diff --git a/.forgejo/setup-trunk/action.yaml b/.forgejo/setup-trunk/action.yaml
deleted file mode 100644
index 6007527..0000000
--- a/.forgejo/setup-trunk/action.yaml
+++ /dev/null
@@ -1,22 +0,0 @@
-# set up the Trunk web build system
-#
-#   https://trunkrs.dev
-#
-# the `curl` call is based on David Tolnay's `rust-toolchain` action
-#
-#   https://github.com/dtolnay/rust-toolchain
-#
-runs:
-  using: "composite"
-  steps:
-    - run: rustup target add wasm32-unknown-unknown
-    
-    # install the Trunk binary to `ci-bin` within the workspace directory, which
-    # is determined by the `github.workspace` label and reflected in the
-    # `GITHUB_WORKSPACE` environment variable. then, make the `trunk` command
-    # available by placing the fully qualified path to `ci-bin` on the
-    # workflow's search path
-    - run: mkdir -p ci-bin
-    - run: curl --output - --proto '=https' --tlsv1.2 --retry 10 --retry-connrefused --location --silent --show-error --fail 'https://github.com/trunk-rs/trunk/releases/download/v0.21.12/trunk-x86_64-unknown-linux-gnu.tar.gz' | tar --gunzip --extract --file -
-      working-directory: ci-bin
-    - run: echo "${{ github.workspace }}/ci-bin" >> $GITHUB_PATH
diff --git a/.forgejo/workflows/continuous-integration.yaml b/.forgejo/workflows/continuous-integration.yaml
deleted file mode 100644
index f3b0130..0000000
--- a/.forgejo/workflows/continuous-integration.yaml
+++ /dev/null
@@ -1,29 +0,0 @@
-on:
-  pull_request:
-  push:
-    branches: [main]
-jobs:
-  # run the automated tests, reporting success if the tests pass and were built
-  # without warnings. the examples are run as tests, because we've configured
-  # each example target with `test = true` and `harness = false` in Cargo.toml.
-  # Trunk build failures caused by problems outside the Rust source code, like
-  # missing assets, should be caught by `trunk_build_test`
-  test:
-    runs-on: docker
-    container:
-      image: cimg/rust:1.86-node
-    defaults:
-      run:
-        # set the default working directory for each `run` step, relative to the
-        # workspace directory. this default only affects `run` steps (and if we
-        # tried to set the `working-directory` label for any other kind of step,
-        # it wouldn't be recognized anyway)
-        working-directory: app-proto
-    steps:
-      # Check out the repository so that its top-level directory is the
-      # workspace directory (action variable `github.workspace`, environment
-      # variable `$GITHUB_WORKSPACE`):
-      - uses: https://code.forgejo.org/actions/checkout@v4
-      
-      - uses: ./.forgejo/setup-trunk
-      - run: RUSTFLAGS='-D warnings' cargo test
\ No newline at end of file
diff --git a/.gitignore b/.gitignore
index ba2944f..3e95fba 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,8 @@
-ci-bin
+node_modules
+site
+docbuild
+__tests__
+coverage
+dyna3.zip
+tmpproj
 *~
diff --git a/README.md b/README.md
index cf3e589..9ea9cbf 100644
--- a/README.md
+++ b/README.md
@@ -17,71 +17,3 @@ Note that currently this is just the barest beginnings of the project, more of a
 * Able to run in browser (so implemented in WASM-compatible language)
 
 * Produce scalable graphics of 3D diagrams, and maybe STL files (or other fabricatable file format) as well.
-
-## Prototype
-
-The latest prototype is in the folder `app-proto`. It includes both a user interface and a numerical constraint-solving engine.
-
-### Install the prerequisites
-
-1. Install [`rustup`](https://rust-lang.github.io/rustup/): the officially recommended Rust toolchain manager
-   - It's available on Ubuntu as a [Snap](https://snapcraft.io/rustup)
-2. Call `rustup default stable` to "download the latest stable release of Rust and set it as your default toolchain"
-   - If you forget, the `rustup` [help system](https://github.com/rust-lang/rustup/blob/d9b3601c3feb2e88cf3f8ca4f7ab4fdad71441fd/src/errors.rs#L109-L112) will remind you
-3. Call `rustup target add wasm32-unknown-unknown` to add the [most generic 32-bit WebAssembly target](https://doc.rust-lang.org/nightly/rustc/platform-support/wasm32-unknown-unknown.html)
-4. Call `cargo install wasm-pack` to install the [WebAssembly toolchain](https://rustwasm.github.io/docs/wasm-pack/)
-5. Call `cargo install trunk` to install the [Trunk](https://trunkrs.dev/) web-build tool
-6. Add the `.cargo/bin` folder in your home directory to your executable search path
-   - This lets you call Trunk, and other tools installed by Cargo, without specifying their paths
-   - On POSIX systems, the search path is stored in the `PATH` environment variable
-
-### Play with the prototype
-
-1. From the `app-proto` folder, call `trunk serve --release` to build and serve the prototype
-   - The crates the prototype depends on will be downloaded and served automatically
-   - For a faster build, at the expense of a much slower prototype, you can call `trunk serve` without the `--release` flag
-   - If you want to stay in the top-level folder, you can call `trunk serve --config app-proto [--release]` from there instead.
-3. In a web browser, visit one of the URLs listed under the message `INFO 📡 server listening at:`
-   - Touching any file in the `app-proto` folder will make Trunk rebuild and live-reload the prototype
-4. Press *ctrl+C* in the shell where Trunk is running to stop serving the prototype
-
-### Run the engine on some example problems
-
-1. Use `sh` to run the script `tools/run-examples.sh`
-   - The script is location-independent, so you can do this from anywhere in the dyna3 repository
-   - The call from the top level of the repository is:
-     
-     ```bash
-     sh tools/run-examples.sh
-     ```
-   - For each example problem, the engine will print the value of the loss function at each optimization step
-   - The first example that prints is the same as the Irisawa hexlet example from the Julia version of the engine prototype. If you go into `engine-proto/gram-test`, launch Julia, and then
-     
-     ```julia
-     include("irisawa-hexlet.jl")
-     for (step, scaled_loss) in enumerate(history_alt.scaled_loss)
-       println(rpad(step-1, 4), " | ", scaled_loss)
-     end
-     ```
-     
-     you should see that it prints basically the same loss history until the last few steps, when the lower default precision of the Rust engine really starts to show
-
-### 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
\ No newline at end of file
diff --git a/app-proto/Cargo.lock b/app-proto/Cargo.lock
deleted file mode 100644
index 4f75c45..0000000
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diff --git a/app-proto/Cargo.toml b/app-proto/Cargo.toml
index 1230b47..e623b26 100644
--- a/app-proto/Cargo.toml
+++ b/app-proto/Cargo.toml
@@ -3,22 +3,18 @@ name = "dyna3"
 version = "0.1.0"
 authors = ["Aaron Fenyes", "Glen Whitney"]
 edition = "2021"
-rust-version = "1.86"
 
 [features]
 default = ["console_error_panic_hook"]
-dev = []
 
 [dependencies]
 itertools = "0.13.0"
 js-sys = "0.3.70"
 lazy_static = "1.5.0"
 nalgebra = "0.33.0"
-readonly = "0.2.12"
-sycamore = "0.9.1"
-
-# We use Charming to help display engine diagnostics
-charming = { version = "0.5.1", features = ["wasm"] }
+rustc-hash = "2.0.0"
+slab = "0.4.9"
+sycamore = "0.9.0-beta.3"
 
 # The `console_error_panic_hook` crate provides better debugging of panics by
 # logging them with `console.error`. This is great for development, but requires
@@ -29,7 +25,6 @@ console_error_panic_hook = { version = "0.1.7", optional = true }
 [dependencies.web-sys]
 version = "0.3.69"
 features = [
-  'DomRect',
   'HtmlCanvasElement',
   'HtmlInputElement',
   'Performance',
@@ -41,41 +36,9 @@ features = [
   'WebGlVertexArrayObject'
 ]
 
-# the self-dependency specifies features to use for tests and examples
-#
-#   https://github.com/rust-lang/cargo/issues/2911#issuecomment-1483256987
-#
 [dev-dependencies]
-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
-
-[[example]]
-name = "irisawa-hexlet"
-test = true
-harness = false
-
-[[example]]
-name = "kaleidocycle"
-test = true
-harness = false
-
-[[example]]
-name = "point-on-sphere"
-test = true
-harness = false
-
-[[example]]
-name = "three-spheres"
-test = true
-harness = false
diff --git a/app-proto/Trunk.toml b/app-proto/Trunk.toml
deleted file mode 100644
index 017deba..0000000
--- a/app-proto/Trunk.toml
+++ /dev/null
@@ -1,2 +0,0 @@
-[build]
-public_url = "./"
\ No newline at end of file
diff --git a/app-proto/examples/common/print.rs b/app-proto/examples/common/print.rs
deleted file mode 100644
index 2aa6a39..0000000
--- a/app-proto/examples/common/print.rs
+++ /dev/null
@@ -1,36 +0,0 @@
-#![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);
-    }
-}
\ No newline at end of file
diff --git a/app-proto/examples/irisawa-hexlet.rs b/app-proto/examples/irisawa-hexlet.rs
deleted file mode 100644
index 0d710ff..0000000
--- a/app-proto/examples/irisawa-hexlet.rs
+++ /dev/null
@@ -1,23 +0,0 @@
-#[path = "common/print.rs"]
-mod print;
-
-use dyna3::engine::{ConfigNeighborhood, examples::realize_irisawa_hexlet};
-
-fn main() {
-    const SCALED_TOL: f64 = 1.0e-12;
-    let realization = realize_irisawa_hexlet(SCALED_TOL);
-    print::title("Irisawa hexlet");
-    print::realization_diagnostics(&realization);
-    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
-        // print the diameters of the chain spheres
-        println!("\nChain diameters:");
-        println!("  {} sun (given)", 1.0 / config[(3, 3)]);
-        for k in 4..9 {
-            println!("  {} sun", 1.0 / config[(3, k)]);
-        }
-        
-        // print the completed Gram matrix
-        print::gram_matrix(&config);
-    }
-    print::loss_history(&realization.history);
-}
\ No newline at end of file
diff --git a/app-proto/examples/kaleidocycle.rs b/app-proto/examples/kaleidocycle.rs
deleted file mode 100644
index ae4eb07..0000000
--- a/app-proto/examples/kaleidocycle.rs
+++ /dev/null
@@ -1,32 +0,0 @@
-#[path = "common/print.rs"]
-mod print;
-
-use nalgebra::{DMatrix, DVector};
-
-use dyna3::engine::{ConfigNeighborhood, examples::realize_kaleidocycle};
-
-fn main() {
-    const SCALED_TOL: f64 = 1.0e-12;
-    let realization = realize_kaleidocycle(SCALED_TOL);
-    print::title("Kaleidocycle");
-    print::realization_diagnostics(&realization);
-    if let Ok(ConfigNeighborhood { config, nbhd: tangent }) = realization.result {
-        // print the completed Gram matrix and the realized configuration
-        print::gram_matrix(&config);
-        print::config(&config);
-        
-        // find the kaleidocycle's twist motion by projecting onto the tangent
-        // space
-        const N_POINTS: usize = 12;
-        let up = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
-        let down = -&up;
-        let twist_motion: DMatrix<_> = (0..N_POINTS).step_by(4).flat_map(
-            |n| [
-                tangent.proj(&up.as_view(), n),
-                tangent.proj(&down.as_view(), n+1),
-            ]
-        ).sum();
-        let normalization = 5.0 / twist_motion[(2, 0)];
-        println!("\nTwist motion:{}", (normalization * twist_motion).to_string().trim_end());
-    }
-}
\ No newline at end of file
diff --git a/app-proto/examples/point-on-sphere.rs b/app-proto/examples/point-on-sphere.rs
deleted file mode 100644
index a73490e..0000000
--- a/app-proto/examples/point-on-sphere.rs
+++ /dev/null
@@ -1,33 +0,0 @@
-#[path = "common/print.rs"]
-mod print;
-
-use dyna3::engine::{
-    point,
-    realize_gram,
-    sphere,
-    ConfigNeighborhood,
-    ConstraintProblem,
-};
-
-fn main() {
-    let mut problem = ConstraintProblem::from_guess(&[
-        point(0.0, 0.0, 2.0),
-        sphere(0.0, 0.0, 0.0, 1.0)
-    ]);
-    for j in 0..2 {
-        for k in j..2 {
-            problem.gram.push_sym(j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
-        }
-    }
-    problem.frozen.push(3, 0, problem.guess[(3, 0)]);
-    let realization = realize_gram(
-        &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
-    );
-    print::title("Point on a sphere");
-    print::realization_diagnostics(&realization);
-    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
-        print::gram_matrix(&config);
-        print::config(&config);
-    }
-    print::loss_history(&realization.history);
-}
\ No newline at end of file
diff --git a/app-proto/examples/three-spheres.rs b/app-proto/examples/three-spheres.rs
deleted file mode 100644
index 7901e31..0000000
--- a/app-proto/examples/three-spheres.rs
+++ /dev/null
@@ -1,34 +0,0 @@
-#[path = "common/print.rs"]
-mod print;
-
-use dyna3::engine::{
-    realize_gram,
-    sphere,
-    ConfigNeighborhood,
-    ConstraintProblem,
-};
-
-fn main() {
-    let mut problem = ConstraintProblem::from_guess({
-        let a: f64 = 0.75_f64.sqrt();
-        &[
-            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),
-        ]
-    });
-    for j in 0..3 {
-        for k in j..3 {
-            problem.gram.push_sym(j, k, if j == k { 1.0 } else { -1.0 });
-        }
-    }
-    let realization = realize_gram(
-        &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
-    );
-    print::title("Three spheres");
-    print::realization_diagnostics(&realization);
-    if let Ok(ConfigNeighborhood { config, .. }) = realization.result {
-        print::gram_matrix(&config);
-    }
-    print::loss_history(&realization.history);
-}
\ No newline at end of file
diff --git a/app-proto/index.html b/app-proto/index.html
index 4fbe52f..92238f4 100644
--- a/app-proto/index.html
+++ b/app-proto/index.html
@@ -6,12 +6,6 @@
     <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>
diff --git a/app-proto/main.css b/app-proto/main.css
index 7981285..204c8c8 100644
--- a/app-proto/main.css
+++ b/app-proto/main.css
@@ -1,47 +1,23 @@
-:root {
-  --text: #fcfcfc; /* almost white */
-  --text-bright: white;
-  --text-invalid: #f58fc2; /* bright pink */
-  --border: #555; /* light gray */
-  --border-focus-dark: #aaa; /* bright gray */
-  --border-focus-light: white;
-  --border-invalid: #70495c; /* dusky pink */
-  --selection-highlight: #444; /* medium gray */
-  --page-background: #222; /* dark gray */
-  --display-background: #020202; /* almost black */
-}
-
 body {
   margin: 0px;
-  color: var(--text);
-  background-color: var(--page-background);
+  color: #fcfcfc;
+  background-color: #222;
   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 {
   display: flex;
   flex-direction: column;
   float: left;
-  width: 500px;
+  width: 450px;
   height: 100vh;
   margin: 0px;
   padding: 0px;
   border-width: 0px 1px 0px 0px;
   border-style: solid;
-  border-color: var(--border);
+  border-color: #555;
 }
 
 /* add-remove */
@@ -53,18 +29,14 @@ body {
 }
 
 #add-remove > button {
+  width: 32px;
   height: 32px;
+  font-size: large;
 }
 
 /* KLUDGE */
-/*
-  for convenience, we're using emoji as temporary icons for some buttons. these
-  buttons need to be displayed in an emoji font
-*/
 #add-remove > button.emoji {
-  width: 32px;
   font-family: 'Noto Emoji', sans-serif;
-  font-size: large;
 }
 
 /* outline */
@@ -85,53 +57,49 @@ summary {
 }
 
 summary.selected {
-  color: var(--text-bright);
-  background-color: var(--selection-highlight);
+  color: #fff;
+  background-color: #444;
 }
 
-summary > div, .regulator {
+summary > div, .cst {
   padding-top: 4px;
   padding-bottom: 4px;
 }
 
-.element, .regulator {
+.elt, .cst {
   display: flex;
   flex-grow: 1;
   padding-left: 8px;
   padding-right: 8px;
 }
 
-.element > input {
-  margin-left: 8px;
-}
-
-.element-switch {
+.elt-switch {
   width: 18px;
   padding-left: 2px;
   text-align: center;
 }
 
-details:has(li) .element-switch::after {
+details:has(li) .elt-switch::after {
   content: '▸';
 }
 
-details[open]:has(li) .element-switch::after {
+details[open]:has(li) .elt-switch::after {
   content: '▾';
 }
 
-.element-label {
+.elt-label {
   flex-grow: 1;
 }
 
-.regulator-label {
+.cst-label {
   flex-grow: 1;
 }
 
-.element-representation {
+.elt-rep {
   display: flex;
 }
 
-.element-representation > div {
+.elt-rep > div {
   padding: 2px 0px 0px 0px;
   font-size: 10pt;
   font-variant-numeric: tabular-nums;
@@ -139,102 +107,53 @@ details[open]:has(li) .element-switch::after {
   width: 56px;
 }
 
-.regulator {
+.cst {
   font-style: italic;
 }
 
-.regulator-type {
-  padding: 2px 8px 0px 8px;
-  font-size: 10pt;
+.cst.invalid {
+  color: #f58fc2;
 }
 
-.regulator-input {
-  margin-right: 4px;
+.cst > input[type=checkbox] {
+  margin: 0px 8px 0px 0px;
+}
+
+.cst > input[type=text] {
   color: inherit;
   background-color: inherit;
-  border: 1px solid var(--border);
+  border: 1px solid #555;
   border-radius: 2px;
 }
 
-.regulator-input::placeholder {
-  color: inherit;
-  opacity: 54%;
-  font-style: italic;
+.cst.invalid > input[type=text] {
+  border-color: #70495c;
 }
 
-.regulator-input.constraint {
-  background-color: var(--display-background);
+.status {
+  width: 20px;
+  padding-left: 4px;
+  text-align: center;
+  font-family: 'Noto Emoji';
+  font-style: normal;
 }
 
-.regulator-input.invalid {
-  color: var(--text-invalid);
-  border-color: var(--border-invalid);
-}
-
-.regulator-input.invalid + .status::after, details:has(.invalid):not([open]) .status::after {
+.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;
+  color: #f58fc2;
 }
 
 /* display */
 
-#display {
+canvas {
   float: left;
   margin-left: 20px;
   margin-top: 20px;
-  background-color: var(--display-background);
-  border: 1px solid var(--border);
+  background-color: #020202;
+  border: 1px solid #555;
   border-radius: 16px;
 }
 
