if set_pt.is_present() {
@ -63,27 +60,27 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
                    "regulator-input invalid"
                }
            },
-            placeholder=measurement.with(|result| result.to_string()),
-            bind:value=value,
-            on:change=move |_| {
+            placeholder = measurement.with(|result| result.to_string()),
+            bind:value = value,
+            on:change = move |_| {
                valid.set(
                    match SpecifiedValue::try_from(value.get_clone_untracked()) {
                        Ok(set_pt) => {
                            set_point.set(set_pt);
                            true
-                        }
-                        Err(_) => false
+                        },
+                        Err(_) => false,
                    }
                )
            },
-            on:keydown={
+            on:keydown = {
                move |event: KeyboardEvent| {
                    match event.key().as_str() {
                        "Escape" => reset_value(),
-                        _ => ()
+                        _ => (),
                    }
                }
-            }
+            },
        )
    }
 }
@ -100,11 +97,11 @@ impl OutlineItem for InversiveDistanceRegulator {
            self.subjects[0].label()
        }.clone();
        view! {
-            li(class="regulator") {
-                div(class="regulator-label") { (other_subject_label) }
-                div(class="regulator-type") { "Inversive distance" }
-                RegulatorInput(regulator=self)
-                div(class="status")
+            li(class = "regulator") {
+                div(class = "regulator-label") { (other_subject_label) }
+                div(class = "regulator-type") { "Inversive distance" }
+                RegulatorInput(regulator = self)
+                div(class = "status")
            }
        }
    }
@ -113,11 +110,25 @@ impl OutlineItem for InversiveDistanceRegulator {
 impl OutlineItem for HalfCurvatureRegulator {
    fn outline_item(self: Rc<Self>, _element: &Rc<dyn Element>) -> View {
        view! {
-            li(class="regulator") {
-                div(class="regulator-label") // for spacing
-                div(class="regulator-type") { "Half-curvature" }
-                RegulatorInput(regulator=self)
-                div(class="status")
+            li(class = "regulator") {
+                div(class = "regulator-label") // for spacing
+                div(class = "regulator-type") { "Half-curvature" }
+                RegulatorInput(regulator = self)
+                div(class = "status")
+            }
+        }
+    }
+}
+
+impl OutlineItem for PointCoordinateRegulator {
+    fn outline_item(self: Rc<Self>, _element: &Rc<dyn Element>) -> View {
+        let name = format!("{} coordinate", self.axis);
+        view! {
+            li(class = "regulator") {
+                div(class = "regulator-label") // for spacing
+                div(class = "regulator-type") { (name) }
+                RegulatorInput(regulator = self)
+                div(class = "status")
            }
        }
    }
@ -151,15 +162,15 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
            .clone()
            .into_iter()
            .sorted_by_key(|reg| reg.subjects().len())
-            .collect()
+            .collect::<Vec<_>>()
    );
    let details_node = create_node_ref();
    view! {
        li {
-            details(ref=details_node) {
+            details(ref = details_node) {
                summary(
-                    class=class.get(),
-                    on:keydown={
+                    class = class.get(),
+                    on:keydown = {
                        let element_for_handler = element.clone();
                        move |event: KeyboardEvent| {
                            match event.key().as_str() {
@ -179,18 +190,18 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
                                        .unchecked_into::<web_sys::Element>()
                                        .remove_attribute("open");
                                },
-                                _ => ()
+                                _ => (),
                            }
                        }
                    }
                ) {
                    div(
-                        class="element-switch",
-                        on:click=|event: MouseEvent| event.stop_propagation()
+                        class = "element-switch",
+                        on:click = |event: MouseEvent| event.stop_propagation()
                    )
                    div(
-                        class="element",
-                        on:click={
+                        class = "element",
+                        on:click = {
                            let state_for_handler = state.clone();
                            let element_for_handler = element.clone();
                            move |event: MouseEvent| {
@ -200,20 +211,20 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
                            }
                        }
                    ) {
-                        div(class="element-label") { (label) }
-                        div(class="element-representation") { (rep_components) }
+                        div(class = "element-label") { (label) }
+                        div(class = "element-representation") { (rep_components) }
                        input(
-                            r#type="checkbox",
-                            bind:checked=element.ghost(),
-                            on:click=|event: MouseEvent| event.stop_propagation()
+                            r#type = "checkbox",
+                            bind:checked = element.ghost(),
+                            on:click = |event: MouseEvent| event.stop_propagation()
                        )
                    }
                }
-                ul(class="regulators") {
+                ul(class = "regulators") {
                    Keyed(
-                        list=regulator_list,
-                        view=move |reg| reg.outline_item(&element),
-                        key=|reg| reg.serial()
+                        list = regulator_list,
+                        view = move |reg| reg.outline_item(&element),
+                        key = |reg| reg.serial()
                    )
                }
            }
@ -230,7 +241,7 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
 #[component]
 pub fn Outline() -> View {
    let state = use_context::<AppState>();
-    
+
    // list the elements alphabetically by ID
    /* TO DO */
    // this code is designed to generalize easily to other sort keys. if we only
@ -241,24 +252,24 @@ pub fn Outline() -> View {
            .clone()
            .into_iter()
            .sorted_by_key(|elt| elt.id().clone())
-            .collect()
+            .collect::<Vec<_>>()
    );
-    
+
    view! {
        ul(
-            id="outline",
-            on:click={
+            id = "outline",
+            on:click = {
                let state = use_context::<AppState>();
                move |_| state.selection.update(|sel| sel.clear())
            }
        ) {
            Keyed(
-                list=element_list,
-                view=|elt| view! {
-                    ElementOutlineItem(element=elt)
+                list = element_list,
+                view = |elt| view! {
+                    ElementOutlineItem(element = elt)
                },
-                key=|elt| elt.serial()
+                key = |elt| elt.serial()
            )
        }
    }
-}
+}
--- a/app-proto/src/components/point.frag
+++ b/app-proto/src/components/point.frag
@ -10,10 +10,10 @@ out vec4 outColor;

 void main() {
    float r = total_radius * length(2.*gl_PointCoord - vec2(1.));
-    
+
    const float POINT_RADIUS = 4.;
    float border = smoothstep(POINT_RADIUS - 1., POINT_RADIUS, r);
    float disk = 1. - smoothstep(total_radius - 1., total_radius, r);
    vec4 color = mix(point_color, vec4(1.), border * point_highlight);
    outColor = vec4(vec3(1.), disk) * color;
-}
+}
--- a/app-proto/src/components/point.vert
+++ b/app-proto/src/components/point.vert
@ -14,11 +14,11 @@ const float focal_slope = 0.3;

