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>
Refactor: rename loaders and adopt 'Self' type convention (#111 )
2025-08-11 03:33:19 +00:00 · 2025-08-07 23:24:07 +00:00 · 2025-08-04 23:34:33 +00:00 · 2025-07-31 22:21:32 +00:00 · 2025-07-22 22:01:37 +00:00 · 2025-07-21 04:18:49 +00:00
31 changed files with 2900 additions and 1037 deletions
--- a/.forgejo/workflows/continuous-integration.yaml
+++ b/.forgejo/workflows/continuous-integration.yaml
@ -11,7 +11,7 @@ jobs:
  test:
    runs-on: docker
    container:
-      image: cimg/rust:1.85-node
+      image: cimg/rust:1.86-node
    defaults:
      run:
        # set the default working directory for each `run` step, relative to the
--- a/README.md
+++ b/README.md
@ -25,32 +25,37 @@ 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)
+   - 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
+   - 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
 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
+   - 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
+   - On POSIX systems, the search path is stored in the `PATH` environment variable
 ### 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*
+   - 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*
+   - 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.
+   - 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*
+   - 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
+1. Use `sh` to run the script `tools/run-examples.sh`
-2. Call `./run-examples`
+   - The script is location-independent, so you can do this from anywhere in the dyna3 repository
-   * *For each example problem, the engine will print the value of the loss function at each optimization step*
+   - The call from the top level of the repository is:
-   * *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*
+     
     ```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
     ```julia
     include("irisawa-hexlet.jl")
@ -59,9 +64,24 @@ The latest prototype is in the folder `app-proto`. It includes both a user inter
     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`
 ### 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
@ -1,6 +1,6 @@
 # This file is automatically @generated by Cargo.
 # It is not intended for manual editing.
-version = 3
+version = 4
 [[package]]
 name = "ahash"
@ -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"
@ -78,10 +137,122 @@ 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",
 "itertools",
@ -89,8 +260,6 @@ dependencies = [
 "lazy_static",
 "nalgebra",
 "readonly",
 "rustc-hash",
 "slab",
 "sycamore",
 "wasm-bindgen-test",
 "web-sys",
@ -108,6 +277,22 @@ 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"
@ -119,6 +304,28 @@ 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"
@ -129,6 +336,12 @@ 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"
@ -138,6 +351,47 @@ 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"
@ -145,7 +399,8 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "68b900aa2f7301e21c36462b170ee99994de34dff39a4a6a528e80e7376d07e5"
 dependencies = [
 "equivalent",
- "hashbrown",
+ "hashbrown 0.14.5",
 "serde",
 ]
 [[package]]
@ -157,6 +412,12 @@ 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"
@ -194,6 +455,12 @@ 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"
@ -250,6 +517,12 @@ 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"
@ -259,6 +532,21 @@ 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"
@ -291,6 +579,57 @@ 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"
@ -366,10 +705,10 @@ dependencies = [
 ]
 [[package]]
-name = "rustc-hash"
+name = "ryu"
-version = "2.0.0"
+version = "1.0.20"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "583034fd73374156e66797ed8e5b0d5690409c9226b22d87cb7f19821c05d152"
+checksum = "28d3b2b1366ec20994f1fd18c3c594f05c5dd4bc44d8bb0c1c632c8d6829481f"
 [[package]]
 name = "safe_arch"
@ -395,6 +734,90 @@ 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"
@ -414,15 +837,6 @@ dependencies = [
 "wide",
 ]
 [[package]]
 name = "slab"
 version = "0.4.9"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "8f92a496fb766b417c996b9c5e57daf2f7ad3b0bebe1ccfca4856390e3d3bb67"
 dependencies = [
 "autocfg",
 ]
 [[package]]
 name = "slotmap"
 version = "1.0.7"
@ -439,13 +853,19 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "3c5e1a9a646d36c3599cd173a41282daf47c44583ad367b8e6837255952e5c67"
 [[package]]
-name = "sycamore"
+name = "strsim"
-version = "0.9.0-beta.3"
+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",
+ "hashbrown 0.14.5",
- "indexmap",
+ "indexmap 2.5.0",
 "paste",
 "sycamore-core",
 "sycamore-macro",
@ -457,20 +877,20 @@ 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",
@ -482,20 +902,21 @@ 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",
@ -504,9 +925,9 @@ 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",
@ -522,21 +943,78 @@ 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"
@ -693,6 +1171,65 @@ 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
@ -3,6 +3,7 @@ name = "dyna3"
 version = "0.1.0"
 authors = ["Aaron Fenyes", "Glen Whitney"]
 edition = "2021"
 rust-version = "1.86"
 [features]
 default = ["console_error_panic_hook"]
@ -14,9 +15,10 @@ js-sys = "0.3.70"
 lazy_static = "1.5.0"
 nalgebra = "0.33.0"
 readonly = "0.2.12"
-rustc-hash = "2.0.0"
+sycamore = "0.9.1"
-slab = "0.4.9"
+
-sycamore = "0.9.0-beta.3"
+# 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
@ -47,6 +49,13 @@ features = [
 dyna3 = { path = ".", default-features = false, features = ["dev"] }
 wasm-bindgen-test = "0.3.34"
 # turn off spurious warnings about the custom config that Sycamore uses
 #
 #   https://sycamore.dev/book/troubleshooting#unexpected-cfg-condition-name--sycamore-force-ssr
 #
 [lints.rust]
 unexpected_cfgs = { level = "warn", check-cfg = ["cfg(sycamore_force_ssr)"] }
 [profile.release]
 opt-level = "s" # optimize for small code size
 debug = true # include debug symbols
--- a/app-proto/Trunk.toml
+++ b/app-proto/Trunk.toml
@ -0,0 +1,2 @@
 [build]
 public_url = "./"
--- 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);