-#display:focus {
-  border-color: var(--border-focus-dark);
-  outline: none;
-}
-
-input:focus {
-  border-color: var(--border-focus-light);
-  outline: none;
+canvas:focus {
+  border-color: #aaa;
 }
\ No newline at end of file
diff --git a/app-proto/run-examples b/app-proto/run-examples
new file mode 100755
index 0000000..6a5e3ae
--- /dev/null
+++ b/app-proto/run-examples
@@ -0,0 +1,8 @@
+# based on "Enabling print statements in Cargo tests", by Jon Almeida
+#
+#   https://jonalmeida.com/posts/2015/01/23/print-cargo/
+#
+
+cargo test -- --nocapture engine::tests::irisawa_hexlet_test
+cargo test -- --nocapture engine::tests::three_spheres_example
+cargo test -- --nocapture engine::tests::point_on_sphere_example
diff --git a/app-proto/src/add_remove.rs b/app-proto/src/add_remove.rs
new file mode 100644
index 0000000..d135449
--- /dev/null
+++ b/app-proto/src/add_remove.rs
@@ -0,0 +1,235 @@
+use sycamore::prelude::*;
+use web_sys::{console, wasm_bindgen::JsValue};
+
+use crate::{engine, AppState, assembly::{Assembly, Constraint, Element}};
+
+/* DEBUG */
+fn load_gen_assemb(assembly: &Assembly) {
+    let _ = assembly.try_insert_element(
+        Element::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(
+        Element::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(
+        Element::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(
+        Element::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(
+        Element::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(
+        Element::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 */
+fn load_low_curv_assemb(assembly: &Assembly) {
+    let a = 0.75_f64.sqrt();
+    let _ = assembly.try_insert_element(
+        Element::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(
+        Element::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(
+        Element::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(
+        Element::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(
+        Element::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(
+        Element::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(
+        Element::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(
+        Element::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)
+        )
+    );
+}
+
+#[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.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),
+                _ => ()
+            };
+        });
+    });
+    
+    view! {
+        div(id="add-remove") {
+            button(
+                on:click=|_| {
+                    let state = use_context::<AppState>();
+                    state.assembly.insert_new_element();
+                    
+                    /* DEBUG */
+                    // print updated list of elements by identifier
+                    console::log_1(&JsValue::from("elements by identifier:"));
+                    for (id, key) in state.assembly.elements_by_id.get_clone().iter() {
+                        console::log_3(
+                            &JsValue::from(" "),
+                            &JsValue::from(id),
+                            &JsValue::from(*key)
+                        );
+                    }
+                }
+            ) { "+" }
+            button(
+                class="emoji", /* KLUDGE */
+                disabled={
+                    let state = use_context::<AppState>();
+                    state.selection.with(|sel| sel.len() != 2)
+                },
+                on:click=|_| {
+                    let state = use_context::<AppState>();
+                    let args = state.selection.with(
+                        |sel| {
+                            let arg_vec: Vec<_> = sel.into_iter().collect();
+                            (arg_vec[0].clone(), arg_vec[1].clone())
+                        }
+                    );
+                    let rep = create_signal(0.0);
+                    let rep_valid = create_signal(false);
+                    let active = create_signal(true);
+                    state.assembly.insert_constraint(Constraint {
+                        args: args,
+                        rep: rep,
+                        rep_text: create_signal(String::new()),
+                        rep_valid: rep_valid,
+                        active: active,
+                    });
+                    state.selection.update(|sel| sel.clear());
+                    
+                    /* DEBUG */
+                    // print updated constraint list
+                    console::log_1(&JsValue::from("Constraints:"));
+                    state.assembly.constraints.with(|csts| {
+                        for (_, cst) in csts.into_iter() {
+                            console::log_5(
+                                &JsValue::from(" "),
+                                &JsValue::from(cst.args.0),
+                                &JsValue::from(cst.args.1),
+                                &JsValue::from(":"),
+                                &JsValue::from(cst.rep.get_untracked())
+                            );
+                        }
+                    });
+                    
+                    // update the realization when the constraint becomes active
+                    // and valid, or is edited while active and valid
+                    create_effect(move || {
+                        console::log_1(&JsValue::from(
+                            format!("Constraint ({}, {}) updated", args.0, args.1)
+                        ));
+                        rep.track();
+                        if active.get() && rep_valid.get() {
+                            state.assembly.realize();
+                        }
+                    });
+                }
+            ) { "🔗" }
+            select(bind:value=assembly_name) { /* DEBUG */
+                option(value="general") { "General" }
+                option(value="low-curv") { "Low-curvature" }
+            }
+        }
+    }
+}
\ No newline at end of file
diff --git a/app-proto/src/assembly.rs b/app-proto/src/assembly.rs
index 94e7b3c..7b7c015 100644
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@@ -1,592 +1,86 @@
-use nalgebra::{DMatrix, DVector, DVectorView};
-use std::{
-    cell::Cell,
-    cmp::Ordering,
-    collections::{BTreeMap, BTreeSet},
-    fmt,
-    fmt::{Debug, Formatter},
-    hash::{Hash, Hasher},
-    rc::Rc,
-    sync::{atomic, atomic::AtomicU64},
-};
+use nalgebra::{DMatrix, DVector};
+use rustc_hash::FxHashMap;
+use slab::Slab;
+use std::collections::BTreeSet;
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 
-use crate::{
-    components::{display::DisplayItem, outline::OutlineItem},
-    engine::{
-        Q,
-        local_unif_to_std,
-        point,
-        project_point_to_normalized,
-        project_sphere_to_normalized,
-        realize_gram,
-        sphere,
-        ConfigNeighborhood,
-        ConfigSubspace,
-        ConstraintProblem,
-        DescentHistory,
-        Realization,
-    },
-    specified::SpecifiedValue,
-};
+use crate::engine::{realize_gram, PartialMatrix};
 
-pub type ElementColor = [f32; 3];
-
-/* KLUDGE */
-// we should reconsider this design when we build a system for switching between
-// assemblies. at that point, we might want to switch to hierarchical keys,
-// where each each item has a key that identifies it within its assembly and
-// each assembly has a key that identifies it within the sesssion
-static NEXT_SERIAL: AtomicU64 = AtomicU64::new(0);
-
-pub trait Serial {
-    // a serial number that uniquely identifies this element
-    fn serial(&self) -> u64;
-    
-    // take the next serial number, panicking if that was the last one left
-    fn next_serial() -> u64 where Self: Sized {
-        // the technique we use to panic on overflow is taken from _Rust Atomics
-        // and Locks_, by Mara Bos
-        //
-        //   https://marabos.nl/atomics/atomics.html#example-handle-overflow
-        //
-        NEXT_SERIAL.fetch_update(
-            atomic::Ordering::SeqCst, atomic::Ordering::SeqCst,
-            |serial| serial.checked_add(1)
-        ).expect("Out of serial numbers for elements")
-    }
-}
-
-impl Hash for dyn Serial {
-    fn hash<H: Hasher>(&self, state: &mut H) {
-        self.serial().hash(state)
-    }
-}
-
-impl PartialEq for dyn Serial {
-    fn eq(&self, other: &Self) -> bool {
-        self.serial() == other.serial()
-    }
-}
-
-impl Eq for dyn Serial {}
-
-impl PartialOrd for dyn Serial {
-    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-        Some(self.cmp(other))
-    }
-}
-
-impl Ord for dyn Serial {
-    fn cmp(&self, other: &Self) -> Ordering {
-        self.serial().cmp(&other.serial())
-    }
-}
-
-pub trait ProblemPoser {
-    fn pose(&self, problem: &mut ConstraintProblem);
-}
-
-pub trait Element: Serial + ProblemPoser + DisplayItem {
-    // the default identifier for an element of this type
-    fn default_id() -> String where Self: Sized;
-    
-    // the default example of an element of this type
-    fn default(id: String, id_num: u64) -> Self where Self: Sized;
-    
-    // the default regulators that come with this element
-    fn default_regulators(self: Rc<Self>) -> Vec<Rc<dyn Regulator>> {
-        Vec::new()
-    }
-    
-    fn id(&self) -> &String;
-    fn label(&self) -> &String;
-    fn representation(&self) -> Signal<DVector<f64>>;
-    fn ghost(&self) -> Signal<bool>;
-    
-    // the regulators the element is subject to. the assembly that owns the
-    // element is responsible for keeping this set up to date
-    fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>>;
-    
-    // project a representation vector for this kind of element onto its
-    // normalization variety
-    fn project_to_normalized(&self, rep: &mut DVector<f64>);
-    
-    // the configuration matrix column index that was assigned to the element
-    // last time the assembly was realized, or `None` if the element has never
-    // been through a realization
-    fn column_index(&self) -> Option<usize>;
-    
-    // assign the element a configuration matrix column index. this method must
-    // be used carefully to preserve invariant (1), described in the comment on
-    // the `tangent` field of the `Assembly` structure
-    fn set_column_index(&self, index: usize);
-}
-
-impl Debug for dyn Element {
-    fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), fmt::Error> {
-        self.id().fmt(f)
-    }
-}
-
-impl Hash for dyn Element {
-    fn hash<H: Hasher>(&self, state: &mut H) {
-        <dyn Serial>::hash(self, state)
-    }
-}
-
-impl PartialEq for dyn Element {
-    fn eq(&self, other: &Self) -> bool {
-        <dyn Serial>::eq(self, other)
-    }
-}
-
-impl Eq for dyn Element {}
-
-impl PartialOrd for dyn Element {
-    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-        <dyn Serial>::partial_cmp(self, other)
-    }
-}
-
-impl Ord for dyn Element {
-    fn cmp(&self, other: &Self) -> Ordering {
-        <dyn Serial>::cmp(self, other)
-    }
-}
-
-pub struct Sphere {
+#[derive(Clone, PartialEq)]
+pub struct Element {
     pub id: String,
     pub label: String,
-    pub color: ElementColor,
-    pub representation: Signal<DVector<f64>>,
-    pub ghost: Signal<bool>,
-    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
-    serial: u64,
-    column_index: Cell<Option<usize>>,
+    pub color: [f32; 3],
+    pub rep: Signal<DVector<f64>>,
+    pub constraints: Signal<BTreeSet<usize>>,
+    
+    // internal properties, not reflected in any view
+    pub index: usize
 }
 
-impl Sphere {
-    const CURVATURE_COMPONENT: usize = 3;
-    
+impl Element {
     pub fn new(
         id: String,
         label: String,
-        color: ElementColor,
-        representation: DVector<f64>,
-    ) -> Self {
-        Self {
-            id,
-            label,
-            color,
-            representation: create_signal(representation),
-            ghost: create_signal(false),
-            regulators: create_signal(BTreeSet::new()),
-            serial: Self::next_serial(),
-            column_index: None.into(),
+        color: [f32; 3],
+        rep: DVector<f64>
+    ) -> Element {
+        Element {
+            id: id,
+            label: label,
+            color: color,
+            rep: create_signal(rep),
+            constraints: create_signal(BTreeSet::default()),
+            index: 0
         }
     }
 }
+            
 
-impl Element for Sphere {
-    fn default_id() -> String {
-        "sphere".to_string()
-    }
-    
-    fn default(id: String, id_num: u64) -> Self {
-        Self::new(
-            id,
-            format!("Sphere {id_num}"),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            sphere(0.0, 0.0, 0.0, 1.0),
-        )
-    }
-    
-    fn default_regulators(self: Rc<Self>) -> Vec<Rc<dyn Regulator>> {
-        vec![Rc::new(HalfCurvatureRegulator::new(self))]
-    }
-    
-    fn id(&self) -> &String {
-        &self.id
-    }
-    
-    fn label(&self) -> &String {
-        &self.label
-    }
-    
-    fn representation(&self) -> Signal<DVector<f64>> {
-        self.representation
-    }
-    
-    fn ghost(&self) -> Signal<bool> {
-        self.ghost
-    }
-    
-    fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>> {
-        self.regulators
-    }
-    
-    fn project_to_normalized(&self, rep: &mut DVector<f64>) {
-        project_sphere_to_normalized(rep);
-    }
-    
-    fn column_index(&self) -> Option<usize> {
-        self.column_index.get()
-    }
-    
-    fn set_column_index(&self, index: usize) {
-        self.column_index.set(Some(index));
-    }
+#[derive(Clone)]
+pub struct Constraint {
+    pub args: (usize, usize),
+    pub rep: Signal<f64>,
+    pub rep_text: Signal<String>,
+    pub rep_valid: Signal<bool>,
+    pub active: Signal<bool>
 }
 
-impl Serial for Sphere {
-    fn serial(&self) -> u64 {
-        self.serial
-    }
-}
-
-impl ProblemPoser for Sphere {
-    fn pose(&self, problem: &mut ConstraintProblem) {
-        let index = self.column_index().expect(
-            format!("Sphere \"{}\" should be indexed before writing problem data", self.id).as_str()
-        );
-        problem.gram.push_sym(index, index, 1.0);
-        problem.guess.set_column(index, &self.representation.get_clone_untracked());
-    }
-}
-
-pub struct Point {
-    pub id: String,
-    pub label: String,
-    pub color: ElementColor,
-    pub representation: Signal<DVector<f64>>,
-    pub ghost: Signal<bool>,
-    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
-    serial: u64,
-    column_index: Cell<Option<usize>>,
-}
-
-impl Point {
-    const WEIGHT_COMPONENT: usize = 3;
-    
-    pub fn new(
-        id: String,
-        label: String,
-        color: ElementColor,
-        representation: DVector<f64>,
-    ) -> Self {
-        Self {
-            id,
-            label,
-            color,
-            representation: create_signal(representation),
-            ghost: create_signal(false),
-            regulators: create_signal(BTreeSet::new()),
-            serial: Self::next_serial(),
-            column_index: None.into(),
-        }
-    }
-}
-
-impl Element for Point {
-    fn default_id() -> String {
-        "point".to_string()
-    }
-    
-    fn default(id: String, id_num: u64) -> Self {
-        Self::new(
-            id,
-            format!("Point {id_num}"),
-            [0.75_f32, 0.75_f32, 0.75_f32],
-            point(0.0, 0.0, 0.0),
-        )
-    }
-    
-    fn id(&self) -> &String {
-        &self.id
-    }
-    
-    fn label(&self) -> &String {
-        &self.label
-    }
-    
-    fn representation(&self) -> Signal<DVector<f64>> {
-        self.representation
-    }
-    
-    fn ghost(&self) -> Signal<bool> {
-        self.ghost
-    }
-    
-    fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>> {
-        self.regulators
-    }
-    
-    fn project_to_normalized(&self, rep: &mut DVector<f64>) {
-        project_point_to_normalized(rep);
-    }
-    
-    fn column_index(&self) -> Option<usize> {
-        self.column_index.get()
-    }
-    
-    fn set_column_index(&self, index: usize) {
-        self.column_index.set(Some(index));
-    }
-}
-
-impl Serial for Point {
-    fn serial(&self) -> u64 {
-        self.serial
-    }
-}
-
-impl ProblemPoser for Point {
-    fn pose(&self, problem: &mut ConstraintProblem) {
-        let index = self.column_index().expect(
-            format!("Point \"{}\" should be indexed before writing problem data", self.id).as_str()
-        );
-        problem.gram.push_sym(index, index, 0.0);
-        problem.frozen.push(Self::WEIGHT_COMPONENT, index, 0.5);
-        problem.guess.set_column(index, &self.representation.get_clone_untracked());
-    }
-}
-
-pub trait Regulator: Serial + ProblemPoser + OutlineItem {
-    fn subjects(&self) -> Vec<Rc<dyn Element>>;
-    fn measurement(&self) -> ReadSignal<f64>;
-    fn set_point(&self) -> Signal<SpecifiedValue>;
-}
-
-impl Hash for dyn Regulator {
-    fn hash<H: Hasher>(&self, state: &mut H) {
-        <dyn Serial>::hash(self, state)
-    }
-}
-
-impl PartialEq for dyn Regulator {
-    fn eq(&self, other: &Self) -> bool {
-        <dyn Serial>::eq(self, other)
-    }
-}
-
-impl Eq for dyn Regulator {}
-
-impl PartialOrd for dyn Regulator {
-    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-        <dyn Serial>::partial_cmp(self, other)
-    }
-}
-
-impl Ord for dyn Regulator {
-    fn cmp(&self, other: &Self) -> Ordering {
-        <dyn Serial>::cmp(self, other)
-    }
-}
-
-pub struct InversiveDistanceRegulator {
-    pub subjects: [Rc<dyn Element>; 2],
-    pub measurement: ReadSignal<f64>,
-    pub set_point: Signal<SpecifiedValue>,
-    serial: u64,
-}
-
-impl InversiveDistanceRegulator {
-    pub fn new(subjects: [Rc<dyn Element>; 2]) -> Self {
-        let representations = subjects.each_ref().map(|subj| subj.representation());
-        let measurement = create_memo(move || {
-            representations[0].with(|rep_0|
-                representations[1].with(|rep_1|
-                    rep_0.dot(&(&*Q * rep_1))
-                )
-            )
-        });
-        
-        let set_point = create_signal(SpecifiedValue::from_empty_spec());
-        let serial = Self::next_serial();
-        
-        Self { subjects, measurement, set_point, serial }
-    }
-}
-
-impl Regulator for InversiveDistanceRegulator {
-    fn subjects(&self) -> Vec<Rc<dyn Element>> {
-        self.subjects.clone().into()
-    }
-    
-    fn measurement(&self) -> ReadSignal<f64> {
-        self.measurement
-    }
-    
-    fn set_point(&self) -> Signal<SpecifiedValue> {
-        self.set_point
-    }
-}
-
-impl Serial for InversiveDistanceRegulator {
-    fn serial(&self) -> u64 {
-        self.serial
-    }
-}
-
-impl ProblemPoser for InversiveDistanceRegulator {
-    fn pose(&self, problem: &mut ConstraintProblem) {
-        self.set_point.with_untracked(|set_pt| {
-            if let Some(val) = set_pt.value {
-                let [row, col] = self.subjects.each_ref().map(
-                    |subj| subj.column_index().expect(
-                        "Subjects should be indexed before inversive distance regulator writes problem data"
-                    )
-                );
-                problem.gram.push_sym(row, col, val);
-            }
-        });
-    }
-}
-
-pub struct HalfCurvatureRegulator {
-    pub subject: Rc<dyn Element>,
-    pub measurement: ReadSignal<f64>,
-    pub set_point: Signal<SpecifiedValue>,
-    serial: u64,
-}
-
-impl HalfCurvatureRegulator {
-    pub fn new(subject: Rc<dyn Element>) -> Self {
-        let measurement = subject.representation().map(
-            |rep| rep[Sphere::CURVATURE_COMPONENT]
-        );
-        
-        let set_point = create_signal(SpecifiedValue::from_empty_spec());
-        let serial = Self::next_serial();
-        
-        Self { subject, measurement, set_point, serial }
-    }
-}
-
-impl Regulator for HalfCurvatureRegulator {
-    fn subjects(&self) -> Vec<Rc<dyn Element>> {
-        vec![self.subject.clone()]
-    }
-    
-    fn measurement(&self) -> ReadSignal<f64> {
-        self.measurement
-    }
-    
-    fn set_point(&self) -> Signal<SpecifiedValue> {
-        self.set_point
-    }
-}
-
-impl Serial for HalfCurvatureRegulator {
-    fn serial(&self) -> u64 {
-        self.serial
-    }
-}
-
-impl ProblemPoser for HalfCurvatureRegulator {
-    fn pose(&self, problem: &mut ConstraintProblem) {
-        self.set_point.with_untracked(|set_pt| {
-            if let Some(val) = set_pt.value {
-                let col = self.subject.column_index().expect(
-                    "Subject should be indexed before half-curvature regulator writes problem data"
-                );
-                problem.frozen.push(Sphere::CURVATURE_COMPONENT, col, val);
-            }
-        });
-    }
-}
-
-// the velocity is expressed in uniform coordinates
-pub struct ElementMotion<'a> {
-    pub element: Rc<dyn Element>,
-    pub velocity: DVectorView<'a, f64>,
-}
-
-type AssemblyMotion<'a> = Vec<ElementMotion<'a>>;
-
 // a complete, view-independent description of an assembly
 #[derive(Clone)]
 pub struct Assembly {
-    // elements and regulators
-    pub elements: Signal<BTreeSet<Rc<dyn Element>>>,
-    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
-    
-    // solution variety tangent space. the basis vectors are stored in
-    // configuration matrix format, ordered according to the elements' column
-    // indices. when you realize the assembly, every element that's present
-    // during realization gets a column index and is reflected in the tangent
-    // space. since the methods in this module never assign column indices
-    // without later realizing the assembly, we get the following invariant:
-    //
-    //  (1) if an element has a column index, its tangent motions can be found
-    //      in that column of the tangent space basis matrices
-    //
-    pub tangent: Signal<ConfigSubspace>,
+    // elements and constraints
+    pub elements: Signal<Slab<Element>>,
+    pub constraints: Signal<Slab<Constraint>>,
     
     // indexing
-    pub elements_by_id: Signal<BTreeMap<String, Rc<dyn Element>>>,
-    
-    // realization control
-    pub realization_trigger: Signal<()>,
-    
-    // realization diagnostics
-    pub realization_status: Signal<Result<(), String>>,
-    pub descent_history: Signal<DescentHistory>,
+    pub elements_by_id: Signal<FxHashMap<String, usize>>
 }
 
 impl Assembly {
     pub fn new() -> Assembly {
-        // create an assembly
-        let assembly = Assembly {
-            elements: create_signal(BTreeSet::new()),
-            regulators: create_signal(BTreeSet::new()),
-            tangent: create_signal(ConfigSubspace::zero(0)),
-            elements_by_id: create_signal(BTreeMap::default()),
-            realization_trigger: create_signal(()),
-            realization_status: create_signal(Ok(())),
-            descent_history: create_signal(DescentHistory::new()),
-        };
-        
-        // realize the assembly whenever the element list, the regulator list,
-        // a regulator's set point, or the realization trigger is updated
-        let assembly_for_effect = assembly.clone();
-        create_effect(move || {
-            assembly_for_effect.elements.track();
-            assembly_for_effect.regulators.with(
-                |regs| for reg in regs {
-                    reg.set_point().track();
-                }
-            );
-            assembly_for_effect.realization_trigger.track();
-            assembly_for_effect.realize();
-        });
-        
-        assembly
+        Assembly {
+            elements: create_signal(Slab::new()),
+            constraints: create_signal(Slab::new()),
+            elements_by_id: create_signal(FxHashMap::default())
+        }
     }
     