 void main() {
    total_radius = 5. + 0.5*selected;
-    
+
    float depth = -focal_slope * position.z;
    gl_Position = vec4(position.xy / depth, 0., 1.);
    gl_PointSize = 2.*total_radius;
-    
+
    point_color = color;
    point_highlight = highlight;
-}
+}
--- a/app-proto/src/components/spheres.frag
+++ b/app-proto/src/components/spheres.frag
@ -75,7 +75,7 @@ Fragment sphere_shading(vecInv v, vec3 pt, vec4 base_color) {
    // point. i calculated it in my head and decided that the result looked good
    // enough for now
    vec3 normal = normalize(-v.sp + 2.*v.lt.s*pt);
-    
+
    float incidence = dot(normal, light_dir);
    float illum = mix(0.4, 1.0, max(incidence, 0.0));
    return Fragment(pt, normal, vec4(illum * base_color.rgb, base_color.a));
@ -110,7 +110,7 @@ vec2 sphere_cast(vecInv v, vec3 dir) {
    float a = -v.lt.s * dot(dir, dir);
    float b = dot(v.sp, dir);
    float c = -v.lt.t;
-    
+
    float adjust = 4.*a*c/(b*b);
    if (adjust < 1.) {
        // as long as `b` is non-zero, the linear approximation of
@ -136,7 +136,7 @@ vec2 sphere_cast(vecInv v, vec3 dir) {
 void main() {
    vec2 scr = (2.*gl_FragCoord.xy - resolution) / shortdim;
    vec3 dir = vec3(focal_slope * scr, -1.);
-    
+
    // cast rays through the spheres
    const int LAYER_MAX = 12;
    TaggedDepth top_hits [LAYER_MAX];
@ -144,7 +144,7 @@ void main() {
    for (int id = 0; id < sphere_cnt; ++id) {
        // find out where the ray hits the sphere
        vec2 hit_depths = sphere_cast(sphere_list[id], dir);
-        
+
        // insertion-sort the points we hit into the hit list
        float dimming = 1.;
        for (int side = 0; side < 2; ++side) {
@ -169,14 +169,14 @@ void main() {
            }
        }
    }
-    
+
    /* DEBUG */
    // in debug mode, show the layer count instead of the shaded image
    if (debug_mode) {
        // at the bottom of the screen, show the color scale instead of the
        // layer count
        if (gl_FragCoord.y < 10.) layer_cnt = int(16. * gl_FragCoord.x / resolution.x);
-        
+
        // convert number to color
        ivec3 bits = layer_cnt / ivec3(1, 2, 4);
        vec3 color = mod(vec3(bits), 2.);
@ -186,7 +186,7 @@ void main() {
        outColor = vec4(color, 1.);
        return;
    }
-    
+
    // composite the sphere fragments
    vec3 color = vec3(0.);
    int layer = layer_cnt - 1;
@ -203,7 +203,7 @@ void main() {
        // load the current fragment
        Fragment frag = frag_next;
        float highlight = highlight_next;
-        
+
        // shade the next fragment
        hit = top_hits[layer];
        sphere_color = color_list[hit.id];
@ -213,23 +213,23 @@ void main() {
            vec4(hit.dimming * sphere_color.rgb, sphere_color.a)
        );
        highlight_next = highlight_list[hit.id];
-        
+
        // highlight intersections
        float ixn_dist = intersection_dist(frag, frag_next);
        float max_highlight = max(highlight, highlight_next);
        float ixn_highlight = 0.5 * max_highlight * (1. - smoothstep(2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist));
        frag.color = mix(frag.color, vec4(1.), ixn_highlight);
        frag_next.color = mix(frag_next.color, vec4(1.), ixn_highlight);
-        
+
        // highlight cusps
        float cusp_cos = abs(dot(dir, frag.normal));
        float cusp_threshold = 2.*sqrt(ixn_threshold * sphere_list[hit.id].lt.s);
        float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
        frag.color = mix(frag.color, vec4(1.), cusp_highlight);
-        
+
        // composite the current fragment
        color = mix(color, frag.color.rgb, frag.color.a);
    }
    color = mix(color, frag_next.color.rgb, frag_next.color.a);
    outColor = vec4(sRGB(color), 1.);
-}
+}
--- a/app-proto/src/components/test_assembly_chooser.rs
+++ b/app-proto/src/components/test_assembly_chooser.rs
@ -0,0 +1,941 @@
+use itertools::izip;
+use std::{f64::consts::{FRAC_1_SQRT_2, PI}, rc::Rc};
+use nalgebra::Vector3;
+use sycamore::prelude::*;
+use web_sys::{console, wasm_bindgen::JsValue};
+
+use crate::{
+    AppState,
+    assembly::{
+        Assembly,
+        Element,
+        ElementColor,
+        InversiveDistanceRegulator,
+        Point,
+        Sphere,
+    },
+    engine,
+    engine::DescentHistory,
+    specified::SpecifiedValue,
+};
+
+// --- loaders ---
+
+/* DEBUG */
+// each of these functions loads an example assembly for testing. once we've
+// done more work on saving and loading assemblies, we should come back to this
+// code to see if it can be simplified
+
+fn load_general(assembly: &Assembly) {
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            String::from("gemini_a"),
+            String::from("Castor"),
+            [1.00_f32, 0.25_f32, 0.00_f32],
+            engine::sphere(0.5, 0.5, 0.0, 1.0),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            String::from("gemini_b"),
+            String::from("Pollux"),
+            [0.00_f32, 0.25_f32, 1.00_f32],
+            engine::sphere(-0.5, -0.5, 0.0, 1.0),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            String::from("ursa_major"),
+            String::from("Ursa major"),
+            [0.25_f32, 0.00_f32, 1.00_f32],
+            engine::sphere(-0.5, 0.5, 0.0, 0.75),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            String::from("ursa_minor"),
+            String::from("Ursa minor"),
+            [0.25_f32, 1.00_f32, 0.00_f32],
+            engine::sphere(0.5, -0.5, 0.0, 0.5),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            String::from("moon_deimos"),
+            String::from("Deimos"),
+            [0.75_f32, 0.75_f32, 0.00_f32],
+            engine::sphere(0.0, 0.15, 1.0, 0.25),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            String::from("moon_phobos"),
+            String::from("Phobos"),
+            [0.00_f32, 0.75_f32, 0.50_f32],
+            engine::sphere(0.0, -0.15, -1.0, 0.25),
+        )
+    );
+}
+
+fn load_low_curvature(assembly: &Assembly) {
+    // create the spheres
+    let a = 0.75_f64.sqrt();
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            "central".to_string(),
+            "Central".to_string(),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::sphere(0.0, 0.0, 0.0, 1.0),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            "assemb_plane".to_string(),
+            "Assembly plane".to_string(),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::sphere_with_offset(0.0, 0.0, 1.0, 0.0, 0.0),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            "side1".to_string(),
+            "Side 1".to_string(),
+            [1.00_f32, 0.00_f32, 0.25_f32],
+            engine::sphere_with_offset(1.0, 0.0, 0.0, 1.0, 0.0),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            "side2".to_string(),
+            "Side 2".to_string(),
+            [0.25_f32, 1.00_f32, 0.00_f32],
+            engine::sphere_with_offset(-0.5, a, 0.0, 1.0, 0.0),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            "side3".to_string(),
+            "Side 3".to_string(),
+            [0.00_f32, 0.25_f32, 1.00_f32],
+            engine::sphere_with_offset(-0.5, -a, 0.0, 1.0, 0.0),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            "corner1".to_string(),
+            "Corner 1".to_string(),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::sphere(-4.0/3.0, 0.0, 0.0, 1.0/3.0),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            "corner2".to_string(),
+            "Corner 2".to_string(),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::sphere(2.0/3.0, -4.0/3.0 * a, 0.0, 1.0/3.0),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            String::from("corner3"),
+            String::from("Corner 3"),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::sphere(2.0/3.0, 4.0/3.0 * a, 0.0, 1.0/3.0),
+        )
+    );
+
+    // impose the desired tangencies and make the sides planar
+    let index_range = 1..=3;
+    let [central, assemb_plane] = ["central", "assemb_plane"].map(
+        |id| assembly.elements_by_id.with_untracked(
+            |elts_by_id| elts_by_id[id].clone()
+        )
+    );
+    let sides = index_range.clone().map(
+        |k| assembly.elements_by_id.with_untracked(
+            |elts_by_id| elts_by_id[&format!("side{k}")].clone()
+        )
+    );
+    let corners = index_range.map(
+        |k| assembly.elements_by_id.with_untracked(
+            |elts_by_id| elts_by_id[&format!("corner{k}")].clone()
+        )
+    );
+    for plane in [assemb_plane.clone()].into_iter().chain(sides.clone()) {
+        // fix the curvature of each plane
+        let curvature = plane.regulators().with_untracked(
+            |regs| regs.first().unwrap().clone()
+        );
+        curvature.set_point().set(SpecifiedValue::try_from("0".to_string()).unwrap());
+    }
+    let all_perpendicular = [central.clone()].into_iter()
+        .chain(sides.clone())
+        .chain(corners.clone());
+    for sphere in all_perpendicular {
+        // make each side and packed sphere perpendicular to the assembly plane
+        let right_angle = InversiveDistanceRegulator::new([sphere, assemb_plane.clone()]);
+        right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+        assembly.insert_regulator(Rc::new(right_angle));
+    }
+    for sphere in sides.clone().chain(corners.clone()) {
+        // make each side and corner sphere tangent to the central sphere
+        let tangency = InversiveDistanceRegulator::new([sphere.clone(), central.clone()]);
+        tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
+        assembly.insert_regulator(Rc::new(tangency));
+    }
+    for (side_index, side) in sides.enumerate() {
+        // make each side tangent to the two adjacent corner spheres
+        for (corner_index, corner) in corners.clone().enumerate() {
+            if side_index != corner_index {
+                let tangency = InversiveDistanceRegulator::new([side.clone(), corner]);
+                tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
+                assembly.insert_regulator(Rc::new(tangency));
+            }
+        }
+    }
+}
+
+fn load_pointed(assembly: &Assembly) {
+    let _ = assembly.try_insert_element(
+        Point::new(
+            format!("point_front"),
+            format!("Front point"),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::point(0.0, 0.0, FRAC_1_SQRT_2),
+        )
+    );
+    let _ = assembly.try_insert_element(
+        Point::new(
+            format!("point_back"),
+            format!("Back point"),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::point(0.0, 0.0, -FRAC_1_SQRT_2),
+        )
+    );
+    for index_x in 0..=1 {
+        for index_y in 0..=1 {
+            let x = index_x as f64 - 0.5;
+            let y = index_y as f64 - 0.5;
+
+            let _ = assembly.try_insert_element(
+                Sphere::new(
+                    format!("sphere{index_x}{index_y}"),
+                    format!("Sphere {index_x}{index_y}"),
+                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
+                    engine::sphere(x, y, 0.0, 1.0),
+                )
+            );
+
+            let _ = assembly.try_insert_element(
+                Point::new(
+                    format!("point{index_x}{index_y}"),
+                    format!("Point {index_x}{index_y}"),
+                    [0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
+                    engine::point(x, y, 0.0),
+                )
+            );
+        }
+    }
+}
+
+// to finish describing the tridiminished icosahedron, set the inversive
+// distance regulators as follows:
+//   A-A   -0.25
+//   A-B     "
+//   B-C     "
+//   C-C     "
+//   A-C   -0.25 * φ^2 = -0.6545084971874737
+fn load_tridiminished_icosahedron(assembly: &Assembly) {
+    // create the vertices
+    const COLOR_A: ElementColor = [1.00_f32, 0.25_f32, 0.25_f32];
+    const COLOR_B: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
+    const COLOR_C: ElementColor = [0.25_f32, 0.50_f32, 1.00_f32];
+    let vertices = [
+        Point::new(
+            "a1".to_string(),
+            "A₁".to_string(),
+            COLOR_A,
+            engine::point(0.25, 0.75, 0.75),
+        ),
+        Point::new(
+            "a2".to_string(),
+            "A₂".to_string(),
+            COLOR_A,
+            engine::point(0.75, 0.25, 0.75),
+        ),
+        Point::new(
+            "a3".to_string(),
+            "A₃".to_string(),
+            COLOR_A,
+            engine::point(0.75, 0.75, 0.25),
+        ),
+        Point::new(
+            "b1".to_string(),
+            "B₁".to_string(),
+            COLOR_B,
+            engine::point(0.75, -0.25, -0.25),
+        ),
+        Point::new(
+            "b2".to_string(),
+            "B₂".to_string(),
+            COLOR_B,
+            engine::point(-0.25, 0.75, -0.25),
+        ),
+        Point::new(
+            "b3".to_string(),
+            "B₃".to_string(),
+            COLOR_B,
+            engine::point(-0.25, -0.25, 0.75),
+        ),
+        Point::new(
+            "c1".to_string(),
+            "C₁".to_string(),
+            COLOR_C,
+            engine::point(0.0, -1.0, -1.0),
+        ),
+        Point::new(
+            "c2".to_string(),
+            "C₂".to_string(),
+            COLOR_C,
+            engine::point(-1.0, 0.0, -1.0),
+        ),
+        Point::new(
+            "c3".to_string(),
+            "C₃".to_string(),
+            COLOR_C,
+            engine::point(-1.0, -1.0, 0.0),
+        ),
+    ];
+    for vertex in vertices {
+        let _ = assembly.try_insert_element(vertex);
+    }
+
+    // create the faces
+    const COLOR_FACE: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
+    let frac_1_sqrt_6 = 1.0 / 6.0_f64.sqrt();
+    let frac_2_sqrt_6 = 2.0 * frac_1_sqrt_6;
+    let faces = [
+        Sphere::new(
+            "face1".to_string(),
+            "Face 1".to_string(),
+            COLOR_FACE,
+            engine::sphere_with_offset(frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
+        ),
+        Sphere::new(
+            "face2".to_string(),
+            "Face 2".to_string(),
+            COLOR_FACE,
+            engine::sphere_with_offset(-frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
+        ),
+        Sphere::new(
+            "face3".to_string(),
+            "Face 3".to_string(),
+            COLOR_FACE,
+            engine::sphere_with_offset(-frac_1_sqrt_6, -frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, 0.0),
+        ),
+    ];
+    for face in faces {
+        face.ghost().set(true);
+        let _ = assembly.try_insert_element(face);
+    }
+
+    let index_range = 1..=3;
+    for j in index_range.clone() {
+        // make each face planar
+        let face = assembly.elements_by_id.with_untracked(
+            |elts_by_id| elts_by_id[&format!("face{j}")].clone()
+        );
+        let curvature_regulator = face.regulators().with_untracked(
+            |regs| regs.first().unwrap().clone()
+        );
+        curvature_regulator.set_point().set(
+            SpecifiedValue::try_from("0".to_string()).unwrap()
+        );
+
+        // put each A vertex on the face it belongs to
+        let vertex_a = assembly.elements_by_id.with_untracked(
+            |elts_by_id| elts_by_id[&format!("a{j}")].clone()
+        );
+        let incidence_a = InversiveDistanceRegulator::new([face.clone(), vertex_a.clone()]);
+        incidence_a.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+        assembly.insert_regulator(Rc::new(incidence_a));
+
+        // regulate the B-C vertex distances
+        let vertices_bc = ["b", "c"].map(
+            |series| assembly.elements_by_id.with_untracked(
+                |elts_by_id| elts_by_id[&format!("{series}{j}")].clone()
+            )
+        );
+        assembly.insert_regulator(
+            Rc::new(InversiveDistanceRegulator::new(vertices_bc))
+        );
+
+        // get the pair of indices adjacent to `j`
+        let adjacent_indices = [j % 3 + 1, (j + 1) % 3 + 1];
+
+        for k in adjacent_indices.clone() {
+            for series in ["b", "c"] {
+                // put each B and C vertex on the faces it belongs to
+                let vertex = assembly.elements_by_id.with_untracked(
+                    |elts_by_id| elts_by_id[&format!("{series}{k}")].clone()
+                );
+                let incidence = InversiveDistanceRegulator::new([face.clone(), vertex.clone()]);
+                incidence.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+                assembly.insert_regulator(Rc::new(incidence));
+
+                // regulate the A-B and A-C vertex distances
+                assembly.insert_regulator(
+                    Rc::new(InversiveDistanceRegulator::new([vertex_a.clone(), vertex]))
+                );
+            }
+        }
+
+        // regulate the A-A and C-C vertex distances
+        let adjacent_pairs = ["a", "c"].map(
+            |series| adjacent_indices.map(
+                |index| assembly.elements_by_id.with_untracked(
+                    |elts_by_id| elts_by_id[&format!("{series}{index}")].clone()
+                )
+            )
+        );
+        for pair in adjacent_pairs {
+            assembly.insert_regulator(
+                Rc::new(InversiveDistanceRegulator::new(pair))
+            );
+        }
+    }
+}
+
+// to finish describing the dodecahedral circle packing, set the inversive
+// distance regulators to -1. some of the regulators have already been set
+fn load_dodecahedral_packing(assembly: &Assembly) {
+    // add the substrate
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            "substrate".to_string(),
+            "Substrate".to_string(),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::sphere(0.0, 0.0, 0.0, 1.0),
+        )
+    );
+    let substrate = assembly.elements_by_id.with_untracked(
+        |elts_by_id| elts_by_id["substrate"].clone()
+    );
+
+    // fix the substrate's curvature
+    substrate.regulators().with_untracked(
+        |regs| regs.first().unwrap().clone()
+    ).set_point().set(
+        SpecifiedValue::try_from("0.5".to_string()).unwrap()
+    );
+
+    // add the circles to be packed
+    const COLOR_A: ElementColor = [1.00_f32, 0.25_f32, 0.00_f32];
+    const COLOR_B: ElementColor = [1.00_f32, 0.00_f32, 0.25_f32];
+    const COLOR_C: ElementColor = [0.25_f32, 0.00_f32, 1.00_f32];
+    let phi = 0.5 + 1.25_f64.sqrt(); /* TO DO */ // replace with std::f64::consts::PHI when that gets stabilized
+    let phi_inv = 1.0 / phi;
+    let coord_scale = (phi + 2.0).sqrt();
+    let face_scales = [phi_inv, (13.0 / 12.0) / coord_scale];
+    let face_radii = [phi_inv, 5.0 / 12.0];
+    let mut faces = Vec::<Rc<dyn Element>>::new();
+    let subscripts = ["₀", "₁"];
+    for j in 0..2 {