+    let realization = realize_irisawa_hexlet(SCALED_TOL);
-    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
+    print::title("Irisawa hexlet");
-    if success {
+    print::realization_diagnostics(&realization);
-        println!("Target accuracy achieved!");
+    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
-    } else {
+        // print the diameters of the chain spheres
        println!("Failed to reach target accuracy");
    }
    println!("Steps: {}", history.scaled_loss.len() - 1);
    println!("Loss: {}", history.scaled_loss.last().unwrap());
    if success {
        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─────┼────────────────────────────────");
+    print::loss_history(&realization.history);
    for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
        println!("{:<4} │ {}", step, scaled_loss);
    }
 }
--- 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);
+    let realization = realize_kaleidocycle(SCALED_TOL);
-    print!("Completed Gram matrix:{}", config.tr_mul(&*Q) * &config);
+    print::title("Kaleidocycle");
-    print!("Configuration:{}", config);
+    print::realization_diagnostics(&realization);
-    if success {
+    if let Ok(ConfigNeighborhood { config, nbhd: tangent }) = realization.result {
-        println!("Target accuracy achieved!");
+        // print the completed Gram matrix and the realized configuration
-    } else {
+        print::gram_matrix(&config);
-        println!("Failed to reach target accuracy");
+        print::config(&config);
    }
    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
+        // 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)
+                tangent.proj(&down.as_view(), n+1),
            ]
        ).sum();
        let normalization = 5.0 / twist_motion[(2, 0)];
-    print!("Twist motion:{}", normalization * twist_motion);
+        println!("\nTwist motion:{}", (normalization * twist_motion).to_string().trim_end());
    }
 }
--- 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 realization = realize_gram(
    let (config, _, success, history) = realize_gram(
        &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
    );
-    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
+    print::title("Point on a sphere");
-    print!("Configuration:{}", config);
+    print::realization_diagnostics(&realization);
-    if success {
+    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
-        println!("Target accuracy achieved!");
+        print::gram_matrix(&config);
-    } else {
+        print::config(&config);
        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::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 realization = realize_gram(
    let (config, _, success, history) = realize_gram(
        &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
    );
-    print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
+    print::title("Three spheres");
-    if success {
+    print::realization_diagnostics(&realization);
-        println!("Target accuracy achieved!");
+    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
-    } else {
+        print::gram_matrix(&config);
        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::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 {
@ -90,6 +101,10 @@ summary > div, .regulator {
  padding-right: 8px;
 }
 .element > input {
  margin-left: 8px;
 }
 .element-switch {
  width: 18px;
  padding-left: 2px;
@ -134,6 +149,7 @@ details[open]:has(li) .element-switch::after {
 }
 .regulator-input {
  margin-right: 4px;
  color: inherit;
  background-color: inherit;
  border: 1px solid var(--border);
@ -155,22 +171,56 @@ 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;
 }
 #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: '⚠';
 }
 .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;
@ -179,7 +229,7 @@ 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
@ -1,257 +0,0 @@
 use std::{f64::consts::FRAC_1_SQRT_2, rc::Rc};
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue};
 use crate::{
    engine,
    AppState,
    assembly::{Assembly, InversiveDistanceRegulator, Point, Sphere}
 };
 /* 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)
        )
    );
 }
 fn load_pointed_assemb(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)
                )
            );
        }
    }
 }
 #[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),
                _ => ()
            };
        });
    });
    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.assembly))
                    );
                    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="empty") { "Empty" }
            }
        }
    }
 }
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
--- 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 +1,256 @@
 use charming::{
    Chart,
    WasmRenderer,
    component::{Axis, DataZoom, Grid},
    element::{AxisType, Symbol},
    series::{Line, Scatter},
 };
 use sycamore::prelude::*;
 use crate::AppState;
 #[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(),
                    }
                ))
            }
        }
    }
 }
 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" }
                }
            }
            DiagnosticsPanel(name = "loss") { LossHistory {} }
            DiagnosticsPanel(name = "spectrum") { SpectrumHistory {} }
        }
    }
 }
--- a/app-proto/src/components/display.rs
+++ b/app-proto/src/components/display.rs
@ -1,5 +1,6 @@
 use core::array;
 use nalgebra::{DMatrix, DVector, Rotation3, Vector3};
 use std::rc::Rc;
 use sycamore::{prelude::*, motion::create_raf};
 use web_sys::{
    console,
@ -11,28 +12,40 @@ use web_sys::{
    WebGlProgram,
    WebGlShader,
    WebGlUniformLocation,
-    wasm_bindgen::{JsCast, JsValue}
+    wasm_bindgen::{JsCast, JsValue},
 };
 use crate::{
    AppState,
-    assembly::{ElementKey, ElementColor, ElementMotion, Point, Sphere}
+    assembly::{Element, ElementColor, ElementMotion, Point, Sphere},
 };
 // --- color ---
 const COLOR_SIZE: usize = 3;