-    // --- inserting elements and regulators ---
+    // --- inserting elements and constraints ---
     
     // insert an element into the assembly without checking whether we already
     // have an element with the same identifier. any element that does have the
     // same identifier will get kicked out of the `elements_by_id` index
-    fn insert_element_unchecked(&self, elt: impl Element + 'static) {
-        // insert the element
-        let id = elt.id().clone();
-        let elt_rc = Rc::new(elt);
-        self.elements.update(|elts| elts.insert(elt_rc.clone()));
-        self.elements_by_id.update(|elts_by_id| elts_by_id.insert(id, elt_rc.clone()));
-        
-        // create and insert the element's default regulators
-        for reg in elt_rc.default_regulators() {
-            self.insert_regulator(reg);
-        }
+    fn insert_element_unchecked(&self, elt: Element) {
+        let id = elt.id.clone();
+        let key = self.elements.update(|elts| elts.insert(elt));
+        self.elements_by_id.update(|elts_by_id| elts_by_id.insert(id, key));
     }
     
-    pub fn try_insert_element(&self, elt: impl Element + 'static) -> bool {
+    pub fn try_insert_element(&self, elt: Element) -> bool {
         let can_insert = self.elements_by_id.with_untracked(
-            |elts_by_id| !elts_by_id.contains_key(elt.id())
+            |elts_by_id| !elts_by_id.contains_key(&elt.id)
         );
         if can_insert {
             self.insert_element_unchecked(elt);
@@ -594,57 +88,36 @@ impl Assembly {
         can_insert
     }
     
-    pub fn insert_element_default<T: Element + 'static>(&self) {
+    pub fn insert_new_element(&self) {
         // find the next unused identifier in the default sequence
-        let default_id = T::default_id();
         let mut id_num = 1;
-        let mut id = format!("{default_id}{id_num}");
+        let mut id = format!("sphere{}", id_num);
         while self.elements_by_id.with_untracked(
             |elts_by_id| elts_by_id.contains_key(&id)
         ) {
             id_num += 1;
-            id = format!("{default_id}{id_num}");
+            id = format!("sphere{}", id_num);
         }
         
-        // create and insert the default example of `T`
-        let _ = self.insert_element_unchecked(T::default(id, id_num));
+        // create and insert a new element
+        self.insert_element_unchecked(
+            Element::new(
+                id,
+                format!("Sphere {}", id_num),
+                [0.75_f32, 0.75_f32, 0.75_f32],
+                DVector::<f64>::from_column_slice(&[0.0, 0.0, 0.0, 0.5, -0.5])
+            )
+        );
     }
     
-    pub fn insert_regulator(&self, regulator: Rc<dyn Regulator>) {
-        // add the regulator to the assembly's regulator list
-        self.regulators.update(
-            |regs| regs.insert(regulator.clone())
+    pub fn insert_constraint(&self, constraint: Constraint) {
+        let args = constraint.args;
+        let key = self.constraints.update(|csts| csts.insert(constraint));
+        let arg_constraints = self.elements.with(
+            |elts| (elts[args.0].constraints, elts[args.1].constraints)
         );
-        
-        // add the regulator to each subject's regulator list
-        let subject_regulators: Vec<_> = regulator.subjects().into_iter().map(
-            |subj| subj.regulators()
-        ).collect();
-        for regulators in subject_regulators {
-            regulators.update(|regs| regs.insert(regulator.clone()));
-        }
-        
-        /* DEBUG */
-        // print an updated list of regulators
-        console_log!("Regulators:");
-        self.regulators.with_untracked(|regs| {
-            for reg in regs.into_iter() {
-                console_log!(
-                    "  {:?}: {}",
-                    reg.subjects(),
-                    reg.set_point().with_untracked(
-                        |set_pt| {
-                            let spec = &set_pt.spec;
-                            if spec.is_empty() {
-                                "__".to_string()
-                            } else {
-                                spec.clone()
-                            }
-                        }
-                    )
-                );
-            }
-        });
+        arg_constraints.0.update(|csts| csts.insert(key));
+        arg_constraints.1.update(|csts| csts.insert(key));
     }
     
     // --- realization ---
@@ -652,248 +125,79 @@ impl Assembly {
     pub fn realize(&self) {
         // index the elements
         self.elements.update_silent(|elts| {
-            for (index, elt) in elts.iter().enumerate() {
-                elt.set_column_index(index);
+            for (index, (_, elt)) in elts.into_iter().enumerate() {
+                elt.index = index;
             }
         });
         
-        // set up the constraint problem
-        let problem = self.elements.with_untracked(|elts| {
-            let mut problem = ConstraintProblem::new(elts.len());
-            for elt in elts {
-                elt.pose(&mut problem);
-            }
-            self.regulators.with_untracked(|regs| {
-                for reg in regs {
-                    reg.pose(&mut problem);
+        // set up the Gram matrix and the initial configuration matrix
+        let (gram, guess) = self.elements.with_untracked(|elts| {
+            // set up the off-diagonal part of the Gram matrix
+            let mut gram_to_be = PartialMatrix::new();
+            self.constraints.with_untracked(|csts| {
+                for (_, cst) in csts {
+                    if cst.active.get_untracked() && cst.rep_valid.get_untracked() {
+                        let args = cst.args;
+                        let row = elts[args.0].index;
+                        let col = elts[args.1].index;
+                        gram_to_be.push_sym(row, col, cst.rep.get_untracked());
+                    }
                 }
             });
-            problem
+            
+            // set up the initial configuration matrix and the diagonal of the
+            // Gram matrix
+            let mut guess_to_be = DMatrix::<f64>::zeros(5, elts.len());
+            for (_, elt) in elts {
+                let index = elt.index;
+                gram_to_be.push_sym(index, index, 1.0);
+                guess_to_be.set_column(index, &elt.rep.get_clone_untracked());
+            }
+            
+            (gram_to_be, guess_to_be)
         });
         
         /* DEBUG */
         // log the Gram matrix
-        console_log!("Gram matrix:\n{}", problem.gram);
+        console::log_1(&JsValue::from("Gram matrix:"));
+        gram.log_to_console();
         
         /* DEBUG */
         // log the initial configuration matrix
-        console_log!("Old configuration:{:>8.3}", problem.guess);
+        console::log_1(&JsValue::from("Old configuration:"));
+        for j in 0..guess.nrows() {
+            let mut row_str = String::new();
+            for k in 0..guess.ncols() {
+                row_str.push_str(format!(" {:>8.3}", guess[(j, k)]).as_str());
+            }
+            console::log_1(&JsValue::from(row_str));
+        }
         
         // look for a configuration with the given Gram matrix
-        let Realization { result, history } = realize_gram(
-            &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
+        let (config, success, history) = realize_gram(
+            &gram, guess, &[],
+            1.0e-12, 0.5, 0.9, 1.1, 200, 110
         );
         
         /* DEBUG */
-        // report the outcome of the search in the browser console
-        if let Err(ref message) = result {
-            console_log!("❌️ {message}");
-        } else {
-            console_log!("✅️ Target accuracy achieved!");
-        }
-        if history.scaled_loss.len() > 0 {
-            console_log!("Steps: {}", history.scaled_loss.len() - 1);
-            console_log!("Loss: {}", history.scaled_loss.last().unwrap());
-        }
-        
-        // report the loss history
-        self.descent_history.set(history);
-        
-        match result {
-            Ok(ConfigNeighborhood { config, nbhd: tangent }) => {
-                /* DEBUG */
-                // report the tangent dimension
-                console_log!("Tangent dimension: {}", tangent.dim());
-                
-                // report the realization status
-                self.realization_status.set(Ok(()));
-                
-                // read out the solution
-                for elt in self.elements.get_clone_untracked() {
-                    elt.representation().update(
-                        |rep| rep.set_column(0, &config.column(elt.column_index().unwrap()))
-                    );
-                }
-                
-                // save the tangent space
-                self.tangent.set_silent(tangent);
-            },
-            Err(message) => {
-                // report the realization status. the `Err(message)` we're
-                // setting the status to has a different type than the
-                // `Err(message)` we received from the match: we're changing the
-                // `Ok` type from `Realization` to `()`
-                self.realization_status.set(Err(message))
-            },
-        }
-    }
-    
-    // --- deformation ---
-    
-    // project the given motion to the tangent space of the solution variety and
-    // move the assembly along it. the implementation is based on invariant (1)
-    // from above and the following additional invariant:
-    //
-    //  (2) if an element is affected by a constraint, it has a column index
-    //
-    // we have this invariant because the assembly gets realized each time you
-    // add a constraint
-    pub fn deform(&self, motion: AssemblyMotion) {
-        /* KLUDGE */
-        // when the tangent space is zero, deformation won't do anything, but
-        // the attempt to deform should be registered in the UI. this console
-        // message will do for now
-        if self.tangent.with(|tan| tan.dim() <= 0 && tan.assembly_dim() > 0) {
-            console::log_1(&JsValue::from("The assembly is rigid"));
-        }
-        
-        // give a column index to each moving element that doesn't have one yet.
-        // this temporarily breaks invariant (1), but the invariant will be
-        // restored when we realize the assembly at the end of the deformation.
-        // in the process, we find out how many matrix columns we'll need to
-        // hold the deformation
-        let realized_dim = self.tangent.with(|tan| tan.assembly_dim());
-        let motion_dim = {
-            let mut next_column_index = realized_dim;
-            for elt_motion in motion.iter() {
-                let moving_elt = &elt_motion.element;
-                if moving_elt.column_index().is_none() {
-                    moving_elt.set_column_index(next_column_index);
-                    next_column_index += 1;
-                }
-            }
-            next_column_index
-        };
-        
-        // project the element motions onto the tangent space of the solution
-        // variety and sum them to get a deformation of the whole assembly. the
-        // matrix `motion_proj` that holds the deformation has extra columns for
-        // any moving elements that aren't reflected in the saved tangent space
-        const ELEMENT_DIM: usize = 5;
-        let mut motion_proj = DMatrix::zeros(ELEMENT_DIM, motion_dim);
-        for elt_motion in motion {
-            // we can unwrap the column index because we know that every moving
-            // element has one at this point
-            let column_index = elt_motion.element.column_index().unwrap();
-            
-            if column_index < realized_dim {
-                // this element had a column index when we started, so by
-                // invariant (1), it's reflected in the tangent space
-                let mut target_columns = motion_proj.columns_mut(0, realized_dim);
-                target_columns += self.tangent.with(
-                    |tan| tan.proj(&elt_motion.velocity, column_index)
-                );
+        // report the outcome of the search
+        console::log_1(&JsValue::from(
+            if success {
+                "Target accuracy achieved!"
             } else {
-                // this element didn't have a column index when we started, so
-                // by invariant (2), it's unconstrained
-                let mut target_column = motion_proj.column_mut(column_index);
-                let unif_to_std = elt_motion.element.representation().with_untracked(
-                    |rep| local_unif_to_std(rep.as_view())
-                );
-                target_column += unif_to_std * elt_motion.velocity;
+                "Failed to reach target accuracy"
             }
-        }
+        ));
+        console::log_2(&JsValue::from("Steps:"), &JsValue::from(history.scaled_loss.len() - 1));
+        console::log_2(&JsValue::from("Loss:"), &JsValue::from(*history.scaled_loss.last().unwrap()));
         