+        for k in 0..2 {
+            let small_coord = face_scales[k] * (2.0*(j as f64) - 1.0);
+            let big_coord = face_scales[k] * (2.0*(k as f64) - 1.0) * phi;
+
+            let id_num = format!("{j}{k}");
+            let label_sub = format!("{}{}", subscripts[j], subscripts[k]);
+
+            // add the A face
+            let id_a = format!("a{id_num}");
+            let _ = assembly.try_insert_element(
+                Sphere::new(
+                    id_a.clone(),
+                    format!("A{label_sub}"),
+                    COLOR_A,
+                    engine::sphere(0.0, small_coord, big_coord, face_radii[k]),
+                )
+            );
+            faces.push(
+                assembly.elements_by_id.with_untracked(
+                    |elts_by_id| elts_by_id[&id_a].clone()
+                )
+            );
+
+            // add the B face
+            let id_b = format!("b{id_num}");
+            let _ = assembly.try_insert_element(
+                Sphere::new(
+                    id_b.clone(),
+                    format!("B{label_sub}"),
+                    COLOR_B,
+                    engine::sphere(small_coord, big_coord, 0.0, face_radii[k]),
+                )
+            );
+            faces.push(
+                assembly.elements_by_id.with_untracked(
+                    |elts_by_id| elts_by_id[&id_b].clone()
+                )
+            );
+
+            // add the C face
+            let id_c = format!("c{id_num}");
+            let _ = assembly.try_insert_element(
+                Sphere::new(
+                    id_c.clone(),
+                    format!("C{label_sub}"),
+                    COLOR_C,
+                    engine::sphere(big_coord, 0.0, small_coord, face_radii[k]),
+                )
+            );
+            faces.push(
+                assembly.elements_by_id.with_untracked(
+                    |elts_by_id| elts_by_id[&id_c].clone()
+                )
+            );
+        }
+    }
+
+    // make each face sphere perpendicular to the substrate
+    for face in faces {
+        let right_angle = InversiveDistanceRegulator::new([face, substrate.clone()]);
+        right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+        assembly.insert_regulator(Rc::new(right_angle));
+    }
+
+    // set up the tangencies that define the packing
+    for [long_edge_plane, short_edge_plane] in [["a", "b"], ["b", "c"], ["c", "a"]] {
+        for k in 0..2 {
+            let long_edge_ids = [
+                format!("{long_edge_plane}{k}0"),
+                format!("{long_edge_plane}{k}1")
+            ];
+            let short_edge_ids = [
+                format!("{short_edge_plane}0{k}"),
+                format!("{short_edge_plane}1{k}")
+            ];
+            let [long_edge, short_edge] = [long_edge_ids, short_edge_ids].map(
+                |edge_ids| edge_ids.map(
+                    |id| assembly.elements_by_id.with_untracked(
+                        |elts_by_id| elts_by_id[&id].clone()
+                    )
+                )
+            );
+
+            // set up the short-edge tangency
+            let short_tangency = InversiveDistanceRegulator::new(short_edge.clone());
+            if k == 0 {
+                short_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
+            }
+            assembly.insert_regulator(Rc::new(short_tangency));
+
+            // set up the side tangencies
+            for i in 0..2 {
+                for j in 0..2 {
+                    let side_tangency = InversiveDistanceRegulator::new(
+                        [long_edge[i].clone(), short_edge[j].clone()]
+                    );
+                    if i == 0 && k == 0 {
+                        side_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
+                    }
+                    assembly.insert_regulator(Rc::new(side_tangency));
+                }
+            }
+        }
+    }
+}
+
+// the initial configuration of this test assembly deliberately violates the
+// constraints, so loading the assembly will trigger a non-trivial realization
+fn load_balanced(assembly: &Assembly) {
+    // create the spheres
+    const R_OUTER: f64 = 10.0;
+    const R_INNER: f64 = 4.0;
+    let spheres = [
+        Sphere::new(
+            "outer".to_string(),
+            "Outer".to_string(),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::sphere(0.0, 0.0, 0.0, R_OUTER),
+        ),
+        Sphere::new(
+            "a".to_string(),
+            "A".to_string(),
+            [1.00_f32, 0.00_f32, 0.25_f32],
+            engine::sphere(0.0, 4.0, 0.0, R_INNER),
+        ),
+        Sphere::new(
+            "b".to_string(),
+            "B".to_string(),
+            [0.00_f32, 0.25_f32, 1.00_f32],
+            engine::sphere(0.0, -4.0, 0.0, R_INNER),
+        ),
+    ];
+    for sphere in spheres {
+        let _ = assembly.try_insert_element(sphere);
+    }
+
+    // get references to the spheres
+    let [outer, a, b] = ["outer", "a", "b"].map(
+        |id| assembly.elements_by_id.with_untracked(
+            |elts_by_id| elts_by_id[id].clone()
+        )
+    );
+
+    // fix the diameters of the outer, sun, and moon spheres
+    for (sphere, radius) in [
+        (outer.clone(), R_OUTER),
+        (a.clone(), R_INNER),
+        (b.clone(), R_INNER),
+    ] {
+        let curvature_regulator = sphere.regulators().with_untracked(
+            |regs| regs.first().unwrap().clone()
+        );
+        let curvature = 0.5 / radius;
+        curvature_regulator.set_point().set(
+            SpecifiedValue::try_from(curvature.to_string()).unwrap()
+        );
+    }
+
+    // set the inversive distances between the spheres. as described above, the
+    // initial configuration deliberately violates these constraints
+    for inner in [a, b] {
+        let tangency = InversiveDistanceRegulator::new([outer.clone(), inner]);
+        tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
+        assembly.insert_regulator(Rc::new(tangency));
+    }
+}
+
+// the initial configuration of this test assembly deliberately violates the
+// constraints, so loading the assembly will trigger a non-trivial realization
+fn load_off_center(assembly: &Assembly) {
+    // create a point almost at the origin and a sphere centered on the origin
+    let _ = assembly.try_insert_element(
+        Point::new(
+            "point".to_string(),
+            "Point".to_string(),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::point(1e-9, 0.0, 0.0),
+        ),
+    );
+    let _ = assembly.try_insert_element(
+        Sphere::new(
+            "sphere".to_string(),
+            "Sphere".to_string(),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::sphere(0.0, 0.0, 0.0, 1.0),
+        ),
+    );
+
+    // get references to the elements
+    let point_and_sphere = ["point", "sphere"].map(
+        |id| assembly.elements_by_id.with_untracked(
+            |elts_by_id| elts_by_id[id].clone()
+        )
+    );
+
+    // put the point on the sphere
+    let incidence = InversiveDistanceRegulator::new(point_and_sphere);
+    incidence.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+    assembly.insert_regulator(Rc::new(incidence));
+}
+
+// setting the inversive distances between the vertices to -2 gives a regular
+// tetrahedron with side length 1, whose insphere and circumsphere have radii
+// sqrt(1/6) and sqrt(3/2), respectively. to measure those radii, set an
+// inversive distance of -1 between the insphere and each face, and then set an
+// inversive distance of 0 between the circumsphere and each vertex
+fn load_radius_ratio(assembly: &Assembly) {
+    let index_range = 1..=4;
+
+    // create the spheres
+    const GRAY: ElementColor = [0.75_f32, 0.75_f32, 0.75_f32];
+    let spheres = [
+        Sphere::new(
+            "sphere_faces".to_string(),
+            "Insphere".to_string(),
+            GRAY,
+            engine::sphere(0.0, 0.0, 0.0, 0.5),
+        ),
+        Sphere::new(
+            "sphere_vertices".to_string(),
+            "Circumsphere".to_string(),
+            GRAY,
+            engine::sphere(0.0, 0.0, 0.0, 0.25),
+        ),
+    ];
+    for sphere in spheres {
+        let _ = assembly.try_insert_element(sphere);
+    }
+
+    // create the vertices
+    let vertices = izip!(
+        index_range.clone(),
+        [
+            [1.00_f32, 0.50_f32, 0.75_f32],
+            [1.00_f32, 0.75_f32, 0.50_f32],
+            [1.00_f32, 1.00_f32, 0.50_f32],
+            [0.75_f32, 0.50_f32, 1.00_f32],
+        ].into_iter(),
+        [
+            engine::point(-0.6, -0.8, -0.6),
+            engine::point(-0.6, 0.8, 0.6),
+            engine::point(0.6, -0.8, 0.6),
+            engine::point(0.6, 0.8, -0.6),
+        ].into_iter()
+    ).map(
+        |(k, color, representation)| {
+            Point::new(
+                format!("v{k}"),
+                format!("Vertex {k}"),
+                color,
+                representation,
+            )
+        }
+    );
+    for vertex in vertices {
+        let _ = assembly.try_insert_element(vertex);
+    }
+
+    // create the faces
+    let base_dir = Vector3::new(1.0, 0.75, 1.0).normalize();
+    let offset = base_dir.dot(&Vector3::new(-0.6, 0.8, 0.6));
+    let faces = izip!(
+        index_range.clone(),
+        [
+            [1.00_f32, 0.00_f32, 0.25_f32],
+            [1.00_f32, 0.25_f32, 0.00_f32],
+            [0.75_f32, 0.75_f32, 0.00_f32],
+            [0.25_f32, 0.00_f32, 1.00_f32],
+        ].into_iter(),
+        [
+            engine::sphere_with_offset(base_dir[0], base_dir[1], base_dir[2], offset, 0.0),
+            engine::sphere_with_offset(base_dir[0], -base_dir[1], -base_dir[2], offset, 0.0),
+            engine::sphere_with_offset(-base_dir[0], base_dir[1], -base_dir[2], offset, 0.0),
+            engine::sphere_with_offset(-base_dir[0], -base_dir[1], base_dir[2], offset, 0.0),
+        ].into_iter()
+    ).map(
+        |(k, color, representation)| {
+            Sphere::new(
+                format!("f{k}"),
+                format!("Face {k}"),
+                color,
+                representation,
+            )
+        }
+    );
+    for face in faces {
+        face.ghost().set(true);
+        let _ = assembly.try_insert_element(face);
+    }
+
+    // impose the constraints
+    for j in index_range.clone() {
+        let [face_j, vertex_j] = [
+            format!("f{j}"),
+            format!("v{j}"),
+        ].map(
+            |id| assembly.elements_by_id.with_untracked(
+                |elts_by_id| elts_by_id[&id].clone()
+            )
+        );
+
+        // make the faces planar
+        let curvature_regulator = face_j.regulators().with_untracked(
+            |regs| regs.first().unwrap().clone()
+        );
+        curvature_regulator.set_point().set(
+            SpecifiedValue::try_from("0".to_string()).unwrap()
+        );
+
+        for k in index_range.clone().filter(|&index| index != j) {
+            let vertex_k = assembly.elements_by_id.with_untracked(
+                |elts_by_id| elts_by_id[&format!("v{k}")].clone()
+            );
+
+            // fix the distances between the vertices
+            if j < k {
+                let distance_regulator = InversiveDistanceRegulator::new(
+                    [vertex_j.clone(), vertex_k.clone()]
+                );
+                assembly.insert_regulator(Rc::new(distance_regulator));
+            }
+
+            // put the vertices on the faces
+            let incidence_regulator = InversiveDistanceRegulator::new([face_j.clone(), vertex_k.clone()]);
+            incidence_regulator.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
+            assembly.insert_regulator(Rc::new(incidence_regulator));
+        }
+    }
+}
+
+// to finish setting up the problem, fix the following curvatures:
+//   sun      1
+//   moon     5/3 = 1.666666666666666...
+//   chain1   2
+// a tiny `x` or `z` nudge of the outer sphere reliably prevents realization
+// failures before they happen, or resolves them after they happen. the result
+// depends sensitively on the translation direction, suggesting that realization
+// is failing because the engine is having trouble breaking a symmetry
+// /* TO DO */
+// the engine's performance on this problem is scale-dependent! with the current
+// initial conditions, realization fails for any order of imposing the remaining
+// curvature constraints. scaling everything up by a factor of ten, as done in
+// the original problem, makes realization succeed reliably. one potentially
+// relevant difference is that a lot of the numbers in the current initial
+// conditions are exactly representable as floats, unlike the analogous numbers
+// in the scaled-up problem. the inexact representations might break the
+// symmetry that's getting the engine stuck
+fn load_irisawa_hexlet(assembly: &Assembly) {
+    let index_range = 1..=6;
+    let colors = [
+        [1.00_f32, 0.00_f32, 0.25_f32],
+        [1.00_f32, 0.25_f32, 0.00_f32],
+        [0.75_f32, 0.75_f32, 0.00_f32],
+        [0.25_f32, 1.00_f32, 0.00_f32],
+        [0.00_f32, 0.25_f32, 1.00_f32],
+        [0.25_f32, 0.00_f32, 1.00_f32],
+    ].into_iter();
+
+    // create the spheres
+    let spheres = [
+        Sphere::new(
+            "outer".to_string(),
+            "Outer".to_string(),
+            [0.5_f32, 0.5_f32, 0.5_f32],
+            engine::sphere(0.0, 0.0, 0.0, 1.5),
+        ),
+        Sphere::new(
+            "sun".to_string(),
+            "Sun".to_string(),
+            [0.75_f32, 0.75_f32, 0.75_f32],
+            engine::sphere(0.0, -0.75, 0.0, 0.75),
+        ),
+        Sphere::new(
+            "moon".to_string(),
+            "Moon".to_string(),
+            [0.25_f32, 0.25_f32, 0.25_f32],
+            engine::sphere(0.0, 0.75, 0.0, 0.75),
+        ),
+    ].into_iter().chain(
+        index_range.clone().zip(colors).map(
+            |(k, color)| {
+                let ang = (k as f64) * PI/3.0;
+                Sphere::new(
+                    format!("chain{k}"),
+                    format!("Chain {k}"),
+                    color,
+                    engine::sphere(1.0 * ang.sin(), 0.0, 1.0 * ang.cos(), 0.5),
+                )
+            }
+        )
+    );
+    for sphere in spheres {
+        let _ = assembly.try_insert_element(sphere);
+    }
+
+    // put the outer sphere in ghost mode and fix its curvature
+    let outer = assembly.elements_by_id.with_untracked(
+        |elts_by_id| elts_by_id["outer"].clone()
+    );
+    outer.ghost().set(true);
+    let outer_curvature_regulator = outer.regulators().with_untracked(
+        |regs| regs.first().unwrap().clone()
+    );
+    outer_curvature_regulator.set_point().set(
+        SpecifiedValue::try_from((1.0 / 3.0).to_string()).unwrap()
+    );
+
+    // impose the desired tangencies
+    let [outer, sun, moon] = ["outer", "sun", "moon"].map(
+        |id| assembly.elements_by_id.with_untracked(
+            |elts_by_id| elts_by_id[id].clone()
+        )
+    );
+    let chain = index_range.map(
+        |k| assembly.elements_by_id.with_untracked(
+            |elts_by_id| elts_by_id[&format!("chain{k}")].clone()
+        )
+    );
+    for (chain_sphere, chain_sphere_next) in chain.clone().zip(chain.cycle().skip(1)) {
+        for (other_sphere, inversive_distance) in [
+            (outer.clone(), "1"),
+            (sun.clone(), "-1"),
+            (moon.clone(), "-1"),
+            (chain_sphere_next.clone(), "-1"),
+        ] {
+            let tangency = InversiveDistanceRegulator::new([chain_sphere.clone(), other_sphere]);
+            tangency.set_point.set(SpecifiedValue::try_from(inversive_distance.to_string()).unwrap());
+            assembly.insert_regulator(Rc::new(tangency));
+        }
+    }
+
+    let outer_sun_tangency = InversiveDistanceRegulator::new([outer.clone(), sun]);
+    outer_sun_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
+    assembly.insert_regulator(Rc::new(outer_sun_tangency));
+
+    let outer_moon_tangency = InversiveDistanceRegulator::new([outer.clone(), moon]);
+    outer_moon_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
+    assembly.insert_regulator(Rc::new(outer_moon_tangency));
+}
+
+// --- chooser ---
+
+/* DEBUG */
+#[component]
+pub fn TestAssemblyChooser() -> View {
+    // create an effect that loads the selected test assembly
+    let assembly_name = create_signal("general".to_string());
+    create_effect(move || {
+        // get name of chosen assembly
+        let name = assembly_name.get_clone();
+        console::log_1(
+            &JsValue::from(format!("Showing assembly \"{}\"", name.clone()))
+        );
+
+        batch(|| {
+            let state = use_context::<AppState>();
+            let assembly = &state.assembly;
+
+            // clear state
+            assembly.regulators.update(|regs| regs.clear());
+            assembly.elements.update(|elts| elts.clear());
+            assembly.elements_by_id.update(|elts_by_id| elts_by_id.clear());
+            assembly.descent_history.set(DescentHistory::new());
+            state.selection.update(|sel| sel.clear());
+
+            // load assembly
+            match name.as_str() {
+                "general" => load_general(assembly),
+                "low-curvature" => load_low_curvature(assembly),
+                "pointed" => load_pointed(assembly),
+                "tridiminished-icosahedron" => load_tridiminished_icosahedron(assembly),
+                "dodecahedral-packing" => load_dodecahedral_packing(assembly),
+                "balanced" => load_balanced(assembly),
+                "off-center" => load_off_center(assembly),
+                "radius-ratio" => load_radius_ratio(assembly),
+                "irisawa-hexlet" => load_irisawa_hexlet(assembly),
+                _ => (),
+            };
+        });
+    });
+
+    // build the chooser
+    view! {
+        select(bind:value = assembly_name) {
+            option(value = "general") { "General" }
+            option(value = "low-curvature") { "Low-curvature" }
+            option(value = "pointed") { "Pointed" }
+            option(value = "tridiminished-icosahedron") { "Tridiminished icosahedron" }
+            option(value = "dodecahedral-packing") { "Dodecahedral packing" }
+            option(value = "balanced") { "Balanced" }
+            option(value = "off-center") { "Off-center" }
+            option(value = "radius-ratio") { "Radius ratio" }
+            option(value = "irisawa-hexlet") { "Irisawa hexlet" }
+            option(value = "empty") { "Empty" }
+        }
+    }
+}
--- a/app-proto/src/engine.rs
+++ b/app-proto/src/engine.rs
@ -1,7 +1,6 @@
 use lazy_static::lazy_static;
 use nalgebra::{Const, DMatrix, DVector, DVectorView, Dyn, SymmetricEigen};
 use std::fmt::{Display, Error, Formatter};
-use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */

 // --- elements ---

@ -17,7 +16,7 @@ pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64) -> DVect
        center_y / radius,
        center_z / radius,
        0.5 / radius,
-        0.5 * (center_norm_sq / radius - radius)
+        0.5 * (center_norm_sq / radius - radius),
    ])
 }

@ -31,7 +30,7 @@ pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f6
        norm_sp * dir_y,
        norm_sp * dir_z,
        0.5 * curv,
-        off * (1.0 + 0.5 * off * curv)
+        off * (1.0 + 0.5 * off * curv),
    ])
 }

@ -50,66 +49,32 @@ pub fn project_point_to_normalized(rep: &mut DVector<f64>) {
    rep.scale_mut(0.5 / rep[3]);
 }

-// given a sphere's representation vector, change the sphere's half-curvature to
-// `half-curv` and then restore normalization by contracting the representation
-// vector toward the curvature axis
-pub fn change_half_curvature(rep: &mut DVector<f64>, half_curv: f64) {
-    // set the sphere's half-curvature to the desired value
-    rep[3] = half_curv;
-    
-    // restore normalization by contracting toward the curvature axis
-    const SIZE_THRESHOLD: f64 = 1e-9;
-    let half_q_lt = -2.0 * half_curv * rep[4];
-    let half_q_lt_sq = half_q_lt * half_q_lt;
-    let mut spatial = rep.fixed_rows_mut::<3>(0);
-    let q_sp = spatial.norm_squared();
-    if q_sp < SIZE_THRESHOLD && half_q_lt_sq < SIZE_THRESHOLD {
-        spatial.copy_from_slice(
-            &[0.0, 0.0, (1.0 - 2.0 * half_q_lt).sqrt()]
-        );
-    } else {
-        let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
-        spatial.scale_mut(1.0 / scaling);
-        rep[4] /= scaling;
-    }
-    
-    /* DEBUG */
-    // verify normalization
-    let rep_for_debug = rep.clone();
-    console::log_1(&JsValue::from(
-        format!(
-            "Sphere self-product after curvature change: {}",
-            rep_for_debug.dot(&(&*Q * &rep_for_debug))
-        )
-    ));
-}
-
 // --- partial matrices ---

 pub struct MatrixEntry {
-    index: (usize, usize),
-    value: f64
+    pub index: (usize, usize),
+    pub value: f64,
 }

 pub struct PartialMatrix(Vec<MatrixEntry>);

 impl PartialMatrix {
-    pub fn new() -> PartialMatrix {
-        PartialMatrix(Vec::<MatrixEntry>::new())
+    pub fn new() -> Self {
+        Self(Vec::<MatrixEntry>::new())
    }
-    
+
    pub fn push(&mut self, row: usize, col: usize, value: f64) {
-        let PartialMatrix(entries) = self;
-        entries.push(MatrixEntry { index: (row, col), value: value });
+        let Self(entries) = self;
+        entries.push(MatrixEntry { index: (row, col), value });
    }
-    
+
    pub fn push_sym(&mut self, row: usize, col: usize, value: f64) {
        self.push(row, col, value);
        if row != col {
            self.push(col, row, value);
        }
    }
-    
+
    fn freeze(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = a.clone();
        for &MatrixEntry { index, value } in self {
@ -117,7 +82,7 @@ impl PartialMatrix {
        }
        result
    }
-    
+
    fn proj(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = DMatrix::<f64>::zeros(a.nrows(), a.ncols());
        for &MatrixEntry { index, .. } in self {
@ -125,7 +90,7 @@ impl PartialMatrix {
        }
        result
    }
-    
+
    fn sub_proj(&self, rhs: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = DMatrix::<f64>::zeros(rhs.nrows(), rhs.ncols());
        for &MatrixEntry { index, value } in self {
@ -147,9 +112,9 @@ impl Display for PartialMatrix {
 impl IntoIterator for PartialMatrix {
    type Item = MatrixEntry;
    type IntoIter = std::vec::IntoIter<Self::Item>;
-    
+
    fn into_iter(self) -> Self::IntoIter {
-        let PartialMatrix(entries) = self;
+        let Self(entries) = self;
        entries.into_iter()
    }
 }
@ -157,7 +122,7 @@ impl IntoIterator for PartialMatrix {
 impl<'a> IntoIterator for &'a PartialMatrix {
    type Item = &'a MatrixEntry;
    type IntoIter = std::slice::Iter<'a, MatrixEntry>;
-    
+
    fn into_iter(self) -> Self::IntoIter {
        let PartialMatrix(entries) = self;
        entries.into_iter()
@ -170,22 +135,26 @@ impl<'a> IntoIterator for &'a PartialMatrix {
 pub struct ConfigSubspace {
    assembly_dim: usize,
    basis_std: Vec<DMatrix<f64>>,
-    basis_proj: Vec<DMatrix<f64>>
+    basis_proj: Vec<DMatrix<f64>>,
 }

 impl ConfigSubspace {
-    pub fn zero(assembly_dim: usize) -> ConfigSubspace {
-        ConfigSubspace {
-            assembly_dim: assembly_dim,
+    pub fn zero(assembly_dim: usize) -> Self {
+        Self {
+            assembly_dim,
            basis_proj: Vec::new(),
-            basis_std: Vec::new()
+            basis_std: Vec::new(),
        }
    }
-    
+
    // approximate the kernel of a symmetric endomorphism of the configuration
    // space for `assembly_dim` elements. we consider an eigenvector to be part
    // of the kernel if its eigenvalue is smaller than the constant `THRESHOLD`
-    fn symmetric_kernel(a: DMatrix<f64>, proj_to_std: DMatrix<f64>, assembly_dim: usize) -> ConfigSubspace {
+    fn symmetric_kernel(
+        a: DMatrix<f64>,
+        proj_to_std: DMatrix<f64>,
+        assembly_dim: usize,
+    ) -> Self {
        // find a basis for the kernel. the basis is expressed in the projection
        // coordinates, and it's orthonormal with respect to the projection
        // inner product
@ -198,21 +167,14 @@ impl ConfigSubspace {
                |(λ, v)| (λ.abs() < THRESHOLD).then_some(v)
            ).collect::<Vec<_>>().as_slice()
        );
-        
-        /* DEBUG */
-        // print the eigenvalues
-        #[cfg(all(target_family = "wasm", target_os = "unknown"))]
-        console::log_1(&JsValue::from(
-            format!("Eigenvalues used to find kernel:{}", eig.eigenvalues)
-        ));
-        
+
        // express the basis in the standard coordinates
        let basis_std = proj_to_std * &basis_proj;
-        
+
        const ELEMENT_DIM: usize = 5;
        const UNIFORM_DIM: usize = 4;
-        ConfigSubspace {
-            assembly_dim: assembly_dim,
+        Self {
+            assembly_dim,
            basis_std: basis_std.column_iter().map(
                |v| Into::<DMatrix<f64>>::into(
                    v.reshape_generic(Dyn(ELEMENT_DIM), Dyn(assembly_dim))
@ -222,18 +184,18 @@ impl ConfigSubspace {
                |v| Into::<DMatrix<f64>>::into(
                    v.reshape_generic(Dyn(UNIFORM_DIM), Dyn(assembly_dim))
                )
-            ).collect()
+            ).collect(),
        }
    }
-    
+
    pub fn dim(&self) -> usize {
        self.basis_std.len()
    }
-    
+
    pub fn assembly_dim(&self) -> usize {
        self.assembly_dim
    }
-    
+
    // find the projection onto this subspace of the motion where the element
    // with the given column index has velocity `v`. the velocity is given in
    // projection coordinates, and the projection is done with respect to the
@ -256,18 +218,18 @@ pub struct DescentHistory {
    pub config: Vec<DMatrix<f64>>,
    pub scaled_loss: Vec<f64>,
    pub neg_grad: Vec<DMatrix<f64>>,
-    pub min_eigval: Vec<f64>,
+    pub hess_eigvals: Vec<DVector<f64>>,
    pub base_step: Vec<DMatrix<f64>>,
-    pub backoff_steps: Vec<i32>
+    pub backoff_steps: Vec<i32>,
 }

 impl DescentHistory {
-    fn new() -> DescentHistory {
-        DescentHistory {
+    pub fn new() -> Self {
+        Self {
            config: Vec::<DMatrix<f64>>::new(),
            scaled_loss: Vec::<f64>::new(),
            neg_grad: Vec::<DMatrix<f64>>::new(),
-            min_eigval: Vec::<f64>::new(),
+            hess_eigvals: Vec::<DVector<f64>>::new(),
            base_step: Vec::<DMatrix<f64>>::new(),
            backoff_steps: Vec::<i32>::new(),
        }
@ -283,21 +245,21 @@ pub struct ConstraintProblem {
 }

 impl ConstraintProblem {
-    pub fn new(element_count: usize) -> ConstraintProblem {
+    pub fn new(element_count: usize) -> Self {
        const ELEMENT_DIM: usize = 5;
-        ConstraintProblem {
+        Self {
            gram: PartialMatrix::new(),
            frozen: PartialMatrix::new(),
-            guess: DMatrix::<f64>::zeros(ELEMENT_DIM, element_count)
+            guess: DMatrix::<f64>::zeros(ELEMENT_DIM, element_count),
        }
    }
-    
+
    #[cfg(feature = "dev")]
-    pub fn from_guess(guess_columns: &[DVector<f64>]) -> ConstraintProblem {
-        ConstraintProblem {
+    pub fn from_guess(guess_columns: &[DVector<f64>]) -> Self {
+        Self {
            gram: PartialMatrix::new(),
            frozen: PartialMatrix::new(),
-            guess: DMatrix::from_columns(guess_columns)
+            guess: DMatrix::from_columns(guess_columns),
        }
    }
 }
@ -311,25 +273,21 @@ lazy_static! {
        0.0, 1.0, 0.0,  0.0,  0.0,
        0.0, 0.0, 1.0,  0.0,  0.0,
        0.0, 0.0, 0.0,  0.0, -2.0,
-        0.0, 0.0, 0.0, -2.0,  0.0
+        0.0, 0.0, 0.0, -2.0,  0.0,
    ]);
 }

 struct SearchState {
    config: DMatrix<f64>,
    err_proj: DMatrix<f64>,
-    loss: f64
+    loss: f64,
 }

 impl SearchState {
-    fn from_config(gram: &PartialMatrix, config: DMatrix<f64>) -> SearchState {
+    fn from_config(gram: &PartialMatrix, config: DMatrix<f64>) -> Self {
        let err_proj = gram.sub_proj(&(config.tr_mul(&*Q) * &config));
        let loss = err_proj.norm_squared();
-        SearchState {
-            config: config,
-            err_proj: err_proj,
-            loss: loss
-        }
+        Self { config, err_proj, loss }
    }
 }

@ -356,7 +314,7 @@ pub fn local_unif_to_std(v: DVectorView<f64>) -> DMatrix<f64> {
            curv,  0.0,  0.0,  0.0, v[0],
             0.0, curv,  0.0,  0.0, v[1],
             0.0,  0.0, curv,  0.0, v[2],
-             0.0,  0.0,  0.0,  0.0,  1.0
+             0.0,  0.0,  0.0,  0.0,  1.0,
        ])
    } else {
        // `v` represents a sphere. the normalization condition says that the
@ -365,7 +323,7 @@ pub fn local_unif_to_std(v: DVectorView<f64>) -> DMatrix<f64> {
                 curv,       0.0,       0.0,       0.0,            v[0],
                  0.0,      curv,       0.0,       0.0,            v[1],
                  0.0,       0.0,      curv,       0.0,            v[2],
-            curv*v[0], curv*v[1], curv*v[2], curv*v[3], curv*v[4] + 1.0
+            curv*v[0], curv*v[1], curv*v[2], curv*v[3], curv*v[4] + 1.0,
        ])
    }
 }
@ -378,7 +336,7 @@ fn seek_better_config(
    base_target_improvement: f64,
    min_efficiency: f64,
    backoff: f64,
-    max_backoff_steps: i32
+    max_backoff_steps: i32,
 ) -> Option<(SearchState, i32)> {
    let mut rate = 1.0;
    for backoff_steps in 0..max_backoff_steps {
@ -393,6 +351,17 @@ fn seek_better_config(
    None
 }