 type ColorWithOpacity = [f32; COLOR_SIZE + 1];
 fn combine_channels(color: ElementColor, opacity: f32) -> ColorWithOpacity {
    let mut color_with_opacity = [0.0; COLOR_SIZE + 1];
    color_with_opacity[..COLOR_SIZE].copy_from_slice(&color);
    color_with_opacity[COLOR_SIZE] = opacity;
    color_with_opacity
 }
 // --- scene data ---
 struct SceneSpheres {
    representations: Vec<DVector<f64>>,
-    colors: Vec<ElementColor>,
+    colors_with_opacity: Vec<ColorWithOpacity>,
-    highlights: Vec<f32>
+    highlights: Vec<f32>,
 }
 impl SceneSpheres {
-    fn new() -> SceneSpheres{
+    fn new() -> Self {
-        SceneSpheres {
+        Self {
            representations: Vec::new(),
-            colors: Vec::new(),
+            colors_with_opacity: Vec::new(),
-            highlights: Vec::new()
+            highlights: Vec::new(),
        }
    }
@ -40,33 +53,39 @@ impl SceneSpheres {
        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, highlight: f32) {
+    fn push(
        &mut self, representation: DVector<f64>,
        color: ElementColor, opacity: f32, highlight: f32,
    ) {
        self.representations.push(representation);
-        self.colors.push(color);
+        self.colors_with_opacity.push(combine_channels(color, opacity));
        self.highlights.push(highlight);
    }
 }
 struct ScenePoints {
    representations: Vec<DVector<f64>>,
-    colors: Vec<ElementColor>,
+    colors_with_opacity: Vec<ColorWithOpacity>,
    highlights: Vec<f32>,
-    selections: Vec<f32>
+    selections: Vec<f32>,
 }
 impl ScenePoints {
-    fn new() -> ScenePoints {
+    fn new() -> Self {
-        ScenePoints {
+        Self {
            representations: Vec::new(),
-            colors: 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, 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.push(color);
+        self.colors_with_opacity.push(combine_channels(color, opacity));
        self.highlights.push(highlight);
        self.selections.push(if selected { 1.0 } else { 0.0 });
    }
@ -74,14 +93,14 @@ impl ScenePoints {
 pub struct Scene {
    spheres: SceneSpheres,
-    points: ScenePoints
+    points: ScenePoints,
 }
 impl Scene {
-    fn new() -> Scene {
+    fn new() -> Self {
-        Scene {
+        Self {
            spheres: SceneSpheres::new(),
-            points: ScenePoints::new()
+            points: ScenePoints::new(),
        }
    }
 }
@ -92,21 +111,36 @@ pub trait DisplayItem {
    // 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 {
    fn show(&self, scene: &mut Scene, selected: bool) {
-        const HIGHLIGHT: f32 = 0.2; /* SCAFFOLDING */
+        /* SCAFFOLDING */
        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, 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;
@ -147,15 +181,24 @@ impl DisplayItem for Sphere {
 impl DisplayItem for Point {
    fn show(&self, scene: &mut Scene, selected: bool) {
-        const HIGHLIGHT: f32 = 0.5; /* SCAFFOLDING */
+        /* 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, highlight, selected);
+        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`
@ -198,7 +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(
@ -238,12 +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())
    })
@ -254,7 +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(
@ -270,7 +313,7 @@ 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();
@ -297,7 +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);
@ -319,9 +362,9 @@ fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
        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,
    )
 }
@ -362,8 +405,9 @@ pub fn Display() -> View {
    let scene_changed = create_signal(true);
    create_effect(move || {
        state.assembly.elements.with(|elts| {
-            for (_, elt) in elts {
+            for elt in elts {
                elt.representation().track();
                elt.ghost().track();
            }
        });
        state.selection.track();
@ -394,7 +438,6 @@ pub fn Display() -> View {
        const SHRINKING_SPEED: f64 = 0.15; // in length units per second
        // display parameters
        const OPACITY: f32 = 0.5; /* SCAFFOLDING */
        const LAYER_THRESHOLD: i32 = 0; /* DEBUG */
        const DEBUG_MODE: i32 = 0; /* DEBUG */
@ -421,14 +464,14 @@ pub fn Display() -> View {
        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 */
@ -445,7 +488,7 @@ 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
@ -468,7 +511,6 @@ pub fn Display() -> View {
        );
        let resolution_loc = ctx.get_uniform_location(&sphere_program, "resolution");
        let shortdim_loc = ctx.get_uniform_location(&sphere_program, "shortdim");
        let opacity_loc = ctx.get_uniform_location(&sphere_program, "opacity");
        let layer_threshold_loc = ctx.get_uniform_location(&sphere_program, "layer_threshold");
        let debug_mode_loc = ctx.get_uniform_location(&sphere_program, "debug_mode");
@ -482,7 +524,7 @@ 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);
@ -548,7 +590,7 @@ pub fn Display() -> View {
            // manipulate the assembly
            if state.selection.with(|sel| sel.len() == 1) {
                let sel = state.selection.with(
-                    |sel| *sel.into_iter().next().unwrap()
+                    |sel| sel.into_iter().next().unwrap().clone()
                );
                let translate_x = translate_pos_x_val - translate_neg_x_val;
                let translate_y = translate_pos_y_val - translate_neg_y_val;
@ -574,8 +616,8 @@ pub fn Display() -> View {
                    assembly_for_raf.deform(
                        vec![
                            ElementMotion {
-                                key: sel,
+                                element: sel,
-                                velocity: elt_motion.as_view()
+                                velocity: elt_motion.as_view(),
                            }
                        ]
                    );
@ -608,15 +650,15 @@ 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 (key, elt) in elts {
+                    |elts| for elt in elts {