-        // step the assembly along the deformation. this changes the elements'
-        // normalizations, so we restore those afterward
-        for elt in self.elements.get_clone_untracked() {
-            elt.representation().update_silent(|rep| {
-                match elt.column_index() {
-                    Some(column_index) => {
-                        // step the element along the deformation and then
-                        // restore its normalization
-                        *rep += motion_proj.column(column_index);
-                        elt.project_to_normalized(rep);
-                    },
-                    None => {
-                        console_log!("No velocity to unpack for fresh element \"{}\"", elt.id())
-                    },
-                };
-            });
-        }
-        
-        // trigger a realization to bring the configuration back onto the
-        // solution variety. this also gets the elements' column indices and the
-        // saved tangent space back in sync
-        self.realization_trigger.set(());
-    }
-}
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-    
-    use crate::engine;
-    
-    #[test]
-    #[should_panic(expected = "Sphere \"sphere\" should be indexed before writing problem data")]
-    fn unindexed_element_test() {
-        let _ = create_root(|| {
-            let elt = Sphere::default("sphere".to_string(), 0);
-            elt.pose(&mut ConstraintProblem::new(1));
-        });
-    }
-    
-    #[test]
-    #[should_panic(expected = "Subjects should be indexed before inversive distance regulator writes problem data")]
-    fn unindexed_subject_test_inversive_distance() {
-        let _ = create_root(|| {
-            let subjects = [0, 1].map(
-                |k| Rc::new(Sphere::default(format!("sphere{k}"), k)) as Rc<dyn Element>
-            );
-            subjects[0].set_column_index(0);
-            InversiveDistanceRegulator {
-                subjects: subjects,
-                measurement: create_memo(|| 0.0),
-                set_point: create_signal(SpecifiedValue::try_from("0.0".to_string()).unwrap()),
-                serial: InversiveDistanceRegulator::next_serial()
-            }.pose(&mut ConstraintProblem::new(2));
-        });
-    }
-    
-    #[test]
-    fn curvature_drift_test() {
-        const INITIAL_RADIUS: f64 = 0.25;
-        let _ = create_root(|| {
-            // set up an assembly containing a single sphere centered at the
-            // origin
-            let assembly = Assembly::new();
-            let sphere_id = "sphere0";
-            let _ = assembly.try_insert_element(
-                // we create the sphere by hand for two reasons: to choose the
-                // curvature (which can affect drift rate) and to make the test
-                // independent of `Sphere::default`
-                Sphere::new(
-                    String::from(sphere_id),
-                    String::from("Sphere 0"),
-                    [0.75_f32, 0.75_f32, 0.75_f32],
-                    engine::sphere(0.0, 0.0, 0.0, INITIAL_RADIUS),
-                )
-            );
-            
-            // nudge the sphere repeatedly along the `z` axis
-            const STEP_SIZE: f64 = 0.0025;
-            const STEP_CNT: usize = 400;
-            let sphere = assembly.elements_by_id.with(|elts_by_id| elts_by_id[sphere_id].clone());
-            let velocity = DVector::from_column_slice(&[0.0, 0.0, STEP_SIZE, 0.0]);
-            for _ in 0..STEP_CNT {
-                assembly.deform(
-                    vec![
-                        ElementMotion {
-                            element: sphere.clone(),
-                            velocity: velocity.as_view(),
-                        }
-                    ]
+        if success {
+            // read out the solution
+            for (_, elt) in self.elements.get_clone_untracked() {
+                elt.rep.update(
+                    |rep| rep.set_column(0, &config.column(elt.index))
                 );
             }
-            
-            // check how much the sphere's curvature has drifted
-            const INITIAL_HALF_CURV: f64 = 0.5 / INITIAL_RADIUS;
-            const DRIFT_TOL: f64 = 0.015;
-            let final_half_curv = sphere.representation().with_untracked(
-                |rep| rep[Sphere::CURVATURE_COMPONENT]
-            );
-            assert!((final_half_curv / INITIAL_HALF_CURV - 1.0).abs() < DRIFT_TOL);
-        });
+        }
     }
 }
\ No newline at end of file
diff --git a/app-proto/src/components.rs b/app-proto/src/components.rs
deleted file mode 100644
index 7387d58..0000000
--- a/app-proto/src/components.rs
+++ /dev/null
@@ -1,5 +0,0 @@
-pub mod add_remove;
-pub mod diagnostics;
-pub mod display;
-pub mod outline;
-pub mod test_assembly_chooser;
\ No newline at end of file
diff --git a/app-proto/src/components/add_remove.rs b/app-proto/src/components/add_remove.rs
deleted file mode 100644
index 4196640..0000000
--- a/app-proto/src/components/add_remove.rs
+++ /dev/null
@@ -1,69 +0,0 @@
-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 {}
-        }
-    }
-}
\ No newline at end of file
diff --git a/app-proto/src/components/diagnostics.rs b/app-proto/src/components/diagnostics.rs
deleted file mode 100644
index e265982..0000000
--- a/app-proto/src/components/diagnostics.rs
+++ /dev/null
@@ -1,256 +0,0 @@
-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 {} }
-        }
-    }
-}
\ No newline at end of file
diff --git a/app-proto/src/components/display.rs b/app-proto/src/components/display.rs
deleted file mode 100644
index da921dd..0000000
--- a/app-proto/src/components/display.rs
+++ /dev/null
@@ -1,921 +0,0 @@
-use core::array;
-use nalgebra::{DMatrix, DVector, Rotation3, Vector3};
-use std::rc::Rc;
-use sycamore::{prelude::*, motion::create_raf};
-use web_sys::{
-    console,
-    window,
-    KeyboardEvent,
-    MouseEvent,
-    WebGl2RenderingContext,
-    WebGlBuffer,
-    WebGlProgram,
-    WebGlShader,
-    WebGlUniformLocation,
-    wasm_bindgen::{JsCast, JsValue},
-};
-
-use crate::{
-    AppState,
-    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_with_opacity: Vec<ColorWithOpacity>,
-    highlights: Vec<f32>,
-}
-
-impl SceneSpheres {
-    fn new() -> Self {
-        Self {
-            representations: Vec::new(),
-            colors_with_opacity: Vec::new(),
-            highlights: Vec::new(),
-        }
-    }
-    
-    fn len_i32(&self) -> i32 {
-        self.representations.len().try_into().expect("Number of spheres must fit in a 32-bit integer")
-    }
-    
-    fn push(
-        &mut self, representation: DVector<f64>,
-        color: ElementColor, opacity: f32, highlight: f32,
-    ) {
-        self.representations.push(representation);
-        self.colors_with_opacity.push(combine_channels(color, opacity));
-        self.highlights.push(highlight);
-    }
-}
-
-struct ScenePoints {
-    representations: Vec<DVector<f64>>,
-    colors_with_opacity: Vec<ColorWithOpacity>,
-    highlights: Vec<f32>,
-    selections: Vec<f32>,
-}
-
-impl ScenePoints {
-    fn new() -> Self {
-        Self {
-            representations: Vec::new(),
-            colors_with_opacity: Vec::new(),
-            highlights: Vec::new(),
-            selections: Vec::new(),
-        }
-    }
-    
-    fn push(
-        &mut self, representation: DVector<f64>,
-        color: ElementColor, opacity: f32, highlight: f32, selected: bool,
-    ) {
-        self.representations.push(representation);
-        self.colors_with_opacity.push(combine_channels(color, opacity));
-        self.highlights.push(highlight);
-        self.selections.push(if selected { 1.0 } else { 0.0 });
-    }
-}
-
-pub struct Scene {
-    spheres: SceneSpheres,
-    points: ScenePoints,
-}
-
-impl Scene {
-    fn new() -> Self {
-        Self {
-            spheres: SceneSpheres::new(),
-            points: ScenePoints::new(),
-        }
-    }
-}
-
-pub trait DisplayItem {
-    fn show(&self, scene: &mut Scene, selected: bool);
-    
-    // the smallest positive depth, represented as a multiple of `dir`, where
-    // the line generated by `dir` hits the element. returns `None` if the line
-    // misses the element
-    fn cast(
-        &self,
-        dir: Vector3<f64>,
-        assembly_to_world: &DMatrix<f64>,
-        pixel_size: f64,
-    ) -> Option<f64>;
-}
-
-impl DisplayItem for Sphere {
-    fn show(&self, scene: &mut Scene, selected: bool) {
-        /* 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, 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> {
-        // if `a/b` is less than this threshold, we approximate
-        // `a*u^2 + b*u + c` by the linear function `b*u + c`
-        const DEG_THRESHOLD: f64 = 1e-9;
-        
-        let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
-        let a = -rep[3] * dir.norm_squared();
-        let b = rep.rows_range(..3).dot(&dir);
-        let c = -rep[4];
-        
-        let adjust = 4.0*a*c/(b*b);
-        if adjust < 1.0 {
-            // as long as `b` is non-zero, the linear approximation of
-            //
-            //   a*u^2 + b*u + c
-            //
-            // at `u = 0` will reach zero at a finite depth `u_lin`. the root of
-            // the quadratic adjacent to `u_lin` is stored in `lin_root`. if
-            // both roots have the same sign, `lin_root` will be the one closer
-            // to `u = 0`
-            let square_rect_ratio = 1.0 + (1.0 - adjust).sqrt();
-            let lin_root = -(2.0*c)/b / square_rect_ratio;
-            if a.abs() > DEG_THRESHOLD * b.abs() {
-                if lin_root > 0.0 {
-                    Some(lin_root)
-                } else {
-                    let other_root = -b/(2.*a) * square_rect_ratio;
-                    (other_root > 0.0).then_some(other_root)
-                }
-            } else {
-                (lin_root > 0.0).then_some(lin_root)
-            }
-        } else {
-            // the line through `dir` misses the sphere completely
-            None
-        }
-    }
-}
-
-impl DisplayItem for Point {
-    fn show(&self, scene: &mut Scene, selected: bool) {
-        /* SCAFFOLDING */
-        const GHOST_OPACITY: f32 = 0.4;
-        const HIGHLIGHT: f32 = 0.5;
-        
-        let representation = self.representation.get_clone_untracked();
-        let color = if selected { self.color.map(|channel| 0.2 + 0.8*channel) } else { self.color };
-        let opacity = if self.ghost.get() { GHOST_OPACITY } else { 1.0 };
-        let highlight = if selected { 1.0 } else { HIGHLIGHT };
-        scene.points.push(representation, color, opacity, highlight, selected);
-    }
-    
-    /* SCAFFOLDING */
-    fn cast(
-        &self,
-        dir: Vector3<f64>,
-        assembly_to_world: &DMatrix<f64>,
-        pixel_size: f64,
-    ) -> Option<f64> {
-        let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
-        if rep[2] < 0.0 {
-            // this constant should be kept synchronized with `point.frag`
-            const POINT_RADIUS_PX: f64 = 4.0;
-            
-            // find the radius of the point in screen projection units
-            let point_radius_proj = POINT_RADIUS_PX * pixel_size;
-            
-            // find the squared distance between the screen projections of the
-            // ray and the point
-            let dir_proj = -dir.fixed_rows::<2>(0) / dir[2];
-            let rep_proj = -rep.fixed_rows::<2>(0) / rep[2];
-            let dist_sq = (dir_proj - rep_proj).norm_squared();
-            
-            // if the ray hits the point, return its depth
-            if dist_sq < point_radius_proj * point_radius_proj {
-                Some(rep[2] / dir[2])
-            } else {
-                None
-            }
-        } else {
-            None
-        }
-    }
-}
-
-// --- WebGL utilities ---
-
-fn compile_shader(
-    context: &WebGl2RenderingContext,
-    shader_type: u32,
-    source: &str,
-) -> WebGlShader {
-    let shader = context.create_shader(shader_type).unwrap();
-    context.shader_source(&shader, source);
-    context.compile_shader(&shader);
-    shader
-}
-
-fn set_up_program(
-    context: &WebGl2RenderingContext,
-    vertex_shader_source: &str,
-    fragment_shader_source: &str,
-) -> WebGlProgram {
-    // compile the shaders
-    let vertex_shader = compile_shader(
-        &context,
-        WebGl2RenderingContext::VERTEX_SHADER,
-        vertex_shader_source,
-    );
-    let fragment_shader = compile_shader(
-        &context,
-        WebGl2RenderingContext::FRAGMENT_SHADER,
-        fragment_shader_source,
-    );
-    
-    // create the program and attach the shaders
-    let program = context.create_program().unwrap();
-    context.attach_shader(&program, &vertex_shader);
-    context.attach_shader(&program, &fragment_shader);
-    context.link_program(&program);
-    
-    /* DEBUG */
-    // report whether linking succeeded
-    let link_status = context
-        .get_program_parameter(&program, WebGl2RenderingContext::LINK_STATUS)
-        .as_bool()
-        .unwrap();
-    let link_msg = if link_status {
-        "Linked successfully"
-    } else {
-        "Linking failed"
-    };
-    console::log_1(&JsValue::from(link_msg));
-    
-    program
-}
-
-fn get_uniform_array_locations<const N: usize>(
-    context: &WebGl2RenderingContext,
-    program: &WebGlProgram,
-    var_name: &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}]"),
-        };
-        context.get_uniform_location(&program, name.as_str())
-    })
-}
-
-// bind the given vertex buffer object to the given vertex attribute
-fn bind_to_attribute(
-    context: &WebGl2RenderingContext,
-    attr_index: u32,
-    attr_size: i32,
-    buffer: &Option<WebGlBuffer>,
-) {
-    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, buffer.as_ref());
-    context.vertex_attrib_pointer_with_i32(
-        attr_index,
-        attr_size,
-        WebGl2RenderingContext::FLOAT,
-        false, // don't normalize
-        0, // zero stride
-        0, // zero offset
-    );
-}
-
-// load the given data into a new vertex buffer object
-fn load_new_buffer(
-    context: &WebGl2RenderingContext,
-    data: &[f32],
-) -> Option<WebGlBuffer> {
-    // create a buffer and bind it to ARRAY_BUFFER
-    let buffer = context.create_buffer();
-    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, buffer.as_ref());
-    
-    // load the given data into the buffer. this block is unsafe because
-    // `Float32Array::view` creates a raw view into our module's
-    // `WebAssembly.Memory` buffer. allocating more memory will change the
-    // buffer, invalidating the view, so we have to make sure we don't allocate
-    // any memory until the view is dropped. we're okay here because the view is
-    // used as soon as it's created
-    unsafe {
-        context.buffer_data_with_array_buffer_view(
-            WebGl2RenderingContext::ARRAY_BUFFER,
-            &js_sys::Float32Array::view(&data),
-            WebGl2RenderingContext::STATIC_DRAW,
-        );
-    }
-    
-    buffer
-}
-
-fn bind_new_buffer_to_attribute(
-    context: &WebGl2RenderingContext,
-    attr_index: u32,
-    attr_size: i32,
-    data: &[f32],
-) {
-    let buffer = load_new_buffer(context, data);
-    bind_to_attribute(context, attr_index, attr_size, &buffer);
-}
-
-// the direction in camera space that a mouse event is pointing along
-fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
-    let target: web_sys::Element = event.target().unwrap().unchecked_into();
-    let rect = target.get_bounding_client_rect();
-    let width = rect.width();
-    let height = rect.height();
-    let shortdim = width.min(height);
-    
-    // this constant should be kept synchronized with `spheres.frag` and
-    // `point.vert`
-    const FOCAL_SLOPE: f64 = 0.3;
-    
-    (
-        Vector3::new(
-            FOCAL_SLOPE * (2.0*(f64::from(event.client_x()) - rect.left()) - width) / shortdim,
-            FOCAL_SLOPE * (2.0*(rect.bottom() - f64::from(event.client_y())) - height) / shortdim,
-            -1.0,
-        ),
-        FOCAL_SLOPE * 2.0 / shortdim,
-    )
-}
-
-// --- display component ---
-
-#[component]
-pub fn Display() -> View {
-    let state = use_context::<AppState>();
-    
-    // canvas
-    let display = create_node_ref();
-    
-    // viewpoint
-    let assembly_to_world = create_signal(DMatrix::<f64>::identity(5, 5));
-    
-    // navigation
-    let pitch_up = create_signal(0.0);
-    let pitch_down = create_signal(0.0);
-    let yaw_right = create_signal(0.0);
-    let yaw_left = create_signal(0.0);
-    let roll_ccw = create_signal(0.0);
-    let roll_cw = create_signal(0.0);
-    let zoom_in = create_signal(0.0);
-    let zoom_out = create_signal(0.0);
-    let turntable = create_signal(false); /* BENCHMARKING */
-    
-    // manipulation
-    let translate_neg_x = create_signal(0.0);
-    let translate_pos_x = create_signal(0.0);
-    let translate_neg_y = create_signal(0.0);
-    let translate_pos_y = create_signal(0.0);
-    let translate_neg_z = create_signal(0.0);
-    let translate_pos_z = create_signal(0.0);
-    let shrink_neg = create_signal(0.0);
-    let shrink_pos = create_signal(0.0);
-    
-    // change listener
-    let scene_changed = create_signal(true);
-    create_effect(move || {
-        state.assembly.elements.with(|elts| {
-            for elt in elts {
-                elt.representation().track();
-                elt.ghost().track();
-            }
-        });
-        state.selection.track();
-        scene_changed.set(true);
-    });
-    
-    /* INSTRUMENTS */
-    const SAMPLE_PERIOD: i32 = 60;
-    let mut last_sample_time = 0.0;
-    let mut frames_since_last_sample = 0;
-    let mean_frame_interval = create_signal(0.0);
-    
-    let assembly_for_raf = state.assembly.clone();
-    on_mount(move || {
-        // timing
-        let mut last_time = 0.0;
-        
-        // viewpoint
-        const ROT_SPEED: f64 = 0.4; // in radians per second
-        const ZOOM_SPEED: f64 = 0.15; // multiplicative rate per second
-        const TURNTABLE_SPEED: f64 = 0.1; /* BENCHMARKING */
-        let mut orientation = DMatrix::<f64>::identity(5, 5);
-        let mut rotation = DMatrix::<f64>::identity(5, 5);
-        let mut location_z: f64 = 5.0;
-        
-        // manipulation
-        const TRANSLATION_SPEED: f64 = 0.15; // in length units per second
-        const SHRINKING_SPEED: f64 = 0.15; // in length units per second
-        
-        // display parameters
-        const LAYER_THRESHOLD: i32 = 0; /* DEBUG */
-        const DEBUG_MODE: i32 = 0; /* DEBUG */
-        
-        /* INSTRUMENTS */
-        let performance = window().unwrap().performance().unwrap();
-        
-        // get the display canvas
-        let canvas = display.get().unchecked_into::<web_sys::HtmlCanvasElement>();
-        let ctx = canvas
-            .get_context("webgl2")
-            .unwrap()
-            .unwrap()
-            .dyn_into::<WebGl2RenderingContext>()
-            .unwrap();
-        
-        // disable depth testing
-        ctx.disable(WebGl2RenderingContext::DEPTH_TEST);
-        
-        // set blend mode
-        ctx.enable(WebGl2RenderingContext::BLEND);
-        ctx.blend_func(WebGl2RenderingContext::SRC_ALPHA, WebGl2RenderingContext::ONE_MINUS_SRC_ALPHA);
-        
-        // set up the sphere rendering program
-        let sphere_program = set_up_program(
-            &ctx,
-            include_str!("identity.vert"),
-            include_str!("spheres.frag"),
-        );
-        
-        // set up the point rendering program
-        let point_program = set_up_program(
-            &ctx,
-            include_str!("point.vert"),
-            include_str!("point.frag"),
-        );
-        
-        /* DEBUG */
-        // print the maximum number of vectors that can be passed as
-        // uniforms to a fragment shader. the OpenGL ES 3.0 standard
-        // requires this maximum to be at least 224, as discussed in the
-        // documentation of the GL_MAX_FRAGMENT_UNIFORM_VECTORS parameter
-        // here:
-        //
-        //   https://registry.khronos.org/OpenGL-Refpages/es3.0/html/glGet.xhtml
-        //
-        // there are also other size limits. for example, on Aaron's
-        // machine, the the length of a float or genType array seems to be
-        // capped at 1024 elements
-        console::log_2(
-            &ctx.get_parameter(WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
-            &JsValue::from("uniform vectors available"),
-        );
-        
-        // find the sphere program's vertex attribute
-        let viewport_position_attr = ctx.get_attrib_location(&sphere_program, "position") as u32;
-        
-        // find the sphere program's uniforms
-        const SPHERE_MAX: usize = 200;
-        let sphere_cnt_loc = ctx.get_uniform_location(&sphere_program, "sphere_cnt");
-        let sphere_sp_locs = get_uniform_array_locations::<SPHERE_MAX>(
-            &ctx, &sphere_program, "sphere_list", Some("sp")
-        );
-        let sphere_lt_locs = get_uniform_array_locations::<SPHERE_MAX>(
-            &ctx, &sphere_program, "sphere_list", Some("lt")
-        );
-        let sphere_color_locs = get_uniform_array_locations::<SPHERE_MAX>(
-            &ctx, &sphere_program, "color_list", None
-        );
-        let sphere_highlight_locs = get_uniform_array_locations::<SPHERE_MAX>(
-            &ctx, &sphere_program, "highlight_list", None
-        );
-        let resolution_loc = ctx.get_uniform_location(&sphere_program, "resolution");
-        let shortdim_loc = ctx.get_uniform_location(&sphere_program, "shortdim");
-        let layer_threshold_loc = ctx.get_uniform_location(&sphere_program, "layer_threshold");
-        let debug_mode_loc = ctx.get_uniform_location(&sphere_program, "debug_mode");
-        
-        // load the viewport vertex positions into a new vertex buffer object
-        const VERTEX_CNT: usize = 6;
-        let viewport_positions: [f32; 3*VERTEX_CNT] = [
-            // northwest triangle
-            -1.0, -1.0, 0.0,
-            -1.0,  1.0, 0.0,
-             1.0,  1.0, 0.0,
-            // southeast triangle
-            -1.0, -1.0, 0.0,
-             1.0,  1.0, 0.0,
-             1.0, -1.0, 0.0,
-        ];
-        let viewport_position_buffer = load_new_buffer(&ctx, &viewport_positions);
-        
-        // find the point program's vertex attributes
-        let point_position_attr = ctx.get_attrib_location(&point_program, "position") as u32;
-        let point_color_attr = ctx.get_attrib_location(&point_program, "color") as u32;
-        let point_highlight_attr = ctx.get_attrib_location(&point_program, "highlight") as u32;
-        let point_selection_attr = ctx.get_attrib_location(&point_program, "selected") as u32;
-        
-        // set up a repainting routine
-        let (_, start_animation_loop, _) = create_raf(move || {
-            // get the time step
-            let time = performance.now();
-            let time_step = 0.001*(time - last_time);
-            last_time = time;
-            
-            // get the navigation state
-            let pitch_up_val = pitch_up.get();
-            let pitch_down_val = pitch_down.get();
-            let yaw_right_val = yaw_right.get();
-            let yaw_left_val = yaw_left.get();
-            let roll_ccw_val = roll_ccw.get();
-            let roll_cw_val = roll_cw.get();
-            let zoom_in_val = zoom_in.get();
-            let zoom_out_val = zoom_out.get();
-            let turntable_val = turntable.get(); /* BENCHMARKING */
-            
-            // get the manipulation state
-            let translate_neg_x_val = translate_neg_x.get();
-            let translate_pos_x_val = translate_pos_x.get();
-            let translate_neg_y_val = translate_neg_y.get();
-            let translate_pos_y_val = translate_pos_y.get();
-            let translate_neg_z_val = translate_neg_z.get();
-            let translate_pos_z_val = translate_pos_z.get();
-            let shrink_neg_val = shrink_neg.get();
-            let shrink_pos_val = shrink_pos.get();
-            
-            // update the assembly's orientation
-            let ang_vel = {
-                let pitch = pitch_up_val - pitch_down_val;
-                let yaw = yaw_right_val - yaw_left_val;
-                let roll = roll_ccw_val - roll_cw_val;
-                if pitch != 0.0 || yaw != 0.0 || roll != 0.0 {
-                    ROT_SPEED * Vector3::new(-pitch, yaw, roll).normalize()
-                } else {
-                    Vector3::zeros()
-                }
-            } /* BENCHMARKING */ + if turntable_val {
-                Vector3::new(0.0, TURNTABLE_SPEED, 0.0)
-            } else {
-                Vector3::zeros()
-            };
-            let mut rotation_sp = rotation.fixed_view_mut::<3, 3>(0, 0);
-            rotation_sp.copy_from(
-                Rotation3::from_scaled_axis(time_step * ang_vel).matrix()
-            );
-            orientation = &rotation * &orientation;
-            
-            // update the assembly's location
-            let zoom = zoom_out_val - zoom_in_val;
-            location_z *= (time_step * ZOOM_SPEED * zoom).exp();
-            
-            // manipulate the assembly
-            if state.selection.with(|sel| sel.len() == 1) {
-                let sel = state.selection.with(
-                    |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;
-                let translate_z = translate_pos_z_val - translate_neg_z_val;
-                let shrink = shrink_pos_val - shrink_neg_val;
-                let translating =
-                    translate_x != 0.0
-                    || translate_y != 0.0
-                    || translate_z != 0.0;
-                if translating || shrink != 0.0 {
-                    let elt_motion = {
-                        let u = if translating {
-                            TRANSLATION_SPEED * Vector3::new(
-                                translate_x, translate_y, translate_z
-                            ).normalize()
-                        } else {
-                            Vector3::zeros()
-                        };
-                        time_step * DVector::from_column_slice(
-                            &[u[0], u[1], u[2], SHRINKING_SPEED * shrink]
-                        )
-                    };
-                    assembly_for_raf.deform(
-                        vec![
-                            ElementMotion {
-                                element: sel,
-                                velocity: elt_motion.as_view(),
-                            }
-                        ]
-                    );
-                    scene_changed.set(true);
-                }
-            }
-            
-            if scene_changed.get() {
-                const SPACE_DIM: usize = 3;
-                const COLOR_SIZE: usize = 3;
-                
-                /* INSTRUMENTS */
-                // measure mean frame interval
-                frames_since_last_sample += 1;
-                if frames_since_last_sample >= SAMPLE_PERIOD {
-                    mean_frame_interval.set((time - last_sample_time) / (SAMPLE_PERIOD as f64));
-                    last_sample_time = time;
-                    frames_since_last_sample = 0;
-                }
-                
-                // --- get the assembly ---
-                
-                let mut scene = Scene::new();
-                
-                // find the map from assembly space to world space
-                let location = {
-                    let u = -location_z;
-                    DMatrix::from_column_slice(5, 5, &[
-                        1.0, 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,   u,
-                        0.0, 0.0, 2.0*u, 1.0, u*u,
-                        0.0, 0.0,   0.0, 0.0, 1.0,
-                    ])
-                };
-                let asm_to_world = &location * &orientation;
-                
-                // set up the scene
-                state.assembly.elements.with_untracked(
-                    |elts| for elt in elts {
-                        let selected = state.selection.with(|sel| sel.contains(elt));
-                        elt.show(&mut scene, selected);
-                    }
-                );
-                let sphere_cnt = scene.spheres.len_i32();
-                
-                // --- draw the spheres ---
-                
-                // use the sphere rendering program
-                ctx.use_program(Some(&sphere_program));
-                
-                // enable the sphere program's vertex attribute
-                ctx.enable_vertex_attrib_array(viewport_position_attr);
-                
-                // write the spheres in world coordinates
-                let sphere_reps_world: Vec<_> = scene.spheres.representations.into_iter().map(
-                    |rep| (&asm_to_world * rep).cast::<f32>()
-                ).collect();
-                
-                // set the resolution
-                let width = canvas.width() as f32;
-                let height = canvas.height() as f32;
-                ctx.uniform2f(resolution_loc.as_ref(), width, height);
-                ctx.uniform1f(shortdim_loc.as_ref(), width.min(height));
-                
-                // pass the scene data
-                ctx.uniform1i(sphere_cnt_loc.as_ref(), sphere_cnt);
-                for n in 0..sphere_reps_world.len() {
-                    let v = &sphere_reps_world[n];
-                    ctx.uniform3fv_with_f32_array(
-                        sphere_sp_locs[n].as_ref(),
-                        v.rows(0, 3).as_slice(),
-                    );
-                    ctx.uniform2fv_with_f32_array(
-                        sphere_lt_locs[n].as_ref(),
-                        v.rows(3, 2).as_slice(),
-                    );
-                    ctx.uniform4fv_with_f32_array(
-                        sphere_color_locs[n].as_ref(),
-                        &scene.spheres.colors_with_opacity[n],
-                    );
-                    ctx.uniform1f(
-                        sphere_highlight_locs[n].as_ref(),
-                        scene.spheres.highlights[n],
-                    );
-                }
-                
-                // pass the display parameters
-                ctx.uniform1i(layer_threshold_loc.as_ref(), LAYER_THRESHOLD);
-                ctx.uniform1i(debug_mode_loc.as_ref(), DEBUG_MODE);
-                
-                // bind the viewport vertex position buffer to the position
-                // attribute in the vertex shader
-                bind_to_attribute(&ctx, viewport_position_attr, SPACE_DIM as i32, &viewport_position_buffer);
-                
-                // draw the scene
-                ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
-                
-                // disable the sphere program's vertex attribute
-                ctx.disable_vertex_attrib_array(viewport_position_attr);
-                
-                // --- draw the points ---
-                
-                if !scene.points.representations.is_empty() {
-                    // use the point rendering program
-                    ctx.use_program(Some(&point_program));
-                    
-                    // enable the point program's vertex attributes
-                    ctx.enable_vertex_attrib_array(point_position_attr);
-                    ctx.enable_vertex_attrib_array(point_color_attr);
-                    ctx.enable_vertex_attrib_array(point_highlight_attr);
-                    ctx.enable_vertex_attrib_array(point_selection_attr);
-                    
-                    // write the points in world coordinates
-                    let asm_to_world_sp = asm_to_world.rows(0, SPACE_DIM);
-                    let point_positions = DMatrix::from_columns(
-                        &scene.points.representations.into_iter().map(
-                            |rep| &asm_to_world_sp * rep
-                        ).collect::<Vec<_>>().as_slice()
-                    ).cast::<f32>();
-                    
-                    // load the point positions and colors into new buffers and
-                    // bind them to the corresponding attributes in the vertex
-                    // shader
-                    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 + 1) as i32, scene.points.colors_with_opacity.concat().as_slice());
-                    bind_new_buffer_to_attribute(&ctx, point_highlight_attr, 1 as i32, scene.points.highlights.as_slice());
-                    bind_new_buffer_to_attribute(&ctx, point_selection_attr, 1 as i32, scene.points.selections.as_slice());
-                    
-                    // draw the scene
-                    ctx.draw_arrays(WebGl2RenderingContext::POINTS, 0, point_positions.ncols() as i32);
-                    
-                    // disable the point program's vertex attributes
-                    ctx.disable_vertex_attrib_array(point_position_attr);
-                    ctx.disable_vertex_attrib_array(point_color_attr);
-                    ctx.disable_vertex_attrib_array(point_highlight_attr);
-                    ctx.disable_vertex_attrib_array(point_selection_attr);
-                }
-                
-                // --- update the display state ---
-                
-                // update the viewpoint
-                assembly_to_world.set(asm_to_world);
-                
-                // clear the scene change flag
-                scene_changed.set(
-                    pitch_up_val != 0.0
-                    || pitch_down_val != 0.0
-                    || yaw_left_val != 0.0
-                    || yaw_right_val != 0.0
-                    || roll_cw_val != 0.0
-                    || roll_ccw_val != 0.0
-                    || zoom_in_val != 0.0
-                    || zoom_out_val != 0.0