+// a first-order neighborhood of a configuration
+pub struct ConfigNeighborhood {
+    #[cfg(feature = "dev")] pub config: DMatrix<f64>,
+    pub nbhd: ConfigSubspace,
+}
+
+pub struct Realization {
+    pub result: Result<ConfigNeighborhood, String>,
+    pub history: DescentHistory,
+}
+
 // seek a matrix `config` that matches the partial matrix `problem.frozen` and
 // has `config' * Q * config` matching the partial matrix `problem.gram`. start
 // at `problem.guess`, set the frozen entries to their desired values, and then
@ -404,30 +373,41 @@ pub fn realize_gram(
    backoff: f64,
    reg_scale: f64,
    max_descent_steps: i32,
-    max_backoff_steps: i32
-) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
+    max_backoff_steps: i32,
+) -> Realization {
    // destructure the problem data
-    let ConstraintProblem {
-        gram, guess, frozen
-    } = problem;
-    
+    let ConstraintProblem { gram, guess, frozen } = problem;
+
    // start the descent history
    let mut history = DescentHistory::new();
-    
+
+    // handle the case where the assembly is empty. our general realization
+    // routine can't handle this case because it builds the Hessian using
+    // `DMatrix::from_columns`, which panics when the list of columns is empty
+    let assembly_dim = guess.ncols();
+    if assembly_dim == 0 {
+        let result = Ok(
+            ConfigNeighborhood {
+                #[cfg(feature = "dev")] config: guess.clone(),
+                nbhd: ConfigSubspace::zero(0),
+            }
+        );
+        return Realization { result, history };
+    }
+
    // find the dimension of the search space
    let element_dim = guess.nrows();
-    let assembly_dim = guess.ncols();
    let total_dim = element_dim * assembly_dim;
-    
+
    // scale the tolerance
    let scale_adjustment = (gram.0.len() as f64).sqrt();
    let tol = scale_adjustment * scaled_tol;
-    
+
    // convert the frozen indices to stacked format
    let frozen_stacked: Vec<usize> = frozen.into_iter().map(
        |MatrixEntry { index: (row, col), .. }| col*element_dim + row
    ).collect();
-    
+
    // use a regularized Newton's method with backtracking
    let mut state = SearchState::from_config(gram, frozen.freeze(guess));
    let mut hess = DMatrix::zeros(element_dim, assembly_dim);
@ -436,7 +416,7 @@ pub fn realize_gram(
        let neg_grad = 4.0 * &*Q * &state.config * &state.err_proj;
        let mut neg_grad_stacked = neg_grad.clone().reshape_generic(Dyn(total_dim), Const::<1>);
        history.neg_grad.push(neg_grad.clone());
-        
+
        // find the negative Hessian of the loss function
        let mut hess_cols = Vec::<DVector<f64>>::with_capacity(total_dim);
        for col in 0..assembly_dim {
@ -455,14 +435,15 @@ pub fn realize_gram(
            }
        }
        hess = DMatrix::from_columns(hess_cols.as_slice());
-        
+
        // regularize the Hessian
-        let min_eigval = hess.symmetric_eigenvalues().min();
+        let hess_eigvals = hess.symmetric_eigenvalues();
+        let min_eigval = hess_eigvals.min();
        if min_eigval <= 0.0 {
            hess -= reg_scale * min_eigval * DMatrix::identity(total_dim, total_dim);
        }
-        history.min_eigval.push(min_eigval);
-        
+        history.hess_eigvals.push(hess_eigvals);
+
        // project the negative gradient and negative Hessian onto the
        // orthogonal complement of the frozen subspace
        let zero_col = DVector::zeros(total_dim);
@ -473,37 +454,47 @@ pub fn realize_gram(
            hess.set_column(k, &zero_col);
            hess[(k, k)] = 1.0;
        }
-        
+
        // stop if the loss is tolerably low
        history.config.push(state.config.clone());
        history.scaled_loss.push(state.loss / scale_adjustment);
        if state.loss < tol { break; }
-        
+
        // compute the Newton step
+        /* TO DO */
        /*
-          we need to either handle or eliminate the case where the minimum
-          eigenvalue of the Hessian is zero, so the regularized Hessian is
-          singular. right now, this causes the Cholesky decomposition to return
-          `None`, leading to a panic when we unrap
+          we should change our regularization to ensure that the Hessian is
+          is positive-definite, rather than just positive-semidefinite. ideally,
+          that would guarantee the success of the Cholesky decomposition---
+          although we'd still need the error-handling routine in case of
+          numerical hiccups
        */
-        let base_step_stacked = hess.clone().cholesky().unwrap().solve(&neg_grad_stacked);
+        let hess_cholesky = match hess.clone().cholesky() {
+            Some(cholesky) => cholesky,
+            None => return Realization {
+                result: Err("Cholesky decomposition failed".to_string()),
+                history,
+            },
+        };
+        let base_step_stacked = hess_cholesky.solve(&neg_grad_stacked);
        let base_step = base_step_stacked.reshape_generic(Dyn(element_dim), Dyn(assembly_dim));
        history.base_step.push(base_step.clone());
-        
+
        // use backtracking line search to find a better configuration
-        match seek_better_config(
+        if let Some((better_state, backoff_steps)) = seek_better_config(
            gram, &state, &base_step, neg_grad.dot(&base_step),
-            min_efficiency, backoff, max_backoff_steps
+            min_efficiency, backoff, max_backoff_steps,
        ) {
-            Some((better_state, backoff_steps)) => {
-                state = better_state;
-                history.backoff_steps.push(backoff_steps);
-            },
-            None => return (state.config, ConfigSubspace::zero(assembly_dim), false, history)
-        };
+            state = better_state;
+            history.backoff_steps.push(backoff_steps);
+        } else {
+            return Realization {
+                result: Err("Line search failed".to_string()),
+                history,
+            };
+        }
    }
-    let success = state.loss < tol;
-    let tangent = if success {
+    let result = if state.loss < tol {
        // express the uniform basis in the standard basis
        const UNIFORM_DIM: usize = 4;
        let total_dim_unif = UNIFORM_DIM * assembly_dim;
@ -514,13 +505,15 @@ pub fn realize_gram(
                .view_mut(block_start, (element_dim, UNIFORM_DIM))
                .copy_from(&local_unif_to_std(state.config.column(n)));
        }
-        
+
        // find the kernel of the Hessian. give it the uniform inner product
-        ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim)
+        let tangent = ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim);
+
+        Ok(ConfigNeighborhood { #[cfg(feature = "dev")] config: state.config, nbhd: tangent })
    } else {
-        ConfigSubspace::zero(assembly_dim)
+        Err("Failed to reach target accuracy".to_string())
    };
-    (state.config, tangent, success, history)
+    Realization { result, history }
 }