-                        let selected = state.selection.with(|sel| sel.contains(&key));
+                        let selected = state.selection.with(|sel| sel.contains(elt));
                        elt.show(&mut scene, selected);
                    }
                );
@ -647,24 +689,23 @@ pub fn Display() -> View {
                    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.uniform3fv_with_f32_array(
+                    ctx.uniform4fv_with_f32_array(
                        sphere_color_locs[n].as_ref(),
-                        &scene.spheres.colors[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.uniform1f(opacity_loc.as_ref(), OPACITY);
                ctx.uniform1i(layer_threshold_loc.as_ref(), LAYER_THRESHOLD);
                ctx.uniform1i(debug_mode_loc.as_ref(), DEBUG_MODE);
@ -702,7 +743,7 @@ pub fn Display() -> View {
                    // bind them to the corresponding attributes in the vertex
                    // shader
                    bind_new_buffer_to_attribute(&ctx, point_position_attr, SPACE_DIM as i32, point_positions.as_slice());
-                    bind_new_buffer_to_attribute(&ctx, point_color_attr, COLOR_SIZE as i32, scene.points.colors.concat().as_slice());
+                    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());
@ -753,7 +794,7 @@ 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);
@ -773,7 +814,7 @@ 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();
@ -785,11 +826,12 @@ pub fn Display() -> View {
        // switch back to integer-valued parameters when that becomes possible
        // again
        canvas(
-            ref=display,
+            ref = display,
-            width="600",
+            id = "display",
-            height="600",
+            width = "600",
-            tabindex="0",
+            height = "600",
-            on:keydown=move |event: KeyboardEvent| {
+            tabindex = "0",
            on:keydown = move |event: KeyboardEvent| {
                if event.key() == "Shift" {
                    // swap navigation inputs
                    roll_cw.set(yaw_right.get());
@ -815,7 +857,7 @@ 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());
@ -837,7 +879,7 @@ 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);
@ -845,31 +887,35 @@ 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()));
-                let mut clicked: Option<(ElementKey, f64)> = None;
+                let mut clicked: Option<(Rc<dyn Element>, f64)> = None;
-                for (key, elt) in state.assembly.elements.get_clone_untracked() {
+                let tangible_elts = state.assembly.elements
                    .get_clone_untracked()
                    .into_iter()
                    .filter(|elt| !elt.ghost().get());
                for elt in tangible_elts {
                    match assembly_to_world.with(|asm_to_world| elt.cast(dir, asm_to_world, pixel_size)) {
                        Some(depth) => match clicked {
                            Some((_, best_depth)) => {
                                if depth < best_depth {
-                                    clicked = Some((key, depth))
+                                    clicked = Some((elt, depth))
                                }
                            },
-                            None => clicked = Some((key, depth))
+                            None => clicked = Some((elt, depth)),
-                        }
+                        },
-                        None => ()
+                        None => (),
                    };
                }
                // if we clicked something, select it
                match clicked {
-                    Some((key, _)) => state.select(key, event.shift_key()),
+                    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
@ -1,22 +1,15 @@
 use itertools::Itertools;
 use std::rc::Rc;
 use sycamore::prelude::*;
-use web_sys::{
+use web_sys::{KeyboardEvent, MouseEvent, wasm_bindgen::JsCast};
    KeyboardEvent,
    MouseEvent,
    wasm_bindgen::JsCast
 };
 use crate::{
    AppState,
    assembly::{
        Element,
        ElementKey,
        ElementRc,
        HalfCurvatureRegulator,
        InversiveDistanceRegulator,
        Regulator,
        RegulatorKey
    },
    specified::SpecifiedValue
 };
@ -52,8 +45,8 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
    view! {
        input(
-            r#type="text",
+            r#type = "text",
-            class=move || {
+            class = move || {
                if valid.get() {
                    set_point.with(|set_pt| {
                        if set_pt.is_present() {
@ -66,87 +59,76 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
                    "regulator-input invalid"
                }
            },
-            placeholder=measurement.with(|result| result.to_string()),
+            placeholder = measurement.with(|result| result.to_string()),
-            bind:value=value,
+            bind:value = value,
-            on:change=move |_| {
+            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(),
-                        _ => ()
+                        _ => (),
                    }
                    }
                }
            },
        )
    }
 }
 pub trait OutlineItem {
-    fn outline_item(self: Rc<Self>, element_key: ElementKey) -> View;
+    fn outline_item(self: Rc<Self>, element: &Rc<dyn Element>) -> View;
 }
 impl OutlineItem for InversiveDistanceRegulator {
-    fn outline_item(self: Rc<Self>, element_key: ElementKey) -> View {
+    fn outline_item(self: Rc<Self>, element: &Rc<dyn Element>) -> View {
-        let state = use_context::<AppState>();
+        let other_subject_label = if self.subjects[0] == element.clone() {
-        let other_subject = if self.subjects[0] == element_key {
+            self.subjects[1].label()
            self.subjects[1]
        } else {
-            self.subjects[0]
+            self.subjects[0].label()
-        };
+        }.clone();
        let other_subject_label = state.assembly.elements.with(