-                    || turntable_val /* BENCHMARKING */
-                );
-            } else {
-                frames_since_last_sample = 0;
-                mean_frame_interval.set(-1.0);
-            }
-        });
-        start_animation_loop();
-    });
-    
-    let set_nav_signal = move |event: &KeyboardEvent, value: f64| {
-        let mut navigating = true;
-        let shift = event.shift_key();
-        match event.key().as_str() {
-            "ArrowUp" if shift => zoom_in.set(value),
-            "ArrowDown" if shift => zoom_out.set(value),
-            "ArrowUp" => pitch_up.set(value),
-            "ArrowDown" => pitch_down.set(value),
-            "ArrowRight" if shift => roll_cw.set(value),
-            "ArrowLeft" if shift => roll_ccw.set(value),
-            "ArrowRight" => yaw_right.set(value),
-            "ArrowLeft" => yaw_left.set(value),
-            _ => navigating = false,
-        };
-        if navigating {
-            scene_changed.set(true);
-            event.prevent_default();
-        }
-    };
-    
-    let set_manip_signal = move |event: &KeyboardEvent, value: f64| {
-        let mut manipulating = true;
-        let shift = event.shift_key();
-        match event.key().as_str() {
-            "d" | "D" => translate_pos_x.set(value),
-            "a" | "A" => translate_neg_x.set(value),
-            "w" | "W" if shift => translate_neg_z.set(value),
-            "s" | "S" if shift => translate_pos_z.set(value),
-            "w" | "W" => translate_pos_y.set(value),
-            "s" | "S" => translate_neg_y.set(value),
-            "]" | "}" => shrink_neg.set(value),
-            "[" | "{" => shrink_pos.set(value),
-            _ => manipulating = false,
-        };
-        if manipulating {
-            event.prevent_default();
-        }
-    };
-    
-    view! {
-        /* TO DO */
-        // switch back to integer-valued parameters when that becomes possible
-        // again
-        canvas(
-            ref = display,
-            id = "display",
-            width = "600",
-            height = "600",
-            tabindex = "0",
-            on:keydown = move |event: KeyboardEvent| {
-                if event.key() == "Shift" {
-                    // swap navigation inputs
-                    roll_cw.set(yaw_right.get());
-                    roll_ccw.set(yaw_left.get());
-                    zoom_in.set(pitch_up.get());
-                    zoom_out.set(pitch_down.get());
-                    yaw_right.set(0.0);
-                    yaw_left.set(0.0);
-                    pitch_up.set(0.0);
-                    pitch_down.set(0.0);
-                    
-                    // swap manipulation inputs
-                    translate_pos_z.set(translate_neg_y.get());
-                    translate_neg_z.set(translate_pos_y.get());
-                    translate_pos_y.set(0.0);
-                    translate_neg_y.set(0.0);
-                } else {
-                    if event.key() == "Enter" { /* BENCHMARKING */
-                        turntable.set_fn(|turn| !turn);
-                        scene_changed.set(true);
-                    }
-                    set_nav_signal(&event, 1.0);
-                    set_manip_signal(&event, 1.0);
-                }
-            },
-            on:keyup = move |event: KeyboardEvent| {
-                if event.key() == "Shift" {
-                    // swap navigation inputs
-                    yaw_right.set(roll_cw.get());
-                    yaw_left.set(roll_ccw.get());
-                    pitch_up.set(zoom_in.get());
-                    pitch_down.set(zoom_out.get());
-                    roll_cw.set(0.0);
-                    roll_ccw.set(0.0);
-                    zoom_in.set(0.0);
-                    zoom_out.set(0.0);
-                    
-                    // swap manipulation inputs
-                    translate_pos_y.set(translate_neg_z.get());
-                    translate_neg_y.set(translate_pos_z.get());
-                    translate_pos_z.set(0.0);
-                    translate_neg_z.set(0.0);
-                } else {
-                    set_nav_signal(&event, 0.0);
-                    set_manip_signal(&event, 0.0);
-                }
-            },
-            on:blur = move |_| {
-                pitch_up.set(0.0);
-                pitch_down.set(0.0);
-                yaw_right.set(0.0);
-                yaw_left.set(0.0);
-                roll_ccw.set(0.0);
-                roll_cw.set(0.0);
-            },
-            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<(Rc<dyn Element>, f64)> = None;
-                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((elt, depth))
-                                }
-                            },
-                            None => clicked = Some((elt, depth)),
-                        },
-                        None => (),
-                    };
-                }
-                
-                // if we clicked something, select it
-                match clicked {
-                    Some((elt, _)) => state.select(&elt, event.shift_key()),
-                    None => state.selection.update(|sel| sel.clear()),
-                };
-            },
-        )
-    }
-}
\ No newline at end of file
diff --git a/app-proto/src/components/outline.rs b/app-proto/src/components/outline.rs
deleted file mode 100644
index 5355042..0000000
--- a/app-proto/src/components/outline.rs
+++ /dev/null
@@ -1,260 +0,0 @@
-use itertools::Itertools;
-use std::rc::Rc;
-use sycamore::prelude::*;
-use web_sys::{KeyboardEvent, MouseEvent, wasm_bindgen::JsCast};
-
-use crate::{
-    AppState,
-    assembly::{
-        Element,
-        HalfCurvatureRegulator,
-        InversiveDistanceRegulator,
-        Regulator,
-    },
-    specified::SpecifiedValue
-};
-
-// an editable view of a regulator
-#[component(inline_props)]
-fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
-    // get the regulator's measurement and set point signals
-    let measurement = regulator.measurement();
-    let set_point = regulator.set_point();
-    
-    // the `valid` signal tracks whether the last entered value is a valid set
-    // point specification
-    let valid = create_signal(true);
-    
-    // the `value` signal holds the current set point specification
-    let value = create_signal(
-        set_point.with_untracked(|set_pt| set_pt.spec.clone())
-    );
-    
-    // this `reset_value` closure resets the input value to the regulator's set
-    // point specification
-    let reset_value = move || {
-        batch(|| {
-            valid.set(true);
-            value.set(set_point.with(|set_pt| set_pt.spec.clone()));
-        })
-    };
-    
-    // reset the input value whenever the regulator's set point specification
-    // is updated
-    create_effect(reset_value);
-    
-    view! {
-        input(
-            r#type = "text",
-            class = move || {
-                if valid.get() {
-                    set_point.with(|set_pt| {
-                        if set_pt.is_present() {
-                            "regulator-input constraint"
-                        } else {
-                            "regulator-input"
-                        }
-                    })
-                } else {
-                    "regulator-input invalid"
-                }
-            },
-            placeholder = measurement.with(|result| result.to_string()),
-            bind:value = value,
-            on:change = move |_| {
-                valid.set(
-                    match SpecifiedValue::try_from(value.get_clone_untracked()) {
-                        Ok(set_pt) => {
-                            set_point.set(set_pt);
-                            true
-                        },
-                        Err(_) => false,
-                    }
-                )
-            },
-            on:keydown = {
-                move |event: KeyboardEvent| {
-                    match event.key().as_str() {
-                        "Escape" => reset_value(),
-                        _ => (),
-                    }
-                }
-            },
-        )
-    }
-}
-
-pub trait OutlineItem {
-    fn outline_item(self: Rc<Self>, element: &Rc<dyn Element>) -> View;
-}
-
-impl OutlineItem for InversiveDistanceRegulator {
-    fn outline_item(self: Rc<Self>, element: &Rc<dyn Element>) -> View {
-        let other_subject_label = if self.subjects[0] == element.clone() {
-            self.subjects[1].label()
-        } else {
-            self.subjects[0].label()
-        }.clone();
-        view! {
-            li(class = "regulator") {
-                div(class = "regulator-label") { (other_subject_label) }
-                div(class = "regulator-type") { "Inversive distance" }
-                RegulatorInput(regulator = self)
-                div(class = "status")
-            }
-        }
-    }
-}
-
-impl OutlineItem for HalfCurvatureRegulator {
-    fn outline_item(self: Rc<Self>, _element: &Rc<dyn Element>) -> View {
-        view! {
-            li(class = "regulator") {
-                div(class = "regulator-label") // for spacing
-                div(class = "regulator-type") { "Half-curvature" }
-                RegulatorInput(regulator = self)
-                div(class = "status")
-            }
-        }
-    }
-}
-
-// a list item that shows an element in an outline view of an assembly
-#[component(inline_props)]
-fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
-    let state = use_context::<AppState>();
-    let class = {
-        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 || {
-        representation.with(
-            |rep| rep.iter().map(
-                |u| {
-                    let u_str = format!("{:.3}", u).replace("-", "\u{2212}");
-                    view! { div { (u_str) } }
-                }
-            ).collect::<Vec<_>>()
-        )
-    };
-    let regulated = element.regulators().map(|regs| regs.len() > 0);
-    let regulator_list = element.regulators().map(
-        |regs| regs
-            .clone()
-            .into_iter()
-            .sorted_by_key(|reg| reg.subjects().len())
-            .collect::<Vec<_>>()
-    );
-    let details_node = create_node_ref();
-    view! {
-        li {
-            details(ref = details_node) {
-                summary(
-                    class = class.get(),
-                    on:keydown = {
-                        let element_for_handler = element.clone();
-                        move |event: KeyboardEvent| {
-                            match event.key().as_str() {
-                                "Enter" => {
-                                    state.select(&element_for_handler, event.shift_key());
-                                    event.prevent_default();
-                                },
-                                "ArrowRight" if regulated.get() => {
-                                    let _ = details_node
-                                        .get()
-                                        .unchecked_into::<web_sys::Element>()
-                                        .set_attribute("open", "");
-                                },
-                                "ArrowLeft" => {
-                                    let _ = details_node
-                                        .get()
-                                        .unchecked_into::<web_sys::Element>()
-                                        .remove_attribute("open");
-                                },
-                                _ => (),
-                            }
-                        }
-                    }
-                ) {
-                    div(
-                        class = "element-switch",
-                        on:click = |event: MouseEvent| event.stop_propagation()
-                    )
-                    div(
-                        class = "element",
-                        on:click = {
-                            let state_for_handler = state.clone();
-                            let element_for_handler = element.clone();
-                            move |event: MouseEvent| {
-                                state_for_handler.select(&element_for_handler, event.shift_key());
-                                event.stop_propagation();
-                                event.prevent_default();
-                            }
-                        }
-                    ) {
-                        div(class = "element-label") { (label) }
-                        div(class = "element-representation") { (rep_components) }
-                        input(
-                            r#type = "checkbox",
-                            bind:checked = element.ghost(),
-                            on:click = |event: MouseEvent| event.stop_propagation()
-                        )
-                    }
-                }
-                ul(class = "regulators") {
-                    Keyed(
-                        list = regulator_list,
-                        view = move |reg| reg.outline_item(&element),
-                        key = |reg| reg.serial()
-                    )
-                }
-            }
-        }
-    }
-}
-
-// a component that lists the elements of the current assembly, showing each
-// element's regulators in a collapsible sub-list. its implementation is based
-// on Kate Morley's HTML + CSS tree views:
-//
-//   https://iamkate.com/code/tree-views/
-//
-#[component]
-pub fn Outline() -> View {
-    let state = use_context::<AppState>();
-    
-    // list the elements alphabetically by ID
-    /* TO DO */
-    // this code is designed to generalize easily to other sort keys. if we only
-    // 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())
-            .collect::<Vec<_>>()
-    );
-    
-    view! {
-        ul(
-            id = "outline",
-            on:click = {
-                let state = use_context::<AppState>();
-                move |_| state.selection.update(|sel| sel.clear())
-            }
-        ) {
-            Keyed(
-                list = element_list,
-                view = |elt| view! {
-                    ElementOutlineItem(element = elt)
-                },
-                key = |elt| elt.serial()
-            )
-        }
-    }
-}
\ No newline at end of file
diff --git a/app-proto/src/components/point.frag b/app-proto/src/components/point.frag
deleted file mode 100644
index 194a072..0000000
--- a/app-proto/src/components/point.frag
+++ /dev/null
@@ -1,19 +0,0 @@
-#version 300 es
-
-precision highp float;
-
-in vec4 point_color;
-in float point_highlight;
-in float total_radius;
-
-out vec4 outColor;
-
-void main() {
-    float r = total_radius * length(2.*gl_PointCoord - vec2(1.));
-    
-    const float POINT_RADIUS = 4.;
-    float border = smoothstep(POINT_RADIUS - 1., POINT_RADIUS, r);
-    float disk = 1. - smoothstep(total_radius - 1., total_radius, r);
-    vec4 color = mix(point_color, vec4(1.), border * point_highlight);
-    outColor = vec4(vec3(1.), disk) * color;
-}
\ No newline at end of file
diff --git a/app-proto/src/components/point.vert b/app-proto/src/components/point.vert
deleted file mode 100644
index 0b76bc1..0000000
--- a/app-proto/src/components/point.vert
+++ /dev/null
@@ -1,24 +0,0 @@
-#version 300 es
-
-in vec4 position;
-in vec4 color;
-in float highlight;
-in float selected;
-
-out vec4 point_color;
-out float point_highlight;
-out float total_radius;
-
-// camera
-const float focal_slope = 0.3;
-
-void main() {
-    total_radius = 5. + 0.5*selected;
-    
-    float depth = -focal_slope * position.z;
-    gl_Position = vec4(position.xy / depth, 0., 1.);
-    gl_PointSize = 2.*total_radius;
-    
-    point_color = color;
-    point_highlight = highlight;
-}
\ No newline at end of file
diff --git a/app-proto/src/components/test_assembly_chooser.rs b/app-proto/src/components/test_assembly_chooser.rs
deleted file mode 100644
index 0d387d3..0000000
--- a/app-proto/src/components/test_assembly_chooser.rs
+++ /dev/null
@@ -1,941 +0,0 @@
-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" }
-        }
-    }
-}
\ No newline at end of file
diff --git a/app-proto/src/display.rs b/app-proto/src/display.rs
new file mode 100644
index 0000000..ce1655d
--- /dev/null
+++ b/app-proto/src/display.rs
@@ -0,0 +1,464 @@
+use core::array;
+use nalgebra::{DMatrix, Rotation3, Vector3};
+use sycamore::{prelude::*, motion::create_raf};
+use web_sys::{
+    console,
+    window,
+    KeyboardEvent,
+    WebGl2RenderingContext,
+    WebGlProgram,
+    WebGlShader,
+    WebGlUniformLocation,
+    wasm_bindgen::{JsCast, JsValue}
+};
+
+use crate::AppState;
+
+fn compile_shader(
+    context: &WebGl2RenderingContext,
+    shader_type: u32,
+    source: &str,
+) -> WebGlShader {
+    let shader = context.create_shader(shader_type).unwrap();
+    context.shader_source(&shader, source);
+    context.compile_shader(&shader);
+    shader
+}
+
+fn get_uniform_array_locations<const N: usize>(
+    context: &WebGl2RenderingContext,
+    program: &WebGlProgram,
+    var_name: &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}]")
+        };
+        context.get_uniform_location(&program, name.as_str())
+    })
+}
+
+// load the given data into the vertex input of the given name
+fn bind_vertex_attrib(
+    context: &WebGl2RenderingContext,
+    index: u32,
+    size: i32,
+    data: &[f32]
+) {
+    // create a data buffer and bind it to ARRAY_BUFFER
+    let buffer = context.create_buffer().unwrap();
+    context.bind_buffer(WebGl2RenderingContext::ARRAY_BUFFER, Some(&buffer));
+    
+    // load the given data into the buffer. the function `Float32Array::view`
+    // creates a raw view into our module's `WebAssembly.Memory` buffer.
+    // allocating more memory will change the buffer, invalidating the view.
+    // that means we have to make sure we don't allocate any memory until the
+    // view is dropped
+    unsafe {
+        context.buffer_data_with_array_buffer_view(
+            WebGl2RenderingContext::ARRAY_BUFFER,
+            &js_sys::Float32Array::view(&data),
+            WebGl2RenderingContext::STATIC_DRAW,
+        );
+    }
+    
+    // allow the target attribute to be used
+    context.enable_vertex_attrib_array(index);
+    
+    // take whatever's bound to ARRAY_BUFFER---here, the data buffer created
+    // above---and bind it to the target attribute
+    //
+    //   https://developer.mozilla.org/en-US/docs/Web/API/WebGLRenderingContext/vertexAttribPointer
+    //
+    context.vertex_attrib_pointer_with_i32(
+        index,
+        size,
+        WebGl2RenderingContext::FLOAT,
+        false, // don't normalize
+        0, // zero stride
+        0, // zero offset
+    );
+}
+
+#[component]
+pub fn Display() -> View {
+    let state = use_context::<AppState>();
+    
+    // canvas
+    let display = create_node_ref();
+    
+    // navigation
+    let pitch_up = create_signal(0.0);
+    let pitch_down = create_signal(0.0);
+    let yaw_right = create_signal(0.0);
+    let yaw_left = create_signal(0.0);
+    let roll_ccw = create_signal(0.0);
+    let roll_cw = create_signal(0.0);
+    let zoom_in = create_signal(0.0);
+    let zoom_out = create_signal(0.0);
+    let turntable = create_signal(false); /* BENCHMARKING */
+    
+    // change listener
+    let scene_changed = create_signal(true);
+    create_effect(move || {
+        state.assembly.elements.with(|elts| {
+            for (_, elt) in elts {
+                elt.rep.track();
+            }
+        });
+        state.selection.track();
+        scene_changed.set(true);
+    });
+    
+    /* INSTRUMENTS */
+    const SAMPLE_PERIOD: i32 = 60;
+    let mut last_sample_time = 0.0;
+    let mut frames_since_last_sample = 0;
+    let mean_frame_interval = create_signal(0.0);
+    
+    on_mount(move || {
+        // timing
+        let mut last_time = 0.0;
+        
+        // viewpoint
+        const ROT_SPEED: f64 = 0.4; // in radians per second
+        const ZOOM_SPEED: f64 = 0.15; // multiplicative rate per second
+        const TURNTABLE_SPEED: f64 = 0.1; /* BENCHMARKING */
+        let mut orientation = DMatrix::<f64>::identity(5, 5);
+        let mut rotation = DMatrix::<f64>::identity(5, 5);
+        let mut location_z: f64 = 5.0;
+        
+        // display parameters
+        const OPACITY: f32 = 0.5; /* SCAFFOLDING */
+        const HIGHLIGHT: f32 = 0.2; /* SCAFFOLDING */
+        const LAYER_THRESHOLD: i32 = 0; /* DEBUG */
+        const DEBUG_MODE: i32 = 0; /* DEBUG */
+        
+        /* INSTRUMENTS */
+        let performance = window().unwrap().performance().unwrap();
+        
+        // get the display canvas
+        let canvas = display.get().unchecked_into::<web_sys::HtmlCanvasElement>();
+        let ctx = canvas
+            .get_context("webgl2")
+            .unwrap()
+            .unwrap()
+            .dyn_into::<WebGl2RenderingContext>()
+            .unwrap();
+        
+        // compile and attach the vertex and fragment shaders
+        let vertex_shader = compile_shader(
+            &ctx,
+            WebGl2RenderingContext::VERTEX_SHADER,
+            include_str!("identity.vert"),
+        );
+        let fragment_shader = compile_shader(
+            &ctx,
+            WebGl2RenderingContext::FRAGMENT_SHADER,
+            include_str!("inversive.frag"),
+        );
+        let program = ctx.create_program().unwrap();
+        ctx.attach_shader(&program, &vertex_shader);
+        ctx.attach_shader(&program, &fragment_shader);
+        ctx.link_program(&program);
+        let link_status = ctx
+            .get_program_parameter(&program, WebGl2RenderingContext::LINK_STATUS)
+            .as_bool()
+            .unwrap();
+        let link_msg = if link_status {
+            "Linked successfully"
+        } else {
+            "Linking failed"
+        };
+        console::log_1(&JsValue::from(link_msg));
+        ctx.use_program(Some(&program));
+        
+        /* DEBUG */
+        // print the maximum number of vectors that can be passed as
+        // uniforms to a fragment shader. the OpenGL ES 3.0 standard
+        // requires this maximum to be at least 224, as discussed in the
+        // documentation of the GL_MAX_FRAGMENT_UNIFORM_VECTORS parameter
+        // here:
+        //
+        //   https://registry.khronos.org/OpenGL-Refpages/es3.0/html/glGet.xhtml
+        //
+        // there are also other size limits. for example, on Aaron's
+        // machine, the the length of a float or genType array seems to be
+        // capped at 1024 elements
+        console::log_2(
+            &ctx.get_parameter(WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
+            &JsValue::from("uniform vectors available")
+        );
+        
+        // find indices of vertex attributes and uniforms
+        const SPHERE_MAX: usize = 200;
+        let position_index = ctx.get_attrib_location(&program, "position") as u32;
+        let sphere_cnt_loc = ctx.get_uniform_location(&program, "sphere_cnt");
+        let sphere_sp_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "sphere_list", Some("sp")
+        );
+        let sphere_lt_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "sphere_list", Some("lt")
+        );
+        let color_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "color_list", None
+        );
+        let highlight_locs = get_uniform_array_locations::<SPHERE_MAX>(
+            &ctx, &program, "highlight_list", None
+        );
+        let resolution_loc = ctx.get_uniform_location(&program, "resolution");
+        let shortdim_loc = ctx.get_uniform_location(&program, "shortdim");
+        let opacity_loc = ctx.get_uniform_location(&program, "opacity");
+        let layer_threshold_loc = ctx.get_uniform_location(&program, "layer_threshold");
+        let debug_mode_loc = ctx.get_uniform_location(&program, "debug_mode");
+        
+        // create a vertex array and bind it to the graphics context
+        let vertex_array = ctx.create_vertex_array().unwrap();
+        ctx.bind_vertex_array(Some(&vertex_array));
+        
+        // set the vertex positions
+        const VERTEX_CNT: usize = 6;
+        let positions: [f32; 3*VERTEX_CNT] = [
+            // northwest triangle
+            -1.0, -1.0, 0.0,
+            -1.0,  1.0, 0.0,
+             1.0,  1.0, 0.0,
+            // southeast triangle
+            -1.0, -1.0, 0.0,
+             1.0,  1.0, 0.0,
+             1.0, -1.0, 0.0
+        ];
+        bind_vertex_attrib(&ctx, position_index, 3, &positions);
+        
+        // set up a repainting routine
+        let (_, start_animation_loop, _) = create_raf(move || {
+            // get the time step
+            let time = performance.now();
+            let time_step = 0.001*(time - last_time);
+            last_time = time;
+            
+            // get the navigation state
+            let pitch_up_val = pitch_up.get();
+            let pitch_down_val = pitch_down.get();
+            let yaw_right_val = yaw_right.get();
+            let yaw_left_val = yaw_left.get();
+            let roll_ccw_val = roll_ccw.get();
+            let roll_cw_val = roll_cw.get();
+            let zoom_in_val = zoom_in.get();
+            let zoom_out_val = zoom_out.get();
+            let turntable_val = turntable.get(); /* BENCHMARKING */
+            
+            // update the assembly's orientation
+            let ang_vel = {
+                let pitch = pitch_up_val - pitch_down_val;
+                let yaw = yaw_right_val - yaw_left_val;
+                let roll = roll_ccw_val - roll_cw_val;
+                if pitch != 0.0 || yaw != 0.0 || roll != 0.0 {
+                    ROT_SPEED * Vector3::new(-pitch, yaw, roll).normalize()
+                } else {
+                    Vector3::zeros()
+                }
+            } /* BENCHMARKING */ + if turntable_val {
+                Vector3::new(0.0, TURNTABLE_SPEED, 0.0)
+            } else {
+                Vector3::zeros()
+            };
+            let mut rotation_sp = rotation.fixed_view_mut::<3, 3>(0, 0);
+            rotation_sp.copy_from(
+                Rotation3::from_scaled_axis(time_step * ang_vel).matrix()
+            );
+            orientation = &rotation * &orientation;
+            
+            // update the assembly's location
+            let zoom = zoom_out_val - zoom_in_val;
+            location_z *= (time_step * ZOOM_SPEED * zoom).exp();
+            
+            if scene_changed.get() {
+                /* INSTRUMENTS */
+                // measure mean frame interval
+                frames_since_last_sample += 1;
+                if frames_since_last_sample >= SAMPLE_PERIOD {
+                    mean_frame_interval.set((time - last_sample_time) / (SAMPLE_PERIOD as f64));
+                    last_sample_time = time;
+                    frames_since_last_sample = 0;
+                }
+                
+                // find the map from assembly space to world space
+                let location = {
+                    let u = -location_z;
+                    DMatrix::from_column_slice(5, 5, &[
+                        1.0, 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,   u,
+                        0.0, 0.0, 2.0*u, 1.0, u*u,
+                        0.0, 0.0,   0.0, 0.0, 1.0
+                    ])
+                };
+                let assembly_to_world = &location * &orientation;
+                
+                // get the assembly
+                let (
+                    elt_cnt,
+                    reps_world,
+                    colors,
+                    highlights
+                ) = state.assembly.elements.with(|elts| {
+                    (
+                        // number of elements
+                        elts.len() as i32,
+                        
+                        // representation vectors in world coordinates
+                        elts.iter().map(
+                            |(_, elt)| elt.rep.with(|rep| &assembly_to_world * rep)
+                        ).collect::<Vec<_>>(),
+                        
+                        // colors
+                        elts.iter().map(|(key, elt)| {
+                            if state.selection.with(|sel| sel.contains(&key)) {
+                                elt.color.map(|ch| 0.2 + 0.8*ch)
+                            } else {
+                                elt.color
+                            }
+                        }).collect::<Vec<_>>(),
+                        
+                        // highlight levels
+                        elts.iter().map(|(key, _)| {
+                            if state.selection.with(|sel| sel.contains(&key)) {
+                                1.0_f32
+                            } else {
+                                HIGHLIGHT
+                            }
+                        }).collect::<Vec<_>>()
+                    )
+                });
+                
+                // set the resolution
+                let width = canvas.width() as f32;
+                let height = canvas.height() as f32;
+                ctx.uniform2f(resolution_loc.as_ref(), width, height);
+                ctx.uniform1f(shortdim_loc.as_ref(), width.min(height));
+                
+                // pass the assembly
+                ctx.uniform1i(sphere_cnt_loc.as_ref(), elt_cnt);
+                for n in 0..reps_world.len() {
+                    let v = &reps_world[n];
+                    ctx.uniform3f(
+                        sphere_sp_locs[n].as_ref(),
+                        v[0] as f32, v[1] as f32, v[2] as f32
+                    );
+                    ctx.uniform2f(
+                        sphere_lt_locs[n].as_ref(),
+                        v[3] as f32, v[4] as f32
+                    );
+                    ctx.uniform3fv_with_f32_array(
+                        color_locs[n].as_ref(),
+                        &colors[n]
+                    );
+                    ctx.uniform1f(
+                        highlight_locs[n].as_ref(),
+                        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);
+                
+                // draw the scene
+                ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
+                
+                // clear the scene change flag
+                scene_changed.set(
+                    pitch_up_val != 0.0
+                    || pitch_down_val != 0.0
+                    || yaw_left_val != 0.0
+                    || yaw_right_val != 0.0
+                    || roll_cw_val != 0.0
+                    || roll_ccw_val != 0.0
+                    || zoom_in_val != 0.0
+                    || zoom_out_val != 0.0
+                    || turntable_val /* BENCHMARKING */
+                );
+            } else {
+                frames_since_last_sample = 0;
+                mean_frame_interval.set(-1.0);
+            }
+        });
+        start_animation_loop();
+    });
+    
+    let set_nav_signal = move |event: KeyboardEvent, value: f64| {
+        let mut navigating = true;
+        let shift = event.shift_key();
+        match event.key().as_str() {
+            "ArrowUp" if shift => zoom_in.set(value),
+            "ArrowDown" if shift => zoom_out.set(value),
+            "ArrowUp" => pitch_up.set(value),
+            "ArrowDown" => pitch_down.set(value),
+            "ArrowRight" if shift => roll_cw.set(value),
+            "ArrowLeft" if shift => roll_ccw.set(value),
+            "ArrowRight" => yaw_right.set(value),
+            "ArrowLeft" => yaw_left.set(value),
+            _ => navigating = false
+        };
+        if navigating {
+            scene_changed.set(true);
+            event.prevent_default();
+        }
+    };
+    
+    view! {
+        /* TO DO */
+        // switch back to integer-valued parameters when that becomes possible
+        // again
+        canvas(
+            ref=display,
+            width="600",
+            height="600",
+            tabindex="0",
+            on:keydown=move |event: KeyboardEvent| {
+                if event.key() == "Shift" {
+                    roll_cw.set(yaw_right.get());
+                    roll_ccw.set(yaw_left.get());
+                    zoom_in.set(pitch_up.get());
+                    zoom_out.set(pitch_down.get());
+                    yaw_right.set(0.0);
+                    yaw_left.set(0.0);
+                    pitch_up.set(0.0);
+                    pitch_down.set(0.0);
+                } else {
+                    if event.key() == "Enter" { /* BENCHMARKING */
+                        turntable.set_fn(|turn| !turn);
+                        scene_changed.set(true);
+                    }
+                    set_nav_signal(event, 1.0);
+                }
+            },
+            on:keyup=move |event: KeyboardEvent| {
+                if event.key() == "Shift" {
+                    yaw_right.set(roll_cw.get());
+                    yaw_left.set(roll_ccw.get());
+                    pitch_up.set(zoom_in.get());
+                    pitch_down.set(zoom_out.get());
+                    roll_cw.set(0.0);
+                    roll_ccw.set(0.0);
+                    zoom_in.set(0.0);
+                    zoom_out.set(0.0);
+                } else {
+                    set_nav_signal(event, 0.0);
+                }
+            },
+            on:blur=move |_| {
+                pitch_up.set(0.0);
+                pitch_down.set(0.0);
+                yaw_right.set(0.0);
+                yaw_left.set(0.0);
+                roll_ccw.set(0.0);
+                roll_cw.set(0.0);
+            }
+        )
+    }
+}
\ No newline at end of file
diff --git a/app-proto/src/engine.rs b/app-proto/src/engine.rs
index d033c01..2978a9a 100644
--- 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 std::fmt::{Display, Error, Formatter};
+use nalgebra::{Const, DMatrix, DVector, Dyn};
+use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
 