 // --- tests ---
@ -528,9 +521,9 @@ pub fn realize_gram(
 #[cfg(feature = "dev")]
 pub mod examples {
    use std::f64::consts::PI;
-    
+
    use super::*;
-    
+
    // this problem is from a sangaku by Irisawa Shintarō Hiroatsu. the article
    // below includes a nice translation of the problem statement, which was
    // recorded in Uchida Itsumi's book _Kokon sankan_ (_Mathematics, Past and
@ -539,12 +532,12 @@ pub mod examples {
    //   "Japan's 'Wasan' Mathematical Tradition", by Abe Haruki
    //   https://www.nippon.com/en/japan-topics/c12801/
    //
-    pub fn realize_irisawa_hexlet(scaled_tol: f64) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
+    pub fn realize_irisawa_hexlet(scaled_tol: f64) -> Realization {
        let mut problem = ConstraintProblem::from_guess(
            [
                sphere(0.0, 0.0, 0.0, 15.0),
                sphere(0.0, 0.0, -9.0, 5.0),
-                sphere(0.0, 0.0, 11.0, 3.0)
+                sphere(0.0, 0.0, 11.0, 3.0),
            ].into_iter().chain(
                (1..=6).map(
                    |k| {
@ -554,43 +547,43 @@ pub mod examples {
                )
            ).collect::<Vec<_>>().as_slice()
        );
-        
+
        for s in 0..9 {
            // each sphere is represented by a spacelike vector
            problem.gram.push_sym(s, s, 1.0);
-            
+
            // the circumscribing sphere is tangent to all of the other
            // spheres, with matching orientation
            if s > 0 {
                problem.gram.push_sym(0, s, 1.0);
            }
-            
+
            if s > 2 {
                // each chain sphere is tangent to the "sun" and "moon"
                // spheres, with opposing orientation
                for n in 1..3 {
                    problem.gram.push_sym(s, n, -1.0);
                }
-                
+
                // each chain sphere is tangent to the next chain sphere,
                // with opposing orientation
                let s_next = 3 + (s-2) % 6;
                problem.gram.push_sym(s, s_next, -1.0);
            }
        }
-        
+
        // the frozen entries fix the radii of the circumscribing sphere, the
        // "sun" and "moon" spheres, and one of the chain spheres
        for k in 0..4 {
            problem.frozen.push(3, k, problem.guess[(3, k)]);
        }
-        
+
        realize_gram(&problem, scaled_tol, 0.5, 0.9, 1.1, 200, 110)
    }
-    
+
    // set up a kaleidocycle, made of points with fixed distances between them,
    // and find its tangent space
-    pub fn realize_kaleidocycle(scaled_tol: f64) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
+    pub fn realize_kaleidocycle(scaled_tol: f64) -> Realization {
        const N_HINGES: usize = 6;
        let mut problem = ConstraintProblem::from_guess(
            (0..N_HINGES).step_by(2).flat_map(
@ -603,12 +596,12 @@ pub mod examples {
                        point(0.0, 0.0, 0.0),
                        point(ang_hor.cos(), ang_hor.sin(), 0.0),
                        point(x_vert, y_vert, -0.5),
-                        point(x_vert, y_vert, 0.5)
+                        point(x_vert, y_vert, 0.5),
                    ]
                }
            ).collect::<Vec<_>>().as_slice()
        );
-        
+
        const N_POINTS: usize = 2 * N_HINGES;
        for block in (0..N_POINTS).step_by(2) {
            let block_next = (block + 2) % N_POINTS;
@ -617,18 +610,18 @@ pub mod examples {
                for k in j..2 {
                    problem.gram.push_sym(block + j, block + k, if j == k { 0.0 } else { -0.5 });
                }
-                
+
                // non-hinge edges
                for k in 0..2 {
                    problem.gram.push_sym(block + j, block_next + k, -0.625);
                }
            }
        }
-        
+
        for k in 0..N_POINTS {
            problem.frozen.push(3, k, problem.guess[(3, k)])
        }
-        
+
        realize_gram(&problem, scaled_tol, 0.5, 0.9, 1.1, 200, 110)
    }
 }
@ -637,47 +630,47 @@ pub mod examples {
 mod tests {
    use nalgebra::Vector3;
    use std::{f64::consts::{FRAC_1_SQRT_2, PI}, iter};
-    
+
    use super::{*, examples::*};
-    
+
    #[test]
    fn freeze_test() {
        let frozen = PartialMatrix(vec![
            MatrixEntry { index: (0, 0), value: 14.0 },
            MatrixEntry { index: (0, 2), value: 28.0 },
            MatrixEntry { index: (1, 1), value: 42.0 },
-            MatrixEntry { index: (1, 2), value: 49.0 }
+            MatrixEntry { index: (1, 2), value: 49.0 },
        ]);
        let config = DMatrix::<f64>::from_row_slice(2, 3, &[
            1.0, 2.0, 3.0,
-            4.0, 5.0, 6.0
+            4.0, 5.0, 6.0,
        ]);
        let expected_result = DMatrix::<f64>::from_row_slice(2, 3, &[
            14.0, 2.0, 28.0,
-            4.0, 42.0, 49.0
+            4.0, 42.0, 49.0,
        ]);
        assert_eq!(frozen.freeze(&config), expected_result);
    }
-    
+
    #[test]
    fn sub_proj_test() {
        let target = PartialMatrix(vec![
            MatrixEntry { index: (0, 0), value: 19.0 },
            MatrixEntry { index: (0, 2), value: 39.0 },
            MatrixEntry { index: (1, 1), value: 59.0 },
-            MatrixEntry { index: (1, 2), value: 69.0 }
+            MatrixEntry { index: (1, 2), value: 69.0 },
        ]);
        let attempt = DMatrix::<f64>::from_row_slice(2, 3, &[
            1.0, 2.0, 3.0,
-            4.0, 5.0, 6.0
+            4.0, 5.0, 6.0,
        ]);
        let expected_result = DMatrix::<f64>::from_row_slice(2, 3, &[
            18.0, 0.0, 36.0,
-            0.0, 54.0, 63.0
+            0.0, 54.0, 63.0,
        ]);
        assert_eq!(target.sub_proj(&attempt), expected_result);
    }
-    
+
    #[test]
    fn zero_loss_test() {
        let mut gram = PartialMatrix::new();
@ -691,13 +684,13 @@ mod tests {
            DMatrix::from_columns(&[
                sphere(1.0, 0.0, 0.0, a),
                sphere(-0.5, a, 0.0, a),
-                sphere(-0.5, -a, 0.0, a)
+                sphere(-0.5, -a, 0.0, a),
            ])
        };
        let state = SearchState::from_config(&gram, config);
        assert!(state.loss.abs() < f64::EPSILON);
    }
-    
+
    /* TO DO */
    // at the frozen indices, the optimization steps should have exact zeros,
    // and the realized configuration should have the desired values
@ -705,7 +698,7 @@ mod tests {
    fn frozen_entry_test() {
        let mut problem = ConstraintProblem::from_guess(&[
            point(0.0, 0.0, 2.0),
-            sphere(0.0, 0.0, 0.0, 0.95)
+            sphere(0.0, 0.0, 0.0, 0.95),
        ]);
        for j in 0..2 {
            for k in j..2 {
@ -714,10 +707,10 @@ mod tests {
        }
        problem.frozen.push(3, 0, problem.guess[(3, 0)]);
        problem.frozen.push(3, 1, 0.5);
-        let (config, _, success, history) = realize_gram(
+        let Realization { result, history } = realize_gram(
            &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
        );
-        assert_eq!(success, true);
+        let config = result.unwrap().config;
        for base_step in history.base_step.into_iter() {
            for &MatrixEntry { index, .. } in &problem.frozen {
                assert_eq!(base_step[index], 0.0);
@ -727,13 +720,13 @@ mod tests {
            assert_eq!(config[index], value);
        }
    }
-    
+
    #[test]
    fn irisawa_hexlet_test() {
        // solve Irisawa's problem
        const SCALED_TOL: f64 = 1.0e-12;
-        let (config, _, _, _) = realize_irisawa_hexlet(SCALED_TOL);
-        
+        let config = realize_irisawa_hexlet(SCALED_TOL).result.unwrap().config;
+
        // check against Irisawa's solution
        let entry_tol = SCALED_TOL.sqrt();
        let solution_diams = [30.0, 10.0, 6.0, 5.0, 15.0, 10.0, 3.75, 2.5, 2.0 + 8.0/11.0];
@ -741,7 +734,7 @@ mod tests {
            assert!((config[(3, k)] - 1.0 / diam).abs() < entry_tol);
        }
    }
-    
+
    #[test]
    fn tangent_test_three_spheres() {
        const SCALED_TOL: f64 = 1.0e-12;
@ -749,7 +742,7 @@ mod tests {
        let mut problem = ConstraintProblem::from_guess(&[
            sphere(0.0, 0.0, 0.0, -2.0),
            sphere(0.0, 0.0, 1.0, 1.0),
-            sphere(0.0, 0.0, -1.0, 1.0)
+            sphere(0.0, 0.0, -1.0, 1.0),
        ]);
        for j in 0..3 {
            for k in j..3 {
@ -759,13 +752,13 @@ mod tests {
        for n in 0..ELEMENT_DIM {
            problem.frozen.push(n, 0, problem.guess[(n, 0)]);
        }
-        let (config, tangent, success, history) = realize_gram(
+        let Realization { result, history } = realize_gram(
            &problem, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
        );
+        let ConfigNeighborhood { config, nbhd: tangent } = result.unwrap();
        assert_eq!(config, problem.guess);
-        assert_eq!(success, true);
        assert_eq!(history.scaled_loss.len(), 1);
-        
+
        // list some motions that should form a basis for the tangent space of
        // the solution variety
        const UNIFORM_DIM: usize = 4;
@ -779,8 +772,8 @@ mod tests {
            DMatrix::<f64>::from_column_slice(UNIFORM_DIM, assembly_dim, &[
                0.0, 0.0,  0.0,  0.0,
                0.0, 0.0, -0.5, -0.5,
-                0.0, 0.0, -0.5,  0.5
-            ])
+                0.0, 0.0, -0.5,  0.5,
+            ]),
        ];
        let tangent_motions_std = vec![
            basis_matrix((0, 1), element_dim, assembly_dim),
@ -790,14 +783,14 @@ mod tests {
            DMatrix::<f64>::from_column_slice(element_dim, assembly_dim, &[
                0.0, 0.0,  0.0,  0.00,  0.0,
                0.0, 0.0, -1.0, -0.25, -1.0,
-                0.0, 0.0, -1.0,  0.25,  1.0
-            ])
+                0.0, 0.0, -1.0,  0.25,  1.0,
+            ]),
        ];
-        
+
        // confirm that the dimension of the tangent space is no greater than
        // expected
        assert_eq!(tangent.basis_std.len(), tangent_motions_std.len());
-        
+
        // confirm that the tangent space contains all the motions we expect it
        // to. since we've already bounded the dimension of the tangent space,
        // this confirms that the tangent space is what we expect it to be
@ -809,13 +802,13 @@ mod tests {
            assert!((motion_std - motion_proj).norm_squared() < tol_sq);
        }
    }
-    
+
    fn translation_motion_unif(vel: &Vector3<f64>, assembly_dim: usize) -> Vec<DVector<f64>> {
        let mut elt_motion = DVector::zeros(4);
        elt_motion.fixed_rows_mut::<3>(0).copy_from(vel);
        iter::repeat(elt_motion).take(assembly_dim).collect()
    }
-    
+
    fn rotation_motion_unif(ang_vel: &Vector3<f64>, points: Vec<DVectorView<f64>>) -> Vec<DVector<f64>> {
        points.into_iter().map(
            |pt| {
@ -826,15 +819,15 @@ mod tests {
            }
        ).collect()
    }
-    
+
    #[test]
    fn tangent_test_kaleidocycle() {
        // set up a kaleidocycle and find its tangent space
        const SCALED_TOL: f64 = 1.0e-12;
-        let (config, tangent, success, history) = realize_kaleidocycle(SCALED_TOL);
-        assert_eq!(success, true);
+        let Realization { result, history } = realize_kaleidocycle(SCALED_TOL);
+        let ConfigNeighborhood { config, nbhd: tangent } = result.unwrap();
        assert_eq!(history.scaled_loss.len(), 1);
-        
+
        // list some motions that should form a basis for the tangent space of
        // the solution variety
        const N_HINGES: usize = 6;
@ -845,12 +838,12 @@ mod tests {
            translation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), assembly_dim),
            translation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), assembly_dim),
            translation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), assembly_dim),
-            
+
            // the rotations about the coordinate axes
            rotation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), config.column_iter().collect()),
            rotation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), config.column_iter().collect()),
            rotation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), config.column_iter().collect()),
-            
+
            // the twist motion. more precisely: a motion that keeps the center
            // of mass stationary and preserves the distances between the
            // vertices to first order. this has to be the twist as long as:
@ -867,10 +860,10 @@ mod tests {
                        DVector::from_column_slice(&[0.0, 0.0, 5.0, 0.0]),
                        DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]),
                        DVector::from_column_slice(&[-vel_vert_x, -vel_vert_y, -3.0, 0.0]),
-                        DVector::from_column_slice(&[vel_vert_x, vel_vert_y, -3.0, 0.0])
+                        DVector::from_column_slice(&[vel_vert_x, vel_vert_y, -3.0, 0.0]),
                    ]
                }
-            ).collect::<Vec<_>>()
+            ).collect::<Vec<_>>(),
        ];
        let tangent_motions_std = tangent_motions_unif.iter().map(
            |motion| DMatrix::from_columns(
@ -879,11 +872,11 @@ mod tests {
                ).collect::<Vec<_>>()
            )
        ).collect::<Vec<_>>();
-        
+
        // confirm that the dimension of the tangent space is no greater than
        // expected
        assert_eq!(tangent.basis_std.len(), tangent_motions_unif.len());
-        
+
        // confirm that the tangent space contains all the motions we expect it
        // to. since we've already bounded the dimension of the tangent space,
        // this confirms that the tangent space is what we expect it to be
@ -895,7 +888,7 @@ mod tests {
            assert!((motion_std - motion_proj).norm_squared() < tol_sq);
        }
    }
-    
+
    fn translation(dis: Vector3<f64>) -> DMatrix<f64> {
        const ELEMENT_DIM: usize = 5;
        DMatrix::from_column_slice(ELEMENT_DIM, ELEMENT_DIM, &[
@ -903,10 +896,10 @@ mod tests {
                   0.0,        1.0,        0.0, 0.0,             dis[1],
                   0.0,        0.0,        1.0, 0.0,             dis[2],
            2.0*dis[0], 2.0*dis[1], 2.0*dis[2], 1.0, dis.norm_squared(),
-                   0.0,        0.0,        0.0, 0.0,                1.0
+                   0.0,        0.0,        0.0, 0.0,                1.0,
        ])
    }
-    
+
    // confirm that projection onto a configuration subspace is equivariant with
    // respect to Euclidean motions
    #[test]
@ -915,49 +908,49 @@ mod tests {
        const SCALED_TOL: f64 = 1.0e-12;
        let mut problem_orig = ConstraintProblem::from_guess(&[
            sphere(0.0, 0.0, 0.5, 1.0),
-            sphere(0.0, 0.0, -0.5, 1.0)
+            sphere(0.0, 0.0, -0.5, 1.0),
        ]);
        problem_orig.gram.push_sym(0, 0, 1.0);
        problem_orig.gram.push_sym(1, 1, 1.0);
        problem_orig.gram.push_sym(0, 1, 0.5);
-        let (config_orig, tangent_orig, success_orig, history_orig) = realize_gram(
+        let Realization { result: result_orig, history: history_orig } = realize_gram(
            &problem_orig, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
        );
+        let ConfigNeighborhood { config: config_orig, nbhd: tangent_orig } = result_orig.unwrap();
        assert_eq!(config_orig, problem_orig.guess);
-        assert_eq!(success_orig, true);
        assert_eq!(history_orig.scaled_loss.len(), 1);
-        
+
        // find another pair of spheres that meet at 120°. we'll think of this
        // solution as a transformed version of the original one
        let guess_tfm = {
            let a = 0.5 * FRAC_1_SQRT_2;
            DMatrix::from_columns(&[
                sphere(a, 0.0, 7.0 + a, 1.0),
-                sphere(-a, 0.0, 7.0 - a, 1.0)
+                sphere(-a, 0.0, 7.0 - a, 1.0),
            ])
        };
        let problem_tfm = ConstraintProblem {
            gram: problem_orig.gram,
+            frozen: problem_orig.frozen,
            guess: guess_tfm,
-            frozen: problem_orig.frozen
        };
-        let (config_tfm, tangent_tfm, success_tfm, history_tfm) = realize_gram(
+        let Realization { result: result_tfm, history: history_tfm } = realize_gram(
            &problem_tfm, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
        );
+        let ConfigNeighborhood { config: config_tfm, nbhd: tangent_tfm } = result_tfm.unwrap();
        assert_eq!(config_tfm, problem_tfm.guess);
-        assert_eq!(success_tfm, true);
        assert_eq!(history_tfm.scaled_loss.len(), 1);
-        
+
        // project a nudge to the tangent space of the solution variety at the
        // original solution
        let motion_orig = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
        let motion_orig_proj = tangent_orig.proj(&motion_orig.as_view(), 0);
-        
+
        // project the equivalent nudge to the tangent space of the solution
        // variety at the transformed solution
        let motion_tfm = DVector::from_column_slice(&[FRAC_1_SQRT_2, 0.0, FRAC_1_SQRT_2, 0.0]);
        let motion_tfm_proj = tangent_tfm.proj(&motion_tfm.as_view(), 0);
-        
+
        // take the transformation that sends the original solution to the
        // transformed solution and apply it to the motion that the original
        // solution makes in response to the nudge
@ -967,11 +960,11 @@ mod tests {
                      0.0, 1.0,            0.0, 0.0, 0.0,
            FRAC_1_SQRT_2, 0.0,  FRAC_1_SQRT_2, 0.0, 0.0,
                      0.0, 0.0,            0.0, 1.0, 0.0,
-                      0.0, 0.0,            0.0, 0.0, 1.0
+                      0.0, 0.0,            0.0, 0.0, 1.0,
        ]);
        let transl = translation(Vector3::new(0.0, 0.0, 7.0));
        let motion_proj_tfm = transl * rot * motion_orig_proj;
-        
+
        // confirm that the projection of the nudge is equivariant. we loosen
        // the comparison tolerance because the transformation seems to
        // introduce some numerical error
@ -979,4 +972,4 @@ mod tests {
        let tol_sq = ((problem_orig.guess.nrows() * problem_orig.guess.ncols()) as f64) * SCALED_TOL_TFM * SCALED_TOL_TFM;
        assert!((motion_proj_tfm - motion_tfm_proj).norm_squared() < tol_sq);
    }
-}
+}
--- a/app-proto/src/main.rs
+++ b/app-proto/src/main.rs
@ -1,8 +1,6 @@
-mod add_remove;
 mod assembly;
-mod display;
+mod components;
 mod engine;
-mod outline;
 mod specified;

 #[cfg(test)]
@ -11,25 +9,28 @@ mod tests;
 use std::{collections::BTreeSet, rc::Rc};
 use sycamore::prelude::*;

-use add_remove::AddRemove;
 use assembly::{Assembly, Element};
-use display::Display;
-use outline::Outline;
+use components::{
+    add_remove::AddRemove,
+    diagnostics::Diagnostics,
+    display::Display,
+    outline::Outline,
+};

 #[derive(Clone)]
 struct AppState {
    assembly: Assembly,
-    selection: Signal<BTreeSet<Rc<dyn Element>>>
+    selection: Signal<BTreeSet<Rc<dyn Element>>>,
 }

 impl AppState {
-    fn new() -> AppState {
-        AppState {
+    fn new() -> Self {
+        Self {
            assembly: Assembly::new(),
-            selection: create_signal(BTreeSet::default())
+            selection: create_signal(BTreeSet::default()),
        }
    }
-    
+
    // in single-selection mode, select the given element. in multiple-selection
    // mode, toggle whether the given element is selected
    fn select(&self, element: &Rc<dyn Element>, multi: bool) {
@ -52,16 +53,17 @@ fn main() {
    // set the console error panic hook
    #[cfg(feature = "console_error_panic_hook")]
    console_error_panic_hook::set_once();
-    
+
    sycamore::render(|| {
        provide_context(AppState::new());
-        
+
        view! {
-            div(id="sidebar") {
+            div(id = "sidebar") {
                AddRemove {}
                Outline {}
+                Diagnostics {}
            }
            Display {}
        }
    });
-}
+}
--- a/app-proto/src/specified.rs
+++ b/app-proto/src/specified.rs
@ -13,32 +13,43 @@ use std::num::ParseFloatError;
 #[readonly::make]
 pub struct SpecifiedValue {
    pub spec: String,
-    pub value: Option<f64>
+    pub value: Option<f64>,
 }

 impl SpecifiedValue {
-    pub fn from_empty_spec() -> SpecifiedValue {
-        SpecifiedValue { spec: String::new(), value: None }
+    pub fn from_empty_spec() -> Self {
+        Self { spec: String::new(), value: None }
    }
-    
+
    pub fn is_present(&self) -> bool {
        matches!(self.value, Some(_))
    }
 }