            |elts| elts[other_subject].label().clone()
        );
        view! {
-            li(class="regulator") {
+            li(class = "regulator") {
-                div(class="regulator-label") { (other_subject_label) }
+                div(class = "regulator-label") { (other_subject_label) }
-                div(class="regulator-type") { "Inversive distance" }
+                div(class = "regulator-type") { "Inversive distance" }
-                RegulatorInput(regulator=self)
+                RegulatorInput(regulator = self)
-                div(class="status")
+                div(class = "status")
            }
        }
    }
 }
 impl OutlineItem for HalfCurvatureRegulator {
-    fn outline_item(self: Rc<Self>, _element_key: ElementKey) -> View {
+    fn outline_item(self: Rc<Self>, _element: &Rc<dyn Element>) -> View {
        view! {
-            li(class="regulator") {
+            li(class = "regulator") {
-                div(class="regulator-label") // for spacing
+                div(class = "regulator-label") // for spacing
-                div(class="regulator-type") { "Half-curvature" }
+                div(class = "regulator-type") { "Half-curvature" }
-                RegulatorInput(regulator=self)
+                RegulatorInput(regulator = self)
-                div(class="status")
+                div(class = "status")
            }
        }
    }
 }
 // a list item that shows a regulator in an outline view of an element
 #[component(inline_props)]
 fn RegulatorOutlineItem(regulator_key: RegulatorKey, element_key: ElementKey) -> View {
    let state = use_context::<AppState>();
    let regulator = state.assembly.regulators.with(
        |regs| regs[regulator_key].clone()
    );
    regulator.outline_item(element_key)
 }
 // a list item that shows an element in an outline view of an assembly
 #[component(inline_props)]
-fn ElementOutlineItem(key: ElementKey, element: Rc<dyn Element>) -> View {
+fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
    let state = use_context::<AppState>();
-    let class = state.selection.map(
+    let class = {
-        move |sel| if sel.contains(&key) { "selected" } else { "" }
+        let element_for_class = element.clone();
-    );
+        state.selection.map(
            move |sel| if sel.contains(&element_for_class) { "selected" } else { "" }
        )
    };
    let label = element.label().clone();
    let representation = element.representation().clone();
    let rep_components = move || {
@ -161,27 +143,24 @@ fn ElementOutlineItem(key: ElementKey, element: Rc<dyn Element>) -> View {
    };
    let regulated = element.regulators().map(|regs| regs.len() > 0);
    let regulator_list = element.regulators().map(
-        move |elt_reg_keys| elt_reg_keys
+        |regs| regs
            .clone()
            .into_iter()
-            .sorted_by_key(
+            .sorted_by_key(|reg| reg.subjects().len())
-                |&reg_key| state.assembly.regulators.with(
+            .collect::<Vec<_>>()
                    |regs| regs[reg_key].subjects().len()
                )
            )
            .collect()
    );
    let details_node = create_node_ref();
    view! {
        li {
-            details(ref=details_node) {
+            details(ref = details_node) {
                summary(
-                    class=class.get(),
+                    class = class.get(),
-                    on:keydown={
+                    on:keydown = {
                        let element_for_handler = element.clone();
                        move |event: KeyboardEvent| {
                            match event.key().as_str() {
                                "Enter" => {
-                                    state.select(key, event.shift_key());
+                                    state.select(&element_for_handler, event.shift_key());
                                    event.prevent_default();
                                },
                                "ArrowRight" if regulated.get() => {
@ -196,51 +175,41 @@ fn ElementOutlineItem(key: ElementKey, element: Rc<dyn Element>) -> View {
                                        .unchecked_into::<web_sys::Element>()
                                        .remove_attribute("open");
                                },
-                                _ => ()
+                                _ => (),
                            }
                        }
                    }
                ) {
                    div(
-                        class="element-switch",
+                        class = "element-switch",
-                        on:click=|event: MouseEvent| event.stop_propagation()
+                        on:click = |event: MouseEvent| event.stop_propagation()
                    )
                    div(
-                        class="element",
+                        class = "element",
-                        on:click={
+                        on:click = {
                            let state_for_handler = state.clone();
                            let element_for_handler = element.clone();
                            move |event: MouseEvent| {
-                                if event.shift_key() {
+                                state_for_handler.select(&element_for_handler, event.shift_key());
                                    state.selection.update(|sel| {
                                        if !sel.remove(&key) {
                                            sel.insert(key);
                                        }
                                    });
                                } else {
                                    state.selection.update(|sel| {
                                        sel.clear();
                                        sel.insert(key);
                                    });
                                }
                                event.stop_propagation();
                                event.prevent_default();
                            }
                        }
                    ) {
-                        div(class="element-label") { (label) }