 // --- 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)
     ])
 }
 
@@ -30,264 +30,112 @@ 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)
     ])
 }
 
-// project a sphere's representation vector to the normalization variety by
-// contracting toward the last coordinate axis
-pub fn project_sphere_to_normalized(rep: &mut DVector<f64>) {
-    let q_sp = rep.fixed_rows::<3>(0).norm_squared();
-    let half_q_lt = -2.0 * rep[3] * rep[4];
-    let half_q_lt_sq = half_q_lt * half_q_lt;
-    let scaling = half_q_lt + (q_sp + half_q_lt_sq).sqrt();
-    rep.fixed_rows_mut::<4>(0).scale_mut(1.0 / scaling);
-}
-
-// normalize a point's representation vector by scaling
-pub fn project_point_to_normalized(rep: &mut DVector<f64>) {
-    rep.scale_mut(0.5 / rep[3]);
-}
-
 // --- partial matrices ---
 
-pub struct MatrixEntry {
+struct MatrixEntry {
     index: (usize, usize),
-    value: f64,
+    value: f64
 }
 
 pub struct PartialMatrix(Vec<MatrixEntry>);
 
 impl PartialMatrix {
-    pub fn new() -> Self {
-        Self(Vec::<MatrixEntry>::new())
-    }
-    
-    pub fn push(&mut self, row: usize, col: usize, value: f64) {
-        let Self(entries) = self;
-        entries.push(MatrixEntry { index: (row, col), value });
+    pub fn new() -> PartialMatrix {
+        PartialMatrix(Vec::<MatrixEntry>::new())
     }
     
     pub fn push_sym(&mut self, row: usize, col: usize, value: f64) {
-        self.push(row, col, value);
+        let PartialMatrix(entries) = self;
+        entries.push(MatrixEntry { index: (row, col), value: value });
         if row != col {
-            self.push(col, row, value);
+            entries.push(MatrixEntry { index: (col, row), value: value });
         }
     }
     
-    fn freeze(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
-        let mut result = a.clone();
-        for &MatrixEntry { index, value } in self {
-            result[index] = value;
+    /* DEBUG */
+    pub fn log_to_console(&self) {
+        let PartialMatrix(entries) = self;
+        for ent in entries {
+            let ent_str = format!("  {} {} {}", ent.index.0, ent.index.1, ent.value);
+            console::log_1(&JsValue::from(ent_str.as_str()));
         }
-        result
     }
     
     fn proj(&self, a: &DMatrix<f64>) -> DMatrix<f64> {
         let mut result = DMatrix::<f64>::zeros(a.nrows(), a.ncols());
-        for &MatrixEntry { index, .. } in self {
-            result[index] = a[index];
+        let PartialMatrix(entries) = self;
+        for ent in entries {
+            result[ent.index] = a[ent.index];
         }
         result
     }
     
     fn sub_proj(&self, rhs: &DMatrix<f64>) -> DMatrix<f64> {
         let mut result = DMatrix::<f64>::zeros(rhs.nrows(), rhs.ncols());
-        for &MatrixEntry { index, value } in self {
-            result[index] = value - rhs[index];
+        let PartialMatrix(entries) = self;
+        for ent in entries {
+            result[ent.index] = ent.value - rhs[ent.index];
         }
         result
     }
 }
 
-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 Self(entries) = self;
-        entries.into_iter()
-    }
-}
-
-impl<'a> IntoIterator for &'a PartialMatrix {
-    type Item = &'a MatrixEntry;
-    type IntoIter = std::slice::Iter<'a, MatrixEntry>;
-    
-    fn into_iter(self) -> Self::IntoIter {
-        let PartialMatrix(entries) = self;
-        entries.into_iter()
-    }
-}
-
-// --- configuration subspaces ---
-
-#[derive(Clone)]
-pub struct ConfigSubspace {
-    assembly_dim: usize,
-    basis_std: Vec<DMatrix<f64>>,
-    basis_proj: Vec<DMatrix<f64>>,
-}
-
-impl ConfigSubspace {
-    pub fn zero(assembly_dim: usize) -> Self {
-        Self {
-            assembly_dim,
-            basis_proj: 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,
-    ) -> 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
-        const THRESHOLD: f64 = 0.1;
-        let eig = SymmetricEigen::new(proj_to_std.tr_mul(&a) * &proj_to_std);
-        let eig_vecs = eig.eigenvectors.column_iter();
-        let eig_pairs = eig.eigenvalues.iter().zip(eig_vecs);
-        let basis_proj = DMatrix::from_columns(
-            eig_pairs.filter_map(
-                |(λ, v)| (λ.abs() < THRESHOLD).then_some(v)
-            ).collect::<Vec<_>>().as_slice()
-        );
-        
-        // 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;
-        Self {
-            assembly_dim,
-            basis_std: basis_std.column_iter().map(
-                |v| Into::<DMatrix<f64>>::into(
-                    v.reshape_generic(Dyn(ELEMENT_DIM), Dyn(assembly_dim))
-                )
-            ).collect(),
-            basis_proj: basis_proj.column_iter().map(
-                |v| Into::<DMatrix<f64>>::into(
-                    v.reshape_generic(Dyn(UNIFORM_DIM), Dyn(assembly_dim))
-                )
-            ).collect(),
-        }
-    }
-    
-    pub fn dim(&self) -> usize {
-        self.basis_std.len()
-    }
-    
-    pub fn assembly_dim(&self) -> usize {
-        self.assembly_dim
-    }
-    
-    // find the projection onto this subspace of the motion where the element
-    // with the given column index has velocity `v`. the velocity is given in
-    // projection coordinates, and the projection is done with respect to the
-    // projection inner product
-    pub fn proj(&self, v: &DVectorView<f64>, column_index: usize) -> DMatrix<f64> {
-        if self.dim() == 0 {
-            const ELEMENT_DIM: usize = 5;
-            DMatrix::zeros(ELEMENT_DIM, self.assembly_dim)
-        } else {
-            self.basis_proj.iter().zip(self.basis_std.iter()).map(
-                |(b_proj, b_std)| b_proj.column(column_index).dot(&v) * b_std
-            ).sum()
-        }
-    }
-}
-
 // --- descent history ---
 
 pub struct DescentHistory {
     pub config: Vec<DMatrix<f64>>,
     pub scaled_loss: Vec<f64>,
     pub neg_grad: Vec<DMatrix<f64>>,
-    pub hess_eigvals: Vec<DVector<f64>>,
+    pub min_eigval: Vec<f64>,
     pub base_step: Vec<DMatrix<f64>>,
-    pub backoff_steps: Vec<i32>,
+    pub backoff_steps: Vec<i32>
 }
 
 impl DescentHistory {
-    pub fn new() -> Self {
-        Self {
+    fn new() -> DescentHistory {
+        DescentHistory {
             config: Vec::<DMatrix<f64>>::new(),
             scaled_loss: Vec::<f64>::new(),
             neg_grad: Vec::<DMatrix<f64>>::new(),
-            hess_eigvals: Vec::<DVector<f64>>::new(),
+            min_eigval: Vec::<f64>::new(),
             base_step: Vec::<DMatrix<f64>>::new(),
             backoff_steps: Vec::<i32>::new(),
         }
     }
 }
 
-// --- constraint problems ---
-
-pub struct ConstraintProblem {
-    pub gram: PartialMatrix,
-    pub frozen: PartialMatrix,
-    pub guess: DMatrix<f64>,
-}
-
-impl ConstraintProblem {
-    pub fn new(element_count: usize) -> Self {
-        const ELEMENT_DIM: usize = 5;
-        Self {
-            gram: PartialMatrix::new(),
-            frozen: PartialMatrix::new(),
-            guess: DMatrix::<f64>::zeros(ELEMENT_DIM, element_count),
-        }
-    }
-    
-    #[cfg(feature = "dev")]
-    pub fn from_guess(guess_columns: &[DVector<f64>]) -> Self {
-        Self {
-            gram: PartialMatrix::new(),
-            frozen: PartialMatrix::new(),
-            guess: DMatrix::from_columns(guess_columns),
-        }
-    }
-}
-
 // --- gram matrix realization ---
 
 // the Lorentz form
 lazy_static! {
-    pub static ref Q: DMatrix<f64> = DMatrix::from_row_slice(5, 5, &[
+    static ref Q: DMatrix<f64> = DMatrix::from_row_slice(5, 5, &[
         1.0, 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, 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>) -> Self {
+    fn from_config(gram: &PartialMatrix, config: DMatrix<f64>) -> SearchState {
         let err_proj = gram.sub_proj(&(config.tr_mul(&*Q) * &config));
         let loss = err_proj.norm_squared();
-        Self { config, err_proj, loss }
+        SearchState {
+            config: config,
+            err_proj: err_proj,
+            loss: loss
+        }
     }
 }
 