+// a `SpecifiedValue` can be constructed from a floating-point option, which is
+// given a canonical specification
+impl From<Option<f64>> for SpecifiedValue {
+    fn from(value: Option<f64>) -> Self {
+        match value {
+            Some(x) => SpecifiedValue{ spec: x.to_string(), value },
+            None => SpecifiedValue::from_empty_spec(),
+        }
+    }
+}
+
 // a `SpecifiedValue` can be constructed from a specification string, formatted
 // as described in the comment on the structure definition. the result is `Ok`
 // if the specification is properly formatted, and `Error` if not
 impl TryFrom<String> for SpecifiedValue {
    type Error = ParseFloatError;
-    
+
    fn try_from(spec: String) -> Result<Self, Self::Error> {
        if spec.is_empty() {
-            Ok(SpecifiedValue::from_empty_spec())
+            Ok(Self::from_empty_spec())
        } else {
            spec.parse::<f64>().map(
-                |value| SpecifiedValue { spec: spec, value: Some(value) }
+                |value| Self { spec, value: Some(value) }
            )
        }
    }
-}
+}
--- a/demo-summer-2025/dyna3/slides/images/by.svg
+++ b/demo-summer-2025/dyna3/slides/images/by.svg
@ -1,20 +0,0 @@
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-<!-- Generator: Adobe Illustrator 13.0.2, SVG Export Plug-In . SVG Version: 6.00 Build 14948)  -->
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">
-<svg version="1.0" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
-	 width="64px" height="64px" viewBox="5.5 -3.5 64 64" enable-background="new 5.5 -3.5 64 64" xml:space="preserve">
-<g>
-	<circle fill="#FFFFFF" cx="37.637" cy="28.806" r="28.276"/>
-	<g>
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-	</g>
-</g>
-</svg>
--- a/demo-summer-2025/dyna3/slides/images/cc.svg
+++ b/demo-summer-2025/dyna3/slides/images/cc.svg
@ -1,27 +0,0 @@
-<?xml version="1.0" encoding="utf-8"?>
-<!-- Generator: Adobe Illustrator 13.0.2, SVG Export Plug-In . SVG Version: 6.00 Build 14948)  -->
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">
-<svg version="1.0" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
-	 width="64px" height="64px" viewBox="5.5 -3.5 64 64" enable-background="new 5.5 -3.5 64 64" xml:space="preserve">
-<g>
-	<circle fill="#FFFFFF" cx="37.785" cy="28.501" r="28.836"/>
-	<path d="M37.441-3.5c8.951,0,16.572,3.125,22.857,9.372c3.008,3.009,5.295,6.448,6.857,10.314
-		c1.561,3.867,2.344,7.971,2.344,12.314c0,4.381-0.773,8.486-2.314,12.313c-1.543,3.828-3.82,7.21-6.828,10.143
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-</g>
-</svg>
--- a/demo-summer-2025/dyna3/slides/images/irisawa-sangaku.png
+++ b/demo-summer-2025/dyna3/slides/images/irisawa-sangaku.png
--- a/demo-summer-2025/dyna3/slides/images/sa.svg
+++ b/demo-summer-2025/dyna3/slides/images/sa.svg
@ -1,22 +0,0 @@
-<?xml version="1.0" encoding="utf-8"?>
-<!-- Generator: Adobe Illustrator 13.0.2, SVG Export Plug-In . SVG Version: 6.00 Build 14948)  -->
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN" "http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">
-<svg version="1.0" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
-	 width="64px" height="64px" viewBox="5.5 -3.5 64 64" enable-background="new 5.5 -3.5 64 64" xml:space="preserve">
-<g>
-	<circle fill="#FFFFFF" cx="36.944" cy="28.631" r="29.105"/>
-	<g>
-		<path d="M37.443-3.5c8.951,0,16.531,3.105,22.742,9.315C66.393,11.987,69.5,19.548,69.5,28.5c0,8.954-3.049,16.457-9.145,22.514
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-	</g>
-</g>
-</svg>
--- a/demo-summer-2025/dyna3/slides/index.html
+++ b/demo-summer-2025/dyna3/slides/index.html
@ -1,132 +0,0 @@
-<!doctype html>
-<html lang="en">
-  <head>
-    <meta charset="utf-8">
-    <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
-    
-    <title>dyna3 tech demo</title>
-    
-    <link rel="stylesheet" href="reveal/reveal.css">
-    <link rel="stylesheet" href="reveal/theme/night-bunny.css">
-    
-    <style>
-      .reveal .note {
-        font-size: smaller;
-        font-style: italic;
-      }
-      
-      .reveal .license {
-        font-size: 45%;
-      }
-      
-      .reveal .license img {
-        vertical-align: text-bottom;
-        max-width: 1em;
-        max-height: 1em;
-        margin: 0em 0em 0.19em 0.2em;
-      }
-    </style>
-  </head>
-  <body>
-    <div class="reveal">
-      <div class="slides">
-        <section>
-          <h1>dyna3</h1>
-          <p>A dynamical geometry exploration tool</p>
-          <!--
-            declaration created with Creative Commons license chooser, using
-            icons downloaded from the Creative Commons press kit
-            
-              https://creativecommons.org/chooser/
-              https://mirrors.creativecommons.org/presskit/icons/
-            
-          -->
-          <p class="license">Slides © 2025 by <a href="https://studioinfinity.org">Studio Infinity</a>, licensed under <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a><img src="images/cc.svg"/><img src="images/by.svg"/><img src="images/sa.svg"/>
-        </section>
-        <section>
-          <h3>Purpose</h3>
-          <h4>Tasks</h4>
-          <p><ul>
-            <li>Explore geometric objects</li>
-            <li>Solve geometry problems</li>
-          </ul></p>
-          <h4>Representations</h4>
-          <p><ul>
-            <li>Described in terms of constraints</li>
-            <li>Fundamentally three-dimensional</li>
-          </ul></p>
-        </section>
-        <section>
-          <h3>Status</h3>
-          <p><ul>
-            <li>We have an engine that works for at least some simple problems</li>
-            <li>We have enough of an <a href="../">interface</a> to start testing the engine interactively</li>
-          </ul></p>
-        </section>
-        <section>
-          <h2>Demos</h2>
-        </section>
-        <section>
-          <h3>How spiky is a tetrahedron?</h3>
-          <p><ul>
-            <li>Take a regular tetrahedron</li>
-            <li>Inscribe a sphere in it</li>
-            <li>Circumscribe a sphere around it</li>
-            <li>What’s the ratio of the spheres’ radii?</li>
-          </ul></p>
-        </section>
-        <section>
-          <h3>Irisawa’s hexlet</h3>
-          <section>
-            <p class="note">A <a href="https://www.nippon.com/en/japan-topics/c12801/">temple problem</a> by Irisawa Shintarō Hiroatsu (1822)</p>
-            <p><img src="images/irisawa-sangaku.png" style="height: 9em"/></p>
-            <p class="license">From “Sangaku of Soddy's hexlet in Samukawa Shrine” by <a href="https://commons.wikimedia.org/wiki/User:Shikishima_Ken-ichi">Shikishima Ken-ichi</a>, licensed under <a href="https://creativecommons.org/licenses/by-sa/3.0/">CC BY-SA 3.0</a></p>
-          </section>
-          <section>
-            <h4>Setup</h4>
-            <p><ul>
-              <li>Six solid spheres form a cyclic chain, each one touching the next</li>
-              <li>Two solid spheres, the “sun” and the “moon,” each touch all the chain spheres</li>
-              <li>A hollow outer sphere encloses and touches all the other spheres</li>
-            </ul></p>
-          </section>
-          <section>
-            <h4>Problem</h4>
-            <p>Fix the diameters of these spheres:</p>
-            <table>
-              <tr><td>Outer</td><td>30</td></tr>
-              <tr><td>Sun</td><td>10</td></tr>
-              <tr><td>Moon</td><td>6</td></tr>
-              <tr><td>One chain sphere</td><td>5</td></tr>
-            </table>
-            <p>What are the diameters of the other chain spheres?</p>
-          </section>
-        </section>
-        <section>
-          <h2>Plans</h2>
-          <p>For summer–fall 2025</p>
-        </section>
-        <section>
-          <h3>Narrow</h3>
-          <p><ul>
-            <li>Make the engine more robust</li>
-            <li>Expand our corpus of test problems</li>
-            <li>To support engine testing, improve the interface as needed</li>
-          </ul></p>
-        </section>
-        <section>
-          <h3>Broad</h3>
-          <p><ul>
-            <li>Explore the “island of usefulness” of our current engine approach
-            <li>Either find some of its boundaries or show that it covers a large swath of interesting problems</li>
-          </ul></p>
-        </section>
-      </div>
-    </div>
-    
-    <script src="reveal/reveal.js"></script>
-    <script>
-      Reveal.initialize({hash: true});
-    </script>
-  </body>
-</html>
--- a/demo-summer-2025/dyna3/slides/reveal/reset.css
+++ b/demo-summer-2025/dyna3/slides/reveal/reset.css
@ -1,30 +0,0 @@
-/* http://meyerweb.com/eric/tools/css/reset/
-   v4.0 | 20180602
-   License: none (public domain)
-*/
-
-html, body, div, span, applet, object, iframe,
-h1, h2, h3, h4, h5, h6, p, blockquote, pre,
-a, abbr, acronym, address, big, cite, code,
-del, dfn, em, img, ins, kbd, q, s, samp,
-small, strike, strong, sub, sup, tt, var,
-b, u, i, center,
-dl, dt, dd, ol, ul, li,
-fieldset, form, label, legend,
-table, caption, tbody, tfoot, thead, tr, th, td,
-article, aside, canvas, details, embed,
-figure, figcaption, footer, header, hgroup,
-main, menu, nav, output, ruby, section, summary,
-time, mark, audio, video {
-  margin: 0;
-  padding: 0;
-  border: 0;
-  font-size: 100%;
-  font: inherit;
-  vertical-align: baseline;
-}
-/* HTML5 display-role reset for older browsers */
-article, aside, details, figcaption, figure,
-footer, header, hgroup, main, menu, nav, section {
-  display: block;
-}
--- a/demo-summer-2025/dyna3/slides/reveal/reveal.css
+++ b/demo-summer-2025/dyna3/slides/reveal/reveal.css
--- a/demo-summer-2025/dyna3/slides/reveal/reveal.esm.js
+++ b/demo-summer-2025/dyna3/slides/reveal/reveal.esm.js
--- a/demo-summer-2025/dyna3/slides/reveal/reveal.esm.js.map
+++ b/demo-summer-2025/dyna3/slides/reveal/reveal.esm.js.map
--- a/demo-summer-2025/dyna3/slides/reveal/reveal.js
+++ b/demo-summer-2025/dyna3/slides/reveal/reveal.js
--- a/demo-summer-2025/dyna3/slides/reveal/reveal.js.map
+++ b/demo-summer-2025/dyna3/slides/reveal/reveal.js.map
--- a/demo-summer-2025/dyna3/slides/reveal/theme/beige.css
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/beige.css
@ -1,366 +0,0 @@
-/**
- * Beige theme for reveal.js.
- *
- * Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
- */
-@import url(./fonts/league-gothic/league-gothic.css);
-@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
-section.has-dark-background, section.has-dark-background h1, section.has-dark-background h2, section.has-dark-background h3, section.has-dark-background h4, section.has-dark-background h5, section.has-dark-background h6 {
-  color: #fff;
-}
-
-/*********************************************
- * GLOBAL STYLES
- *********************************************/
-:root {
-  --r-background-color: #f7f3de;
-  --r-main-font: Lato, sans-serif;
-  --r-main-font-size: 40px;
-  --r-main-color: #333;
-  --r-block-margin: 20px;
-  --r-heading-margin: 0 0 20px 0;
-  --r-heading-font: League Gothic, Impact, sans-serif;
-  --r-heading-color: #333;
-  --r-heading-line-height: 1.2;
-  --r-heading-letter-spacing: normal;
-  --r-heading-text-transform: uppercase;
-  --r-heading-text-shadow: none;
-  --r-heading-font-weight: normal;
-  --r-heading1-text-shadow: 0 1px 0 #ccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaa, 0 6px 1px rgba(0, 0, 0, 0.1), 0 0 5px rgba(0, 0, 0, 0.1), 0 1px 3px rgba(0, 0, 0, 0.3), 0 3px 5px rgba(0, 0, 0, 0.2), 0 5px 10px rgba(0, 0, 0, 0.25), 0 20px 20px rgba(0, 0, 0, 0.15);
-  --r-heading1-size: 3.77em;
-  --r-heading2-size: 2.11em;
-  --r-heading3-size: 1.55em;
-  --r-heading4-size: 1em;
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--- a/demo-summer-2025/dyna3/slides/reveal/theme/blood.css
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--- a/demo-summer-2025/dyna3/slides/reveal/theme/dracula.css
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/dracula.css
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--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/LICENSE
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/LICENSE
@ -1,2 +0,0 @@
-SIL Open Font License (OFL)
-http://scripts.sil.org/cms/scripts/page.php?site_id=nrsi&id=OFL
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/league-gothic.css
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/league-gothic.css
@ -1,10 +0,0 @@
-@font-face {
-    font-family: 'League Gothic';
-    src: url('./league-gothic.eot');
-    src: url('./league-gothic.eot?#iefix') format('embedded-opentype'),
-         url('./league-gothic.woff') format('woff'),
-         url('./league-gothic.ttf') format('truetype');
-
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-    font-style: normal;
-}
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/league-gothic.eot
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/league-gothic.eot
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/league-gothic.ttf
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/league-gothic.ttf
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/league-gothic.woff
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/league-gothic/league-gothic.woff
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/LICENSE
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/LICENSE
@ -1,45 +0,0 @@
-SIL Open Font License
-
-Copyright 2010, 2012 Adobe Systems Incorporated (http://www.adobe.com/), with Reserved Font Name ‘Source’. All Rights Reserved. Source is a trademark of Adobe Systems Incorporated in the United States and/or other countries.
-
-This Font Software is licensed under the SIL Open Font License, Version 1.1.
-This license is copied below, and is also available with a FAQ at: http://scripts.sil.org/OFL
-
-—————————————————————————————-
-SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
-—————————————————————————————-
-
-PREAMBLE
-The goals of the Open Font License (OFL) are to stimulate worldwide development of collaborative font projects, to support the font creation efforts of academic and linguistic communities, and to provide a free and open framework in which fonts may be shared and improved in partnership with others.
-
-The OFL allows the licensed fonts to be used, studied, modified and redistributed freely as long as they are not sold by themselves. The fonts, including any derivative works, can be bundled, embedded, redistributed and/or sold with any software provided that any reserved names are not used by derivative works. The fonts and derivatives, however, cannot be released under any other type of license. The requirement for fonts to remain under this license does not apply to any document created using the fonts or their derivatives.
-
-DEFINITIONS
-“Font Software” refers to the set of files released by the Copyright Holder(s) under this license and clearly marked as such. This may include source files, build scripts and documentation.
-
-“Reserved Font Name” refers to any names specified as such after the copyright statement(s).
-
-“Original Version” refers to the collection of Font Software components as distributed by the Copyright Holder(s).
-
-“Modified Version” refers to any derivative made by adding to, deleting, or substituting—in part or in whole—any of the components of the Original Version, by changing formats or by porting the Font Software to a new environment.
-
-“Author” refers to any designer, engineer, programmer, technical writer or other person who contributed to the Font Software.
-
-PERMISSION & CONDITIONS
-Permission is hereby granted, free of charge, to any person obtaining a copy of the Font Software, to use, study, copy, merge, embed, modify, redistribute, and sell modified and unmodified copies of the Font Software, subject to the following conditions:
-
-1) Neither the Font Software nor any of its individual components, in Original or Modified Versions, may be sold by itself.
-
-2) Original or Modified Versions of the Font Software may be bundled, redistributed and/or sold with any software, provided that each copy contains the above copyright notice and this license. These can be included either as stand-alone text files, human-readable headers or in the appropriate machine-readable metadata fields within text or binary files as long as those fields can be easily viewed by the user.
-
-3) No Modified Version of the Font Software may use the Reserved Font Name(s) unless explicit written permission is granted by the corresponding Copyright Holder. This restriction only applies to the primary font name as presented to the users.
-
-4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font Software shall not be used to promote, endorse or advertise any Modified Version, except to acknowledge the contribution(s) of the Copyright Holder(s) and the Author(s) or with their explicit written permission.
-
-5) The Font Software, modified or unmodified, in part or in whole, must be distributed entirely under this license, and must not be distributed under any other license. The requirement for fonts to remain under this license does not apply to any document created using the Font Software.
-
-TERMINATION
-This license becomes null and void if any of the above conditions are not met.
-
-DISCLAIMER
-THE FONT SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM OTHER DEALINGS IN THE FONT SOFTWARE.
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-italic.eot
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-italic.eot
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-italic.ttf
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-italic.ttf
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-italic.woff
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-italic.woff
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-regular.eot
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-regular.eot
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-regular.ttf
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-regular.ttf
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-regular.woff
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-regular.woff
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibold.eot
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibold.eot
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibold.ttf
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibold.ttf
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibold.woff
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibold.woff
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibolditalic.eot
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibolditalic.eot
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibolditalic.ttf
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibolditalic.ttf
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibolditalic.woff
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro-semibolditalic.woff
--- a/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro.css
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/fonts/source-sans-pro/source-sans-pro.css
@ -1,39 +0,0 @@
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--- a/demo-summer-2025/dyna3/slides/reveal/theme/league.css
+++ b/demo-summer-2025/dyna3/slides/reveal/theme/league.css
@ -1,368 +0,0 @@
-/**
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--- a/demo-summer-2025/.gitignore
+++ b/demo-summer-2025/.gitignore
--- a/notes/inversive.md
+++ b/notes/inversive.md
@ -33,7 +33,7 @@ The unification of spheres/planes is indeed attractive for a project like Dyna3.
 Discussed coordinates with Alex Kontorovich. He was suggesting "inversive coordinates" -- for a sphere, that's 1/coradius, 1/radius, center/radius (where coradius is radius of sphere inverted in the unit sphere.) The advantage is tangent to and perpendicular to are linear in these coordinates (in the sense that if one is known, the condition of being tangent to or perpendicular to that one are linear). Planes have 1/radius = 0, and in fact, you can take the coordinates to be (2s, 0, x, y, z) where s is the distance to the origin and x,y,z are the normal direction. (Note the normal direction is only determined up to a scalar multiple. So could always scale so that the first non-zero coordinate is 1, or if you like only allow x, y to vary and let z be determined as sqrt(1-x^2^-y^2^). ) Points can be given by (r^2,1,x,y,z) where x,y,z are the coordinates and r is the distance to the origin. Quadratic form that tells you if something is a sphere/plane, or in the boundary, or up in the hyperbolic plane above. There are some details, but not quite explicit for modeling R^3, at http://sites.math.rutgers.edu/~alexk/files/LetterToDuke.pdf -- all this emphasize need to be agnostic with respect to geometric model so that we can experiment. Not really sure exactly how this relates or not to conformal geometric algebra, and whether it can be combined with geometric algebra. As formulated, there are clear-ish reps for planes/spheres and for points, but not as clear for lines. Have to see how to compute distance and/or specify a given distance. To combine inversive coordinates and geometric algebra, maybe think dually; there should be a lift from a normal vector and distance from origin to the five-vector; bivectors would rep circles/lines; trivectors would rep point pairs/points. What is the signature of this algebra, i.e. how many coordinates square to +1, -1, or 0? But it doesn't seem worth it for three dimensions, because there is a natural representation of points, as follows:

 The signature of Q will be (1,4), and in fact Q(I1,I2) = 1/2(ab+ba) - E1\dot E2, where a is the "first" or "coradius" coordinate, "b" is the "second" or "radius" coordinate, and E is the Euclidean part (x,y,z). Then the inversive coordinates of a sphere with center (x,y,z) and radius r will be I = (1/\hat{r},1/r,x/r,y/r,z/r) where \hat{r} = r/(|E|^2 -r^2). These coordinates satisfy Q(I,I) = -1. For this to make sense, of course r > 0, but we get planes by letting the radius of a tangent sphere to the plane go to infinity, and we get I = (2s, 0, x0, y0, z0) where (x0,y0,z0) is the unit normal to the plane and s is the perpendicular distance from the plane to the origin. Still Q(I,I) = -1.
-Since r>0, we can't represent individual points this way. Instead we will use some coordinates J for which Q(J,J) = 0. In particular, if you take for the Euclidean point E = (u,v,w) the coordinates J = (`|E|`^2,1,u,v,w) then Q(J,J) = 0 and moreover it comes out that Q(I,J) = 0 
+Since r>0, we can't represent individual points this way. Instead we will use some coordinates J for which Q(J,J) = 0. In particular, if you take for the Euclidean point E = (u,v,w) the coordinates J = (`|E|`^2,1,u,v,w) then Q(J,J) = 0 and moreover it comes out that Q(I,J) = 0
 whenever E lies on the sphere or plane described by some I with Q(I,I) = -1.
 The condition that two spheres I1 and I2 are tangent seems to be that Q(I1,I2) = 1. So given a fixed sphere, the condition that another sphere be tangent to it is linear in the coordinates of that other sphere.
 This system does seem promising for encoding points, spheres, and planes, and doing basic computations with them. I guess I would just encode a circle as the intersection of the concentric sphere and the containing plane, and a line as either a pair of points or a pair of planes (modulo some equivalence relation, since I can't see any canonical choice of either two planes or two points). Or actually as described below, there is a more canonical choice.
@ -62,4 +62,4 @@ In the engine's coordinate conventions, a sphere with radius $r > 0$ centered on
 $$I'_s = \left(\frac{P_x}{r}, \frac{P_y}{r}, \frac{P_z}{r}, \frac1{2r}, \frac{\|P\|^2 - r^2}{2r}\right),$$
 which has the normalization $Q'(I'_s, I'_s) = 1$. The point $P$ is represented by the vector
 $$I'_P = \left(P_x, P_y, P_z, \frac{1}{2}, \frac{\|P\|^2}{2}\right).$$
-In the `engine` module, these formulas are encoded in the `sphere` and `point` functions.
+In the `engine` module, these formulas are encoded in the `sphere` and `point` functions.
--- a/notes/theory.md
+++ b/notes/theory.md
@ -24,7 +24,7 @@ His final mathematical advice was reasonably encouraging, however:
 "But still I would consider it all more or less doable. One should very precisely think about a doable scope.
 I think three things are essential for the math no matter what you exactly plan.

-1. Think projectively, 
+1. Think projectively.
   Use Projective Geometry, Homogeneous Coordinates (or to a certain extent Quaternions, and Clifford Algebras, which are more or less an elegant way to merge Complex numbers with projective concepts.)
 2. Consider ambient complex spaces.
   The true nature of the objects can only be understood if embedded into a complex ambient space.
@ -37,10 +37,8 @@ I think three things are essential for the math no matter what you exactly plan.

 It would be nice to see how Jürgen handled some of these issues in a 2D system that he designed. Unfortunately, Cinderella was and remains closed-source; it was distributed for profit for some stretch of time. However, (a part of?) it was reimplemented in JavaScript as CindyJS, which is open source. I took a relatively quick look at that source code at one point, and these were my observations:

-CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically.  There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.) 
+CindyJS uses very concrete basic objects: 2D points are represented via projective geometry as a list of three floating-point numbers, and everything is done numerically.  There are no symbolic representations or exact algebraic numbers. (Not sure how a point on a circle or line is handled, that would take further investigation.)

 Lines are given by explicit coordinates as well (not sure of the internal details/exact coordinatization, or of how a "LineThrough" is represented).

 Was unclear to me how the complex parametrization for preserving continuity was handled in the code, even though Jürgen harps on complex ambient spaces; where are the complex numbers? Perhaps that part of Cinderella was never re-implemented?
-
-
--- a/src/index.html
+++ b/src/index.html
@ -7,5 +7,3 @@
  <body><script type="module" src="dyna3.js"></script>
  </body>
 </html>
-
-    
--- a/tools/package-demo
+++ b/tools/package-demo
@ -1,18 +0,0 @@
-#!/bin/bash
-
-# set paths. this technique for getting the script location comes from
-# `mklement0` on Stack Overflow
-#
-#   https://stackoverflow.com/a/24114056
-#
-tools=$(dirname -- "$(readlink -f -- "$BASH_SOURCE")")
-dist_src="$tools/../app-proto/dist"
-dist_dest="$tools/../demo-summer-2025/dyna3"
-
-# remove the old hash-named files
-[ -e "$dist_dest"/dyna3-*.js ] && rm "$dist_dest"/dyna3-*.js
-[ -e "$dist_dest"/dyna3-*.wasm ] && rm "$dist_dest"/dyna3-*.wasm
-[ -e "$dist_dest"/main-*.css ] && rm "$dist_dest"/main-*.css
-
-# copy the distribution
-cp -r "$dist_src/." "$dist_dest"
--- a/tools/package-for-deployment.sh
+++ b/tools/package-for-deployment.sh
@ -0,0 +1,16 @@
+# set paths. this technique for getting the script location comes from
+# `mklement0` on Stack Overflow
+#
+#   https://stackoverflow.com/a/24114056
+#
+TOOLS=$(dirname -- $0)
+SRC="$TOOLS/../app-proto/dist"
+DEST="$TOOLS/../deploy/dyna3"
+
+# remove the old hash-named files
+[ -e "$DEST"/dyna3-*.js ] && rm "$DEST"/dyna3-*.js
+[ -e "$DEST"/dyna3-*.wasm ] && rm "$DEST"/dyna3-*.wasm
+[ -e "$DEST"/main-*.css ] && rm "$DEST"/main-*.css
+
+# copy the distribution
+cp -r "$SRC/." "$DEST"
--- a/tools/run-examples.sh
+++ b/tools/run-examples.sh
@ -0,0 +1,20 @@
+# run all Cargo examples, as described here:
+#
+#   Karol Kuczmarski. "Add examples to your Rust libraries"
+#   http://xion.io/post/code/rust-examples.html
+#
+# you should invoke this script by calling `sh` or another interpreter, rather
+# than calling `souce`, to ensure that the script can find the manifest file for
+# the application prototype
+
+# find the manifest file for the application prototype
+MANIFEST="$(dirname -- $0)/../app-proto/Cargo.toml"
+
+# set up the command that runs each example
+RUN_EXAMPLE="cargo run --manifest-path $MANIFEST --example"
+
+# run the examples
+$RUN_EXAMPLE irisawa-hexlet; echo
+$RUN_EXAMPLE three-spheres; echo
+$RUN_EXAMPLE point-on-sphere; echo
+$RUN_EXAMPLE kaleidocycle
Author	SHA1	Message	Date
Glen Whitney	6c3a48fb52	chore: Remove trailing whitespace (#129 ) Switch to the convention of using no trailing whitespace, even on blank lines. Also remove some unintended trailing whitespace on non-blank lines and fix a few typos. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#129 Reviewed-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-authored-by: Glen Whitney <glen@studioinfinity.org> Co-committed-by: Glen Whitney <glen@studioinfinity.org>	2025-11-11 00:47:40 +00:00
Glen Whitney	2c8c09d20d	feat: Point coordinate regulators (#118 ) Implement regulators for the Euclidean coordinates of `Point` entities, automatically creating all three of them for each added point entity. When such a regulator is set, it freezes the corresponding representation coordinate to the set point. In addition, if all three coordinates of a given `Point` are set, the coradius coordinate (which holds the norm of the point) is frozen as well. Note that a `PointCoordinateRegulator` must be created with a `Point` as the subject. This commit modifies `HalfCurvatureRegulator` analogously, so that it can only be created with a `Sphere`. Co-authored-by: Glen Whitney <glen@studioinfinity.org> Co-committed-by: Glen Whitney <glen@studioinfinity.org>	2025-10-13 22:52:02 +00:00
Vectornaut	978f70aac7	Rewind through the descent history (#114 ) You can now rewind through the descent history of the last realization using the Step control that's been added to the diagnostics panel. The starting value of the Step control depends on the realization status. After a successful realization, we show the realized state (the last step). After an unsuccessful realization, we show the initial guess (step zero). Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#114 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-09-18 23:31:17 +00:00
Vectornaut	af18a8e7d1	Write a deployment packaging script (#113 ) Adds a packaging script to help automate deployment. Documents the deployment process in `README.md`. Also, moves `run-examples.sh` into the tools folder that we created for the packaging script. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#113 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-08-11 03:33:19 +00:00
Vectornaut	a4565281d5	Refactor: rename loaders and adopt 'Self' type convention (#111 ) Resolves #109. Resolves #110. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#111 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-08-07 23:24:07 +00:00
Vectornaut	ef1a579ac0	refactor: Code formatting (#108 ) Primarily, switch to using trailing commas. Also uniformizes commas with respect to switch branches, makes function call layout more consistent, line breaking more consistent, alphabetizes imports, uses the field init shorthand when possible, etc. Resolves #99. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#108 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-08-04 23:34:33 +00:00
Vectornaut	2eba80fb69	Simplify the realization triggering system (#105 ) Simplifies the system that reactively triggers realizations, at the cost of removing the preconditioning step described in issue #101 and doing unnecessary realizations after certain kinds of updates. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#105 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-07-31 22:21:32 +00:00
Vectornaut	0801200210	Add more test assemblies (#103 ) This PR helps probe the capabilities of the engine. Also adjusts the realization triggering system to reduce redundant realizations as we set an assembly's regulators during loading. Specificially, consolidates all calls to `realize()` into a single effect, which is triggered by the `needs_realization` signal. Also introduces a `keep_realized` signal and use it to pause realization while loading assemblies, but this signal is planned for removal as ultimately we do not want a separate "mode" of interpreting commands during loading, for maximal reproducibility of results (and simplicity of system). Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#103 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-07-22 22:01:37 +00:00
Vectornaut	5864017e6f	feat: Engine diagnostics (#92 ) Adds a `Diagnostics` component that shows the following diagnostics from the last realization: - Confirmation of success or a short description of what failed. - The value of the loss function at each step. - The spectrum of the Hessian at each step. The loss and spectrum plots are shown on switchable panels. Also includes some refactoring/renaming of existing code. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#92 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-07-21 04:18:49 +00:00
Vectornaut	4cb3262555	chore: Update Sycamore to 0.9.1 (#91 ) Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#91 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-06-26 22:11:02 +00:00