+                        div(class = "element-label") { (label) }
-                        div(class="element-representation") { (rep_components) }
+                        div(class = "element-representation") { (rep_components) }
-                        div(class="status")
+                        input(
-                    }
+                            r#type = "checkbox",
-                }
+                            bind:checked = element.ghost(),
-                ul(class="regulators") {
+                            on:click = |event: MouseEvent| event.stop_propagation()
                    Keyed(
                        list=regulator_list,
                        view=move |reg_key| view! {
                            RegulatorOutlineItem(
                                regulator_key=reg_key,
                                element_key=key
                        )
-                        },
+                    }
-                        key=|reg_key| reg_key.clone()
+                }
                ul(class = "regulators") {
                    Keyed(
                        list = regulator_list,
                        view = move |reg| reg.outline_item(&element),
                        key = |reg| reg.serial()
                    )
                }
            }
@ -259,29 +228,32 @@ 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
    // ever wanted to sort by ID, we could do that more simply using the
    // `elements_by_id` index
    let element_list = state.assembly.elements.map(
        |elts| elts
            .clone()
            .into_iter()
-            .sorted_by_key(|(_, elt)| elt.id().clone())
+            .sorted_by_key(|elt| elt.id().clone())
-            .map(|(key, elt)| (key, ElementRc(elt)))
+            .collect::<Vec<_>>()
            .collect()
    );
    view! {
        ul(
-            id="outline",
+            id = "outline",
-            on:click={
+            on:click = {
                let state = use_context::<AppState>();
                move |_| state.selection.update(|sel| sel.clear())
            }
        ) {
            Keyed(
-                list=element_list,
+                list = element_list,
-                view=|(key, ElementRc(elt))| view! {
+                view = |elt| view! {
-                    ElementOutlineItem(key=key, element=elt)
+                    ElementOutlineItem(element = elt)
                },
-                key=|(_, ElementRc(elt))| elt.serial()
+                key = |elt| elt.serial()
            )
        }
    }
--- a/app-proto/src/components/point.frag
+++ b/app-proto/src/components/point.frag
@ -2,7 +2,7 @@
 precision highp float;
-in vec3 point_color;
+in vec4 point_color;
 in float point_highlight;
 in float total_radius;
@ -13,6 +13,7 @@ void main() {
    const float POINT_RADIUS = 4.;
    float border = smoothstep(POINT_RADIUS - 1., POINT_RADIUS, r);
-    vec3 color = mix(point_color, vec3(1.), border * point_highlight);
+    float disk = 1. - smoothstep(total_radius - 1., total_radius, r);
-    outColor = vec4(color, 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
@ -1,11 +1,11 @@
 #version 300 es
 in vec4 position;
-in vec3 color;
+in vec4 color;
 in float highlight;
 in float selected;
-out vec3 point_color;
+out vec4 point_color;
 out float point_highlight;
 out float total_radius;
--- a/app-proto/src/components/spheres.frag
+++ b/app-proto/src/components/spheres.frag
@ -17,7 +17,7 @@ struct vecInv {
 const int SPHERE_MAX = 200;
 uniform int sphere_cnt;
 uniform vecInv sphere_list[SPHERE_MAX];
-uniform vec3 color_list[SPHERE_MAX];
+uniform vec4 color_list[SPHERE_MAX];
 uniform float highlight_list[SPHERE_MAX];
 // view
@ -25,7 +25,6 @@ uniform vec2 resolution;
 uniform float shortdim;
 // controls
 uniform float opacity;
 uniform int layer_threshold;
 uniform bool debug_mode;
@ -69,7 +68,7 @@ struct Fragment {
    vec4 color;
 };
-Fragment sphere_shading(vecInv v, vec3 pt, vec3 base_color) {
+Fragment sphere_shading(vecInv v, vec3 pt, vec4 base_color) {
    // the expression for normal needs to be checked. it's supposed to give the
    // negative gradient of the lorentz product between the impact point vector
    // and the sphere vector with respect to the coordinates of the impact
@ -79,7 +78,7 @@ Fragment sphere_shading(vecInv v, vec3 pt, vec3 base_color) {
    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, opacity));
+    return Fragment(pt, normal, vec4(illum * base_color.rgb, base_color.a));
 }
 float intersection_dist(Fragment a, Fragment b) {
@ -192,10 +191,11 @@ void main() {
    vec3 color = vec3(0.);
    int layer = layer_cnt - 1;
    TaggedDepth hit = top_hits[layer];
    vec4 sphere_color = color_list[hit.id];
    Fragment frag_next = sphere_shading(
        sphere_list[hit.id],
        hit.depth * dir,
-        hit.dimming * color_list[hit.id]
+        vec4(hit.dimming * sphere_color.rgb, sphere_color.a)
    );
    float highlight_next = highlight_list[hit.id];
    --layer;
@ -206,10 +206,11 @@ void main() {
        // shade the next fragment
        hit = top_hits[layer];
        sphere_color = color_list[hit.id];
        frag_next = sphere_shading(
            sphere_list[hit.id],
            hit.depth * dir,
-            hit.dimming * color_list[hit.id]
+            vec4(hit.dimming * sphere_color.rgb, sphere_color.a)
        );
        highlight_next = highlight_list[hit.id];
--- 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
@ -1,6 +1,6 @@
 use lazy_static::lazy_static;
 use nalgebra::{Const, DMatrix, DVector, DVectorView, Dyn, SymmetricEigen};
-use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
+use std::fmt::{Display, Error, Formatter};
 // --- elements ---
@ -16,7 +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),
    ])
 }
@ -30,61 +30,42 @@ 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),
    ])
 }
-// given a sphere's representation vector, change the sphere's half-curvature to
+// project a sphere's representation vector to the normalization variety by
-// `half-curv` and then restore normalization by contracting the representation