@@ -297,37 +145,6 @@ fn basis_matrix(index: (usize, usize), nrows: usize, ncols: usize) -> DMatrix<f6
     result
 }
 
-// given a normalized vector `v` representing an element, build a basis for the
-// element's linear configuration space consisting of:
-// - the unit translation motions of the element
-// - the unit shrinking motion of the element, if it's a sphere
-// - one or two vectors whose coefficients vanish on the tangent space of the
-//   normalization variety
-pub fn local_unif_to_std(v: DVectorView<f64>) -> DMatrix<f64> {
-    const ELEMENT_DIM: usize = 5;
-    const UNIFORM_DIM: usize = 4;
-    let curv = 2.0*v[3];
-    if v.dot(&(&*Q * v)) < 0.5 {
-        // `v` represents a point. the normalization condition says that the
-        // curvature component of `v` is 1/2
-        DMatrix::from_column_slice(ELEMENT_DIM, UNIFORM_DIM, &[
-            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,
-        ])
-    } else {
-        // `v` represents a sphere. the normalization condition says that the
-        // Lorentz product of `v` with itself is 1
-        DMatrix::from_column_slice(ELEMENT_DIM, UNIFORM_DIM, &[
-                 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,
-        ])
-    }
-}
-
 // use backtracking line search to find a better configuration
 fn seek_better_config(
     gram: &PartialMatrix,
@@ -336,7 +153,7 @@ 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 {
@@ -351,52 +168,25 @@ 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
-// use a regularized Newton's method to seek the desired Gram matrix
+// seek a matrix `config` for which `config' * Q * config` matches the partial
+// matrix `gram`. use gradient descent starting from `guess`
 pub fn realize_gram(
-    problem: &ConstraintProblem,
+    gram: &PartialMatrix,
+    guess: DMatrix<f64>,
+    frozen: &[(usize, usize)],
     scaled_tol: f64,
     min_efficiency: f64,
     backoff: f64,
     reg_scale: f64,
     max_descent_steps: i32,
-    max_backoff_steps: i32,
-) -> Realization {
-    // destructure the problem data
-    let ConstraintProblem { gram, guess, frozen } = problem;
-    
+    max_backoff_steps: i32
+) -> (DMatrix<f64>, bool, DescentHistory) {
     // 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
@@ -405,13 +195,17 @@ pub fn realize_gram(
     
     // convert the frozen indices to stacked format
     let frozen_stacked: Vec<usize> = frozen.into_iter().map(
-        |MatrixEntry { index: (row, col), .. }| col*element_dim + row
+        |index| index.1*element_dim + index.0
     ).collect();
     
-    // use a regularized Newton's method with backtracking
-    let mut state = SearchState::from_config(gram, frozen.freeze(guess));
-    let mut hess = DMatrix::zeros(element_dim, assembly_dim);
+    // use Newton's method with backtracking and gradient descent backup
+    let mut state = SearchState::from_config(gram, guess);
     for _ in 0..max_descent_steps {
+        // stop if the loss is tolerably low
+        history.config.push(state.config.clone());
+        history.scaled_loss.push(state.loss / scale_adjustment);
+        if state.loss < tol { break; }
+        
         // find the negative gradient of the loss function
         let neg_grad = 4.0 * &*Q * &state.config * &state.err_proj;
         let mut neg_grad_stacked = neg_grad.clone().reshape_generic(Dyn(total_dim), Const::<1>);
@@ -434,15 +228,14 @@ pub fn realize_gram(
                 hess_cols.push(deriv_grad.reshape_generic(Dyn(total_dim), Const::<1>));
             }
         }
-        hess = DMatrix::from_columns(hess_cols.as_slice());
+        let mut hess = DMatrix::from_columns(hess_cols.as_slice());
         
         // regularize the Hessian
-        let hess_eigvals = hess.symmetric_eigenvalues();
-        let min_eigval = hess_eigvals.min();
+        let min_eigval = hess.symmetric_eigenvalues().min();
         if min_eigval <= 0.0 {
             hess -= reg_scale * min_eigval * DMatrix::identity(total_dim, total_dim);
         }
-        history.hess_eigvals.push(hess_eigvals);
+        history.min_eigval.push(min_eigval);
         
         // project the negative gradient and negative Hessian onto the
         // orthogonal complement of the frozen subspace
@@ -455,75 +248,85 @@ pub fn realize_gram(
             hess[(k, k)] = 1.0;
         }
         
-        // stop if the loss is tolerably low
-        history.config.push(state.config.clone());
-        history.scaled_loss.push(state.loss / scale_adjustment);
-        if state.loss < tol { break; }
-        
         // compute the Newton step
-        /* TO DO */
         /*
-          we should change our regularization to ensure that the Hessian is
-          is positive-definite, rather than just positive-semidefinite. ideally,
-          that would guarantee the success of the Cholesky decomposition---
-          although we'd still need the error-handling routine in case of
-          numerical hiccups
+          we need to either handle or eliminate the case where the minimum
+          eigenvalue of the Hessian is zero, so the regularized Hessian is
+          singular. right now, this causes the Cholesky decomposition to return
+          `None`, leading to a panic when we unrap
         */
-        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_stacked = hess.cholesky().unwrap().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
-        if let Some((better_state, backoff_steps)) = seek_better_config(
+        match seek_better_config(
             gram, &state, &base_step, neg_grad.dot(&base_step),
-            min_efficiency, backoff, max_backoff_steps,
+            min_efficiency, backoff, max_backoff_steps
         ) {
-            state = better_state;
-            history.backoff_steps.push(backoff_steps);
-        } else {
-            return Realization {
-                result: Err("Line search failed".to_string()),
-                history,
-            };
-        }
+            Some((better_state, backoff_steps)) => {
+                state = better_state;
+                history.backoff_steps.push(backoff_steps);
+            },
+            None => return (state.config, false, history)
+        };
     }
-    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;
-        let mut unif_to_std = DMatrix::<f64>::zeros(total_dim, total_dim_unif);
-        for n in 0..assembly_dim {
-            let block_start = (element_dim * n, UNIFORM_DIM * n);
-            unif_to_std
-                .view_mut(block_start, (element_dim, UNIFORM_DIM))
-                .copy_from(&local_unif_to_std(state.config.column(n)));
-        }
-        
-        // find the kernel of the Hessian. give it the uniform inner product
-        let tangent = ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim);
-        
-        Ok(ConfigNeighborhood { config: state.config, nbhd: tangent })
-    } else {
-        Err("Failed to reach target accuracy".to_string())
-    };
-    Realization { result, history }
+    (state.config, state.loss < tol, history)
 }
 
 // --- tests ---
 
-#[cfg(feature = "dev")]
-pub mod examples {
-    use std::f64::consts::PI;
+#[cfg(test)]
+mod tests {
+    use std::{array, f64::consts::PI};
     
     use super::*;
     
+    #[test]
+    fn sub_proj_test() {
+        let target = PartialMatrix(vec![
+            MatrixEntry { index: (0, 0), value: 19.0 },
+            MatrixEntry { index: (0, 2), value: 39.0 },
+            MatrixEntry { index: (1, 1), value: 59.0 },
+            MatrixEntry { index: (1, 2), value: 69.0 }
+        ]);
+        let attempt = DMatrix::<f64>::from_row_slice(2, 3, &[
+            1.0, 2.0, 3.0,
+            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
+        ]);
+        assert_eq!(target.sub_proj(&attempt), expected_result);
+    }
+    
+    #[test]
+    fn zero_loss_test() {
+        let gram = PartialMatrix({
+            let mut entries = Vec::<MatrixEntry>::new();
+            for j in 0..3 {
+                for k in 0..3 {
+                    entries.push(MatrixEntry {
+                        index: (j, k),
+                        value: if j == k { 1.0 } else { -1.0 }
+                    });
+                }
+            }
+            entries
+        });
+        let config = {
+            let a: f64 = 0.75_f64.sqrt();
+            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)
+            ])
+        };
+        let state = SearchState::from_config(&gram, config);
+        assert!(state.loss.abs() < f64::EPSILON);
+    }
+    
     // this problem is from a sangaku by Irisawa Shintarō Hiroatsu. the article
     // below includes a nice translation of the problem statement, which was
     // recorded in Uchida Itsumi's book _Kokon sankan_ (_Mathematics, Past and
@@ -532,12 +335,43 @@ 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) -> Realization {
-        let mut problem = ConstraintProblem::from_guess(
+    #[test]
+    fn irisawa_hexlet_test() {
+        let gram = PartialMatrix({
+            let mut entries = Vec::<MatrixEntry>::new();
+            for s in 0..9 {
+                // each sphere is represented by a spacelike vector
+                entries.push(MatrixEntry { index: (s, s), value: 1.0 });
+                
+                // the circumscribing sphere is tangent to all of the other
+                // spheres, with matching orientation
+                if s > 0 {
+                    entries.push(MatrixEntry { index: (0, s), value: 1.0 });
+                    entries.push(MatrixEntry { index: (s, 0), value: 1.0 });
+                }
+                
+                if s > 2 {
+                    // each chain sphere is tangent to the "sun" and "moon"
+                    // spheres, with opposing orientation
+                    for n in 1..3 {
+                        entries.push(MatrixEntry { index: (s, n), value: -1.0 });
+                        entries.push(MatrixEntry { index: (n, s), value: -1.0 });
+                    }
+                    
+                    // each chain sphere is tangent to the next chain sphere,
+                    // with opposing orientation
+                    let s_next = 3 + (s-2) % 6;
+                    entries.push(MatrixEntry { index: (s, s_next), value: -1.0 });
+                    entries.push(MatrixEntry { index: (s_next, s), value: -1.0 });
+                }
+            }
+            entries
+        });
+        let guess = DMatrix::from_columns(
             [
                 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| {
@@ -547,429 +381,122 @@ pub mod examples {
                 )
             ).collect::<Vec<_>>().as_slice()
         );
-        
-        for s in 0..9 {
-            // each sphere is represented by a spacelike vector
-            problem.gram.push_sym(s, s, 1.0);
-            
-            // the circumscribing sphere is tangent to all of the other
-            // spheres, with matching orientation
-            if s > 0 {
-                problem.gram.push_sym(0, s, 1.0);
-            }
-            
-            if s > 2 {
-                // each chain sphere is tangent to the "sun" and "moon"
-                // spheres, with opposing orientation
-                for n in 1..3 {
-                    problem.gram.push_sym(s, n, -1.0);
-                }
-                
-                // each chain sphere is tangent to the next chain sphere,
-                // with opposing orientation
-                let s_next = 3 + (s-2) % 6;
-                problem.gram.push_sym(s, s_next, -1.0);
-            }
-        }
-        
-        // the frozen entries fix the radii of the circumscribing sphere, the
-        // "sun" and "moon" spheres, and one of the chain spheres
-        for k in 0..4 {
-            problem.frozen.push(3, k, problem.guess[(3, k)]);
-        }
-        
-        realize_gram(&problem, scaled_tol, 0.5, 0.9, 1.1, 200, 110)
-    }
-    
-    // set up a kaleidocycle, made of points with fixed distances between them,
-    // and find its tangent space
-    pub fn realize_kaleidocycle(scaled_tol: f64) -> Realization {
-        const N_HINGES: usize = 6;
-        let mut problem = ConstraintProblem::from_guess(
-            (0..N_HINGES).step_by(2).flat_map(
-                |n| {
-                    let ang_hor = (n as f64) * PI/3.0;
-                    let ang_vert = ((n + 1) as f64) * PI/3.0;
-                    let x_vert = ang_vert.cos();
-                    let y_vert = ang_vert.sin();
-                    [
-                        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),
-                    ]
-                }
-            ).collect::<Vec<_>>().as_slice()
-        );
-        
-        const N_POINTS: usize = 2 * N_HINGES;
-        for block in (0..N_POINTS).step_by(2) {
-            let block_next = (block + 2) % N_POINTS;
-            for j in 0..2 {
-                // diagonal and hinge edges
-                for k in j..2 {
-                    problem.gram.push_sym(block + j, block + k, if j == k { 0.0 } else { -0.5 });
-                }
-                
-                // non-hinge edges
-                for k in 0..2 {
-                    problem.gram.push_sym(block + j, block_next + k, -0.625);
-                }
-            }
-        }
-        
-        for k in 0..N_POINTS {
-            problem.frozen.push(3, k, problem.guess[(3, k)])
-        }
-        
-        realize_gram(&problem, scaled_tol, 0.5, 0.9, 1.1, 200, 110)
-    }
-}
-
-#[cfg(test)]
-mod tests {
-    use nalgebra::Vector3;
-    use std::{f64::consts::{FRAC_1_SQRT_2, PI}, iter};
-    
-    use super::{*, examples::*};
-    
-    #[test]
-    fn freeze_test() {
-        let frozen = PartialMatrix(vec![
-            MatrixEntry { index: (0, 0), value: 14.0 },
-            MatrixEntry { index: (0, 2), value: 28.0 },
-            MatrixEntry { index: (1, 1), value: 42.0 },
-            MatrixEntry { index: (1, 2), value: 49.0 },
-        ]);
-        let config = DMatrix::<f64>::from_row_slice(2, 3, &[
-            1.0, 2.0, 3.0,
-            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,
-        ]);
-        assert_eq!(frozen.freeze(&config), expected_result);
-    }
-    
-    #[test]
-    fn sub_proj_test() {
-        let target = PartialMatrix(vec![
-            MatrixEntry { index: (0, 0), value: 19.0 },
-            MatrixEntry { index: (0, 2), value: 39.0 },
-            MatrixEntry { index: (1, 1), value: 59.0 },
-            MatrixEntry { index: (1, 2), value: 69.0 },
-        ]);
-        let attempt = DMatrix::<f64>::from_row_slice(2, 3, &[
-            1.0, 2.0, 3.0,
-            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,
-        ]);
-        assert_eq!(target.sub_proj(&attempt), expected_result);
-    }
-    
-    #[test]
-    fn zero_loss_test() {
-        let mut gram = PartialMatrix::new();
-        for j in 0..3 {
-            for k in 0..3 {
-                gram.push(j, k, if j == k { 1.0 } else { -1.0 });
-            }
-        }
-        let config = {
-            let a = 0.75_f64.sqrt();
-            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),
-            ])
-        };
-        let state = SearchState::from_config(&gram, config);
-        assert!(state.loss.abs() < f64::EPSILON);
-    }
-    
-    /* TO DO */
-    // at the frozen indices, the optimization steps should have exact zeros,
-    // and the realized configuration should have the desired values
-    #[test]
-    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),
-        ]);
-        for j in 0..2 {
-            for k in j..2 {
-                problem.gram.push_sym(j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
-            }
-        }
-        problem.frozen.push(3, 0, problem.guess[(3, 0)]);
-        problem.frozen.push(3, 1, 0.5);
-        let Realization { result, history } = realize_gram(
-            &problem, 1.0e-12, 0.5, 0.9, 1.1, 200, 110
-        );
-        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);
-            }
-        }
-        for MatrixEntry { index, value } in problem.frozen {
-            assert_eq!(config[index], value);
-        }
-    }
-    
-    #[test]
-    fn irisawa_hexlet_test() {
-        // solve Irisawa's problem
+        let frozen: [(usize, usize); 4] = array::from_fn(|k| (3, k));
         const SCALED_TOL: f64 = 1.0e-12;
-        let config = realize_irisawa_hexlet(SCALED_TOL).result.unwrap().config;
-        
-        // check against Irisawa's solution
+        let (config, success, history) = realize_gram(
+            &gram, guess, &frozen,
+            SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
+        );
         let entry_tol = SCALED_TOL.sqrt();
         let solution_diams = [30.0, 10.0, 6.0, 5.0, 15.0, 10.0, 3.75, 2.5, 2.0 + 8.0/11.0];
         for (k, diam) in solution_diams.into_iter().enumerate() {
             assert!((config[(3, k)] - 1.0 / diam).abs() < entry_tol);
         }
-    }
-    
-    #[test]
-    fn tangent_test_three_spheres() {
-        const SCALED_TOL: f64 = 1.0e-12;
-        const ELEMENT_DIM: usize = 5;
-        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),
-        ]);
-        for j in 0..3 {
-            for k in j..3 {
-                problem.gram.push_sym(j, k, if j == k { 1.0 } else { -1.0 });
+        print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
+        if success {
+            println!("Target accuracy achieved!");
+        } else {
+            println!("Failed to reach target accuracy");
+        }
+        println!("Steps: {}", history.scaled_loss.len() - 1);
+        println!("Loss: {}", history.scaled_loss.last().unwrap());
+        if success {
+            println!("\nChain diameters:");
+            println!("  {} sun (given)", 1.0 / config[(3, 3)]);
+            for k in 4..9 {
+                println!("  {} sun", 1.0 / config[(3, k)]);
             }
         }
-        for n in 0..ELEMENT_DIM {
-            problem.frozen.push(n, 0, problem.guess[(n, 0)]);
-        }
-        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!(history.scaled_loss.len(), 1);
-        
-        // list some motions that should form a basis for the tangent space of
-        // the solution variety
-        const UNIFORM_DIM: usize = 4;
-        let element_dim = problem.guess.nrows();
-        let assembly_dim = problem.guess.ncols();
-        let tangent_motions_unif = vec![
-            basis_matrix((0, 1), UNIFORM_DIM, assembly_dim),
-            basis_matrix((1, 1), UNIFORM_DIM, assembly_dim),
-            basis_matrix((0, 2), UNIFORM_DIM, assembly_dim),
-            basis_matrix((1, 2), UNIFORM_DIM, assembly_dim),
-            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,
-            ]),
-        ];
-        let tangent_motions_std = vec![
-            basis_matrix((0, 1), element_dim, assembly_dim),
-            basis_matrix((1, 1), element_dim, assembly_dim),
-            basis_matrix((0, 2), element_dim, assembly_dim),
-            basis_matrix((1, 2), element_dim, assembly_dim),
-            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,
-            ]),
-        ];
-        
-        // confirm that the dimension of the tangent space is no greater than
-        // expected
-        assert_eq!(tangent.basis_std.len(), tangent_motions_std.len());
-        
-        // confirm that the tangent space contains all the motions we expect it
-        // to. since we've already bounded the dimension of the tangent space,
-        // this confirms that the tangent space is what we expect it to be
-        let tol_sq = ((element_dim * assembly_dim) as f64) * SCALED_TOL * SCALED_TOL;
-        for (motion_unif, motion_std) in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
-            let motion_proj: DMatrix<_> = motion_unif.column_iter().enumerate().map(
-                |(k, v)| tangent.proj(&v, k)
-            ).sum();
-            assert!((motion_std - motion_proj).norm_squared() < tol_sq);
+        println!("\nStep │ Loss\n─────┼────────────────────────────────");
+        for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
+            println!("{:<4} │ {}", step, scaled_loss);
         }
     }
     
-    fn translation_motion_unif(vel: &Vector3<f64>, assembly_dim: usize) -> Vec<DVector<f64>> {
-        let mut elt_motion = DVector::zeros(4);
-        elt_motion.fixed_rows_mut::<3>(0).copy_from(vel);
-        iter::repeat(elt_motion).take(assembly_dim).collect()
-    }
+    // --- process inspection examples ---
     
-    fn rotation_motion_unif(ang_vel: &Vector3<f64>, points: Vec<DVectorView<f64>>) -> Vec<DVector<f64>> {
-        points.into_iter().map(
-            |pt| {
-                let vel = ang_vel.cross(&pt.fixed_rows::<3>(0));
-                let mut elt_motion = DVector::zeros(4);
-                elt_motion.fixed_rows_mut::<3>(0).copy_from(&vel);
-                elt_motion
-            }
-        ).collect()
-    }
+    // these tests are meant for human inspection, not automated use. run them
+    // one at a time in `--nocapture` mode and read through the results and
+    // optimization histories that they print out. the `run-examples` script
+    // will run all of them
     