+// contracting toward the last coordinate axis
-// vector toward the curvature axis
+pub fn project_sphere_to_normalized(rep: &mut DVector<f64>) {
-pub fn change_half_curvature(rep: &mut DVector<f64>, half_curv: f64) {
+    let q_sp = rep.fixed_rows::<3>(0).norm_squared();
-    // set the sphere's half-curvature to the desired value
+    let half_q_lt = -2.0 * rep[3] * rep[4];
    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.fixed_rows_mut::<4>(0).scale_mut(1.0 / scaling);
-        rep[4] /= scaling;
+}
    }
-    /* DEBUG */
+// normalize a point's representation vector by scaling
-    // verify normalization
+pub fn project_point_to_normalized(rep: &mut DVector<f64>) {
-    let rep_for_debug = rep.clone();
+    rep.scale_mut(0.5 / rep[3]);
    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
+    value: f64,
 }
 pub struct PartialMatrix(Vec<MatrixEntry>);
 impl PartialMatrix {
-    pub fn new() -> PartialMatrix {
+    pub fn new() -> Self {
-        PartialMatrix(Vec::<MatrixEntry>::new())
+        Self(Vec::<MatrixEntry>::new())
    }
    pub fn push(&mut self, row: usize, col: usize, value: f64) {
-        let PartialMatrix(entries) = self;
+        let Self(entries) = self;
-        entries.push(MatrixEntry { index: (row, col), value: value });
+        entries.push(MatrixEntry { index: (row, col), value });
    }
    pub fn push_sym(&mut self, row: usize, col: usize, value: f64) {
@ -94,15 +75,6 @@ impl PartialMatrix {
        }
    }
    /* DEBUG */
    pub fn log_to_console(&self) {
        for &MatrixEntry { index: (row, col), value } in self {
            console::log_1(&JsValue::from(
                format!("  {} {} {}", row, col, value)
            ));
        }
    }
    fn freeze(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
        let mut result = a.clone();
        for &MatrixEntry { index, value } in self {
@ -128,12 +100,21 @@ impl PartialMatrix {
    }
 }
 impl Display for PartialMatrix {
    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error> {
        for &MatrixEntry { index: (row, col), value } in self {
            writeln!(f, "  {row} {col} {value}")?;
        }
        Ok(())
    }
 }
 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()
    }
 }
@ -154,22 +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 {
+    pub fn zero(assembly_dim: usize) -> Self {
-        ConfigSubspace {
+        Self {
-            assembly_dim: assembly_dim,
+            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
@ -183,20 +168,13 @@ impl ConfigSubspace {
            ).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 {
+        Self {
-            assembly_dim: assembly_dim,
+            assembly_dim,
            basis_std: basis_std.column_iter().map(
                |v| Into::<DMatrix<f64>>::into(
                    v.reshape_generic(Dyn(ELEMENT_DIM), Dyn(assembly_dim))
@ -206,7 +184,7 @@ impl ConfigSubspace {
                |v| Into::<DMatrix<f64>>::into(
                    v.reshape_generic(Dyn(UNIFORM_DIM), Dyn(assembly_dim))
                )
-            ).collect()
+            ).collect(),
        }
    }
@ -240,18 +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 {
+    pub fn new() -> Self {
-        DescentHistory {
+        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(),
        }
@ -267,21 +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 {
+    pub fn from_guess(guess_columns: &[DVector<f64>]) -> Self {
-        ConstraintProblem {
+        Self {
            gram: PartialMatrix::new(),
            frozen: PartialMatrix::new(),
-            guess: DMatrix::from_columns(guess_columns)
+            guess: DMatrix::from_columns(guess_columns),
        }
    }
 }
@ -295,25 +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 {
+        Self { config, err_proj, loss }
            config: config,
            err_proj: err_proj,
            loss: loss
        }
    }
 }
@ -340,7 +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
@ -349,7 +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,
        ])
    }
 }
@ -362,7 +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 {
@ -377,6 +351,17 @@ fn seek_better_config(
    None
 }
 // a first-order neighborhood of a configuration
 pub struct ConfigNeighborhood {
    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
@ -388,19 +373,30 @@ pub fn realize_gram(
    backoff: f64,
    reg_scale: f64,
    max_descent_steps: i32,
-    max_backoff_steps: i32
+    max_backoff_steps: i32,
-) -> (DMatrix<f64>, ConfigSubspace, bool, DescentHistory) {
+) -> Realization {
    // destructure the problem data
-    let ConstraintProblem {
+    let ConstraintProblem { gram, guess, frozen } = problem;
        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 {
                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
@ -441,11 +437,12 @@ 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
@ -464,30 +461,40 @@ pub fn realize_gram(
        if state.loss < tol { break; }
        // compute the Newton step
        /* TO DO */
        /*
-          we need to either handle or eliminate the case where the minimum
+          we should change our regularization to ensure that the Hessian is
-          eigenvalue of the Hessian is zero, so the regularized Hessian is
+          is positive-definite, rather than just positive-semidefinite. ideally,
-          singular. right now, this causes the Cholesky decomposition to return
+          that would guarantee the success of the Cholesky decomposition---
-          `None`, leading to a panic when we unrap
+          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);
-            },
+        } else {
-            None => return (state.config, ConfigSubspace::zero(assembly_dim), false, history)
+            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;
@ -500,11 +507,13 @@ pub fn realize_gram(
        }
        // 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 { 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 ---
@ -523,12 +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| {
@ -574,7 +583,7 @@ pub mod examples {
    // 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(
@ -587,7 +596,7 @@ 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()
@ -630,15 +639,15 @@ mod tests {
            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);
    }
@ -649,15 +658,15 @@ mod tests {
            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);
    }
@ -675,7 +684,7 @@ 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);
@ -689,7 +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 {
@ -698,10 +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);
@ -716,7 +725,7 @@ mod tests {
    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();
@ -733,7 +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 {
@ -743,11 +752,11 @@ 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
@ -763,8 +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),
@ -774,8 +783,8 @@ 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
@ -815,8 +824,8 @@ mod tests {
    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);
+        let Realization { result, history } = realize_kaleidocycle(SCALED_TOL);
-        assert_eq!(success, true);
+        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
@ -851,10 +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(
@ -887,7 +896,7 @@ 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,
        ])
    }
@ -899,16 +908,16 @@ 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
@ -917,19 +926,19 @@ mod tests {
            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
@ -951,7 +960,7 @@ 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;
--- a/app-proto/src/main.rs
+++ b/app-proto/src/main.rs
@ -1,49 +1,49 @@
 mod add_remove;
 mod assembly;
-mod display;
+mod components;
 mod engine;
 mod outline;
 mod specified;
 #[cfg(test)]
 mod tests;
-use rustc_hash::FxHashSet;
+use std::{collections::BTreeSet, rc::Rc};
 use sycamore::prelude::*;
-use add_remove::AddRemove;
+use assembly::{Assembly, Element};
-use assembly::{Assembly, ElementKey};
+use components::{
-use display::Display;
+    add_remove::AddRemove,
-use outline::Outline;
+    diagnostics::Diagnostics,
    display::Display,
    outline::Outline,
 };
 #[derive(Clone)]
 struct AppState {
    assembly: Assembly,
-    selection: Signal<FxHashSet<ElementKey>>
+    selection: Signal<BTreeSet<Rc<dyn Element>>>,
 }
 impl AppState {
-    fn new() -> AppState {
+    fn new() -> Self {
-        AppState {
+        Self {
            assembly: Assembly::new(),
-            selection: create_signal(FxHashSet::default())
+            selection: create_signal(BTreeSet::default()),
        }
    }
-    // in single-selection mode, select the element with the given key. in
+    // in single-selection mode, select the given element. in multiple-selection
-    // multiple-selection mode, toggle whether the element with the given key
+    // mode, toggle whether the given element is selected
-    // is selected
+    fn select(&self, element: &Rc<dyn Element>, multi: bool) {
    fn select(&self, key: ElementKey, multi: bool) {
        if multi {
            self.selection.update(|sel| {
-                if !sel.remove(&key) {
+                if !sel.remove(element) {
-                    sel.insert(key);
+                    sel.insert(element.clone());
                }
            });
        } else {
            self.selection.update(|sel| {
                sel.clear();
-                sel.insert(key);
+                sel.insert(element.clone());
            });
        }
    }
@ -58,9 +58,10 @@ fn main() {
        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
@ -13,12 +13,12 @@ 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 {
+    pub fn from_empty_spec() -> Self {
-        SpecifiedValue { spec: String::new(), value: None }
+        Self { spec: String::new(), value: None }
    }
    pub fn is_present(&self) -> bool {
@ -34,10 +34,10 @@ impl TryFrom<String> for SpecifiedValue {
    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/deploy/.gitignore
+++ b/deploy/.gitignore
@ -0,0 +1,5 @@
 /dyna3.zip
 /dyna3/index.html
 /dyna3/dyna3-*.js
 /dyna3/dyna3-*.wasm
 /dyna3/main-*.css
--- 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
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
Vectornaut	e447e7ea96	Dispatch normalization routines correctly (#87 ) Addresses issue #86 by correctly dispatching the routine used to normalize spheres during nudging. Adds a test that would have detected the issue. Since the tests aren't built for WebAssembly, we have to replace `console::log` with `console_log!` in all of the functions used by `assembly::curvature_drift_test`. We'll eventually want to do this replacement everywhere. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#87 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-06-04 21:01:12 +00:00
Vectornaut	a671a8273a	Introduce ghost mode for elements (#85 ) Allows any element to be put in "ghost mode," decreasing its opacity and making it insensitive to click-to-select. Ghost mode is toggled using a checkbox in the outline view. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#85 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-06-02 15:56:06 +00:00
Vectornaut	2adf4669f4	Refactor: Use pointers to refer to elements and regulators (#84 ) Previously, dyna3 used storage keys to refer to elements, necessitating passing around element containers to various functions so that they could access the relevant elements. These storage keys have been replaced with reference-counted pointers, used for tasks like these: - Specifying the subjects of regulators. - Collecting the regulators each element is subject to - Handling selection. - Creating interface components. Also, systematizes the handling of serial numbers for entities, through a Serial trait. And updates to rust 1.86 and institutes explicit checking of the rust version. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: StudioInfinity/dyna3#84 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net>	2025-05-06 19:17:30 +00:00