     #[test]
-    fn tangent_test_kaleidocycle() {
-        // set up a kaleidocycle and find its tangent space
-        const SCALED_TOL: f64 = 1.0e-12;
-        let Realization { result, history } = realize_kaleidocycle(SCALED_TOL);
-        let ConfigNeighborhood { config, nbhd: tangent } = result.unwrap();
-        assert_eq!(history.scaled_loss.len(), 1);
-        
-        // list some motions that should form a basis for the tangent space of
-        // the solution variety
-        const N_HINGES: usize = 6;
-        let element_dim = config.nrows();
-        let assembly_dim = config.ncols();
-        let tangent_motions_unif = vec![
-            // the translations along the coordinate axes
-            translation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), assembly_dim),
-            translation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), assembly_dim),
-            translation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), assembly_dim),
-            
-            // the rotations about the coordinate axes
-            rotation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), config.column_iter().collect()),
-            rotation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), config.column_iter().collect()),
-            rotation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), config.column_iter().collect()),
-            
-            // the twist motion. more precisely: a motion that keeps the center
-            // of mass stationary and preserves the distances between the
-            // vertices to first order. this has to be the twist as long as:
-            //   - twisting is the kaleidocycle's only internal degree of
-            //     freedom
-            //   - every first-order motion of the kaleidocycle comes from an
-            //     actual motion
-            (0..N_HINGES).step_by(2).flat_map(
-                |n| {
-                    let ang_vert = ((n + 1) as f64) * PI/3.0;
-                    let vel_vert_x = 4.0 * ang_vert.cos();
-                    let vel_vert_y = 4.0 * ang_vert.sin();
-                    [
-                        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]),
-                    ]
+    fn three_spheres_example() {
+        let gram = PartialMatrix({
+            let mut entries = Vec::<MatrixEntry>::new();
+            for j in 0..3 {
+                for k in 0..3 {
+                    entries.push(MatrixEntry {
+                        index: (j, k),
+                        value: if j == k { 1.0 } else { -1.0 }
+                    });
                 }
-            ).collect::<Vec<_>>(),
-        ];
-        let tangent_motions_std = tangent_motions_unif.iter().map(
-            |motion| DMatrix::from_columns(
-                &config.column_iter().zip(motion).map(
-                    |(v, elt_motion)| local_unif_to_std(v) * elt_motion
-                ).collect::<Vec<_>>()
-            )
-        ).collect::<Vec<_>>();
-        
-        // confirm that the dimension of the tangent space is no greater than
-        // expected
-        assert_eq!(tangent.basis_std.len(), tangent_motions_unif.len());
-        
-        // confirm that the tangent space contains all the motions we expect it
-        // to. since we've already bounded the dimension of the tangent space,
-        // this confirms that the tangent space is what we expect it to be
-        let tol_sq = ((element_dim * assembly_dim) as f64) * SCALED_TOL * SCALED_TOL;
-        for (motion_unif, motion_std) in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
-            let motion_proj: DMatrix<_> = motion_unif.into_iter().enumerate().map(
-                |(k, v)| tangent.proj(&v.as_view(), k)
-            ).sum();
-            assert!((motion_std - motion_proj).norm_squared() < tol_sq);
-        }
-    }
-    
-    fn translation(dis: Vector3<f64>) -> DMatrix<f64> {
-        const ELEMENT_DIM: usize = 5;
-        DMatrix::from_column_slice(ELEMENT_DIM, ELEMENT_DIM, &[
-                   1.0,        0.0,        0.0, 0.0,             dis[0],
-                   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,
-        ])
-    }
-    
-    // confirm that projection onto a configuration subspace is equivariant with
-    // respect to Euclidean motions
-    #[test]
-    fn proj_equivar_test() {
-        // find a pair of spheres that meet at 120°
-        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),
-        ]);
-        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 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!(history_orig.scaled_loss.len(), 1);
-        
-        // find another pair of spheres that meet at 120°. we'll think of this
-        // solution as a transformed version of the original one
-        let guess_tfm = {
-            let a = 0.5 * FRAC_1_SQRT_2;
+            }
+            entries
+        });
+        let guess = {
+            let a: f64 = 0.75_f64.sqrt();
             DMatrix::from_columns(&[
-                sphere(a, 0.0, 7.0 + a, 1.0),
-                sphere(-a, 0.0, 7.0 - a, 1.0),
+                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)
             ])
         };
-        let problem_tfm = ConstraintProblem {
-            gram: problem_orig.gram,
-            frozen: problem_orig.frozen,
-            guess: guess_tfm,
-        };
-        let Realization { result: result_tfm, history: history_tfm } = realize_gram(
-            &problem_tfm, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
+        println!();
+        let (config, success, history) = realize_gram(
+            &gram, guess, &[],
+            1.0e-12, 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!(history_tfm.scaled_loss.len(), 1);
-        
-        // project a nudge to the tangent space of the solution variety at the
-        // original solution
-        let motion_orig = DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]);
-        let motion_orig_proj = tangent_orig.proj(&motion_orig.as_view(), 0);
-        
-        // project the equivalent nudge to the tangent space of the solution
-        // variety at the transformed solution
-        let motion_tfm = DVector::from_column_slice(&[FRAC_1_SQRT_2, 0.0, FRAC_1_SQRT_2, 0.0]);
-        let motion_tfm_proj = tangent_tfm.proj(&motion_tfm.as_view(), 0);
-        
-        // take the transformation that sends the original solution to the
-        // transformed solution and apply it to the motion that the original
-        // solution makes in response to the nudge
-        const ELEMENT_DIM: usize = 5;
-        let rot = DMatrix::from_column_slice(ELEMENT_DIM, ELEMENT_DIM, &[
-            FRAC_1_SQRT_2, 0.0, -FRAC_1_SQRT_2, 0.0, 0.0,
-                      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,
+        print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
+        if success {
+            println!("Target accuracy achieved!");
+        } else {
+            println!("Failed to reach target accuracy");
+        }
+        println!("Steps: {}", history.scaled_loss.len() - 1);
+        println!("Loss: {}", history.scaled_loss.last().unwrap());
+        println!("\nStep │ Loss\n─────┼────────────────────────────────");
+        for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
+            println!("{:<4} │ {}", step, scaled_loss);
+        }
+    }
+    
+    #[test]
+    fn point_on_sphere_example() {
+        let gram = PartialMatrix({
+            let mut entries = Vec::<MatrixEntry>::new();
+            for j in 0..2 {
+                for k in 0..2 {
+                    entries.push(MatrixEntry {
+                        index: (j, k),
+                        value: if (j, k) == (1, 1) { 1.0 } else { 0.0 }
+                    });
+                }
+            }
+            entries
+        });
+        let guess = DMatrix::from_columns(&[
+            point(0.0, 0.0, 2.0),
+            sphere(0.0, 0.0, 0.0, 1.0)
         ]);
-        let transl = translation(Vector3::new(0.0, 0.0, 7.0));
-        let motion_proj_tfm = transl * rot * motion_orig_proj;
-        
-        // confirm that the projection of the nudge is equivariant. we loosen
-        // the comparison tolerance because the transformation seems to
-        // introduce some numerical error
-        const SCALED_TOL_TFM: f64 = 1.0e-9;
-        let tol_sq = ((problem_orig.guess.nrows() * problem_orig.guess.ncols()) as f64) * SCALED_TOL_TFM * SCALED_TOL_TFM;
-        assert!((motion_proj_tfm - motion_tfm_proj).norm_squared() < tol_sq);
+        let frozen = [(3, 0)];
+        println!();
+        let (config, success, history) = realize_gram(
+            &gram, guess, &frozen,
+            1.0e-12, 0.5, 0.9, 1.1, 200, 110
+        );
+        print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
+        print!("Configuration:{}", config);
+        if success {
+            println!("Target accuracy achieved!");
+        } else {
+            println!("Failed to reach target accuracy");
+        }
+        println!("Steps: {}", history.scaled_loss.len() - 1);
+        println!("Loss: {}", history.scaled_loss.last().unwrap());
+        println!("\nStep │ Loss\n─────┼────────────────────────────────");
+        for (step, scaled_loss) in history.scaled_loss.into_iter().enumerate() {
+            println!("{:<4} │ {}", step, scaled_loss);
+        }
     }
 }
\ No newline at end of file
diff --git a/app-proto/src/components/identity.vert b/app-proto/src/identity.vert
similarity index 100%
rename from app-proto/src/components/identity.vert
rename to app-proto/src/identity.vert
diff --git a/app-proto/src/components/spheres.frag b/app-proto/src/inversive.frag
similarity index 95%
rename from app-proto/src/components/spheres.frag
rename to app-proto/src/inversive.frag
index fa317a8..d50cb1e 100644
--- a/app-proto/src/components/spheres.frag
+++ b/app-proto/src/inversive.frag
@@ -17,7 +17,7 @@ struct vecInv {
 const int SPHERE_MAX = 200;
 uniform int sphere_cnt;
 uniform vecInv sphere_list[SPHERE_MAX];
-uniform vec4 color_list[SPHERE_MAX];
+uniform vec3 color_list[SPHERE_MAX];
 uniform float highlight_list[SPHERE_MAX];
 
 // view
@@ -25,6 +25,7 @@ uniform vec2 resolution;
 uniform float shortdim;
 
 // controls
+uniform float opacity;
 uniform int layer_threshold;
 uniform bool debug_mode;
 
@@ -68,7 +69,7 @@ struct Fragment {
     vec4 color;
 };
 
-Fragment sphere_shading(vecInv v, vec3 pt, vec4 base_color) {
+Fragment sphere_shading(vecInv v, vec3 pt, vec3 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
@@ -78,7 +79,7 @@ Fragment sphere_shading(vecInv v, vec3 pt, vec4 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.rgb, base_color.a));
+    return Fragment(pt, normal, vec4(illum * base_color, opacity));
 }
 
 float intersection_dist(Fragment a, Fragment b) {
@@ -191,11 +192,10 @@ 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,
-        vec4(hit.dimming * sphere_color.rgb, sphere_color.a)
+        hit.dimming * color_list[hit.id]
     );
     float highlight_next = highlight_list[hit.id];
     --layer;
@@ -206,11 +206,10 @@ 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,
-            vec4(hit.dimming * sphere_color.rgb, sphere_color.a)
+            hit.dimming * color_list[hit.id]
         );
         highlight_next = highlight_list[hit.id];
         
diff --git a/app-proto/src/lib.rs b/app-proto/src/lib.rs
deleted file mode 100644
index 0d9bc4a..0000000
--- a/app-proto/src/lib.rs
+++ /dev/null
@@ -1 +0,0 @@
-pub mod engine;
\ No newline at end of file
diff --git a/app-proto/src/main.rs b/app-proto/src/main.rs
index a03b026..2c71a83 100644
--- a/app-proto/src/main.rs
+++ b/app-proto/src/main.rs
@@ -1,67 +1,40 @@
+mod add_remove;
 mod assembly;
-mod components;
+mod display;
 mod engine;
-mod specified;
+mod outline;
 
-#[cfg(test)]
-mod tests;
-
-use std::{collections::BTreeSet, rc::Rc};
+use rustc_hash::FxHashSet;
 use sycamore::prelude::*;
 
-use assembly::{Assembly, Element};
-use components::{
-    add_remove::AddRemove,
-    diagnostics::Diagnostics,
-    display::Display,
-    outline::Outline,
-};
+use add_remove::AddRemove;
+use assembly::Assembly;
+use display::Display;
+use outline::Outline;
 
 #[derive(Clone)]
 struct AppState {
     assembly: Assembly,
-    selection: Signal<BTreeSet<Rc<dyn Element>>>,
+    selection: Signal<FxHashSet<usize>>
 }
 
 impl AppState {
-    fn new() -> Self {
-        Self {
+    fn new() -> AppState {
+        AppState {
             assembly: Assembly::new(),
-            selection: create_signal(BTreeSet::default()),
-        }
-    }
-    
-    // in single-selection mode, select the given element. in multiple-selection
-    // mode, toggle whether the given element is selected
-    fn select(&self, element: &Rc<dyn Element>, multi: bool) {
-        if multi {
-            self.selection.update(|sel| {
-                if !sel.remove(element) {
-                    sel.insert(element.clone());
-                }
-            });
-        } else {
-            self.selection.update(|sel| {
-                sel.clear();
-                sel.insert(element.clone());
-            });
+            selection: create_signal(FxHashSet::default())
         }
     }
 }
 
 fn main() {
-    // set the console error panic hook
-    #[cfg(feature = "console_error_panic_hook")]
-    console_error_panic_hook::set_once();
-    
     sycamore::render(|| {
         provide_context(AppState::new());
         
         view! {
-            div(id = "sidebar") {
+            div(id="sidebar") {
                 AddRemove {}
                 Outline {}
-                Diagnostics {}
             }
             Display {}
         }
diff --git a/app-proto/src/outline.rs b/app-proto/src/outline.rs
new file mode 100644
index 0000000..11cc061
--- /dev/null
+++ b/app-proto/src/outline.rs
@@ -0,0 +1,207 @@
+use itertools::Itertools;
+use sycamore::prelude::*;
+use web_sys::{
+    Event,
+    HtmlInputElement,
+    KeyboardEvent,
+    MouseEvent,
+    wasm_bindgen::JsCast
+};
+
+use crate::{AppState, assembly, assembly::Constraint};
+
+// an editable view of the Lorentz product representing a constraint
+#[component(inline_props)]
+fn LorentzProductInput(constraint: Constraint) -> View {
+    view! {
+        input(
+            r#type="text",
+            bind:value=constraint.rep_text,
+            on:change=move |event: Event| {
+                let target: HtmlInputElement = event.target().unwrap().unchecked_into();
+                match target.value().parse::<f64>() {
+                    Ok(rep) => batch(|| {
+                        constraint.rep.set(rep);
+                        constraint.rep_valid.set(true);
+                    }),
+                    Err(_) => constraint.rep_valid.set(false)
+                };
+            }
+        )
+    }
+}
+
+// a list item that shows a constraint in an outline view of an element
+#[component(inline_props)]
+fn ConstraintOutlineItem(constraint_key: usize, element_key: usize) -> View {
+    let state = use_context::<AppState>();
+    let assembly = &state.assembly;
+    let constraint = assembly.constraints.with(|csts| csts[constraint_key].clone());
+    let other_arg = if constraint.args.0 == element_key {
+        constraint.args.1
+    } else {
+        constraint.args.0
+    };
+    let other_arg_label = assembly.elements.with(|elts| elts[other_arg].label.clone());
+    let class = constraint.rep_valid.map(
+        |&rep_valid| if rep_valid { "cst" } else { "cst invalid" }
+    );
+    view! {
+        li(class=class.get()) {
+            input(r#type="checkbox", bind:checked=constraint.active)
+            div(class="cst-label") { (other_arg_label) }
+            LorentzProductInput(constraint=constraint)
+            div(class="status")
+        }
+    }
+}
+
+// a list item that shows an element in an outline view of an assembly
+#[component(inline_props)]
+fn ElementOutlineItem(key: usize, element: assembly::Element) -> View {
+    let state = use_context::<AppState>();
+    let class = state.selection.map(
+        move |sel| if sel.contains(&key) { "selected" } else { "" }
+    );
+    let label = element.label.clone();
+    let rep_components = element.rep.map(
+        |rep| rep.iter().map(
+            |u| format!("{:.3}", u).replace("-", "\u{2212}")
+        ).collect()
+    );
+    let constrained = element.constraints.map(|csts| csts.len() > 0);
+    let constraint_list = element.constraints.map(
+        |csts| csts.clone().into_iter().collect()
+    );
+    let details_node = create_node_ref();
+    view! {
+        li {
+            details(ref=details_node) {
+                summary(
+                    class=class.get(),
+                    on:keydown={
+                        move |event: KeyboardEvent| {
+                            match event.key().as_str() {
+                                "Enter" => {
+                                    if 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.prevent_default();
+                                },
+                                "ArrowRight" if constrained.get() => {
+                                    let _ = details_node
+                                        .get()
+                                        .unchecked_into::<web_sys::Element>()
+                                        .set_attribute("open", "");
+                                },
+                                "ArrowLeft" => {
+                                    let _ = details_node
+                                        .get()
+                                        .unchecked_into::<web_sys::Element>()
+                                        .remove_attribute("open");
+                                },
+                                _ => ()
+                            }
+                        }
+                    }
+                ) {
+                    div(
+                        class="elt-switch",
+                        on:click=|event: MouseEvent| event.stop_propagation()
+                    )
+                    div(
+                        class="elt",
+                        on:click={
+                            move |event: MouseEvent| {
+                                if 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="elt-label") { (label) }
+                        div(class="elt-rep") {
+                            Indexed(
+                                list=rep_components,
+                                view=|coord_str| view! {
+                                    div { (coord_str) }
+                                }
+                            )
+                        }
+                        div(class="status")
+                    }
+                }
+                ul(class="constraints") {
+                    Keyed(
+                        list=constraint_list,
+                        view=move |cst_key| view! {
+                            ConstraintOutlineItem(
+                                constraint_key=cst_key,
+                                element_key=key
+                            )
+                        },
+                        key=|cst_key| cst_key.clone()
+                    )
+                }
+            }
+        }
+    }
+}
+
+// a component that lists the elements of the current assembly, showing the
+// constraints on each element as a collapsible sub-list. its implementation
+// is based on Kate Morley's HTML + CSS tree views:
+//
+//   https://iamkate.com/code/tree-views/
+//
+#[component]
+pub fn Outline() -> View {
+    let state = use_context::<AppState>();
+    
+    // list the elements alphabetically by ID
+    let element_list = state.assembly.elements.map(
+        |elts| elts
+            .clone()
+            .into_iter()
+            .sorted_by_key(|(_, elt)| elt.id.clone())
+            .collect()
+    );
+    
+    view! {
+        ul(
+            id="outline",
+            on:click={
+                let state = use_context::<AppState>();
+                move |_| state.selection.update(|sel| sel.clear())
+            }
+        ) {
+            Keyed(
+                list=element_list,
+                view=|(key, elt)| view! {
+                    ElementOutlineItem(key=key, element=elt)
+                },
+                key=|(key, _)| key.clone()
+            )
+        }
+    }
+}
\ No newline at end of file
diff --git a/app-proto/src/specified.rs b/app-proto/src/specified.rs
deleted file mode 100644
index 788460b..0000000
--- a/app-proto/src/specified.rs
+++ /dev/null
@@ -1,44 +0,0 @@
-use std::num::ParseFloatError;
-
-// a real number described by a specification string. since the structure is
-// read-only, we can guarantee that `spec` always specifies `value` in the
-// following format
-//   ┌──────────────────────────────────────────────────────┬───────────┐
-//   │ `spec`                                               │ `value`   │
-//   ┝━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┿━━━━━━━━━━━┥
-//   │ a string that parses to the floating-point value `x` │ `Some(x)` │
-//   ├──────────────────────────────────────────────────────┼───────────┤
-//   │ the empty string                                     │ `None`    │
-//   └──────────────────────────────────────────────────────┴───────────┘
-#[readonly::make]
-pub struct SpecifiedValue {
-    pub spec: String,
-    pub value: Option<f64>,
-}
-
-impl SpecifiedValue {
-    pub fn from_empty_spec() -> Self {
-        Self { spec: String::new(), value: None }
-    }
-    
-    pub fn is_present(&self) -> bool {
-        matches!(self.value, Some(_))
-    }
-}
-
-// a `SpecifiedValue` can be constructed from a specification string, formatted
-// as described in the comment on the structure definition. the result is `Ok`
-// if the specification is properly formatted, and `Error` if not
-impl TryFrom<String> for SpecifiedValue {
-    type Error = ParseFloatError;
-    
-    fn try_from(spec: String) -> Result<Self, Self::Error> {
-        if spec.is_empty() {
-            Ok(Self::from_empty_spec())
-        } else {
-            spec.parse::<f64>().map(
-                |value| Self { spec, value: Some(value) }
-            )
-        }
-    }
-}
\ No newline at end of file
diff --git a/app-proto/src/tests.rs b/app-proto/src/tests.rs
deleted file mode 100644
index 2c5436b..0000000
--- a/app-proto/src/tests.rs
+++ /dev/null
@@ -1,14 +0,0 @@
-use std::process::Command;
-
-// build and bundle the application, reporting success if there are no errors or
-// warnings. to see this test fail while others succeed, try moving `index.html`
-// or one of the assets that it links to
-#[test]
-fn trunk_build_test() {
-    let build_status = Command::new("trunk")
-        .arg("build")
-        .env("RUSTFLAGS", "-D warnings")
-        .status()
-        .expect("Call to Trunk failed");
-    assert!(build_status.success());
-}
\ No newline at end of file
diff --git a/deploy/.gitignore b/deploy/.gitignore
deleted file mode 100644
index 192f529..0000000
--- a/deploy/.gitignore
+++ /dev/null
@@ -1,5 +0,0 @@
-/dyna3.zip
-/dyna3/index.html
-/dyna3/dyna3-*.js
-/dyna3/dyna3-*.wasm
-/dyna3/main-*.css
\ No newline at end of file
diff --git a/notes/inversive.md b/notes/inversive.md
index 933eb35..5ee6329 100644
--- a/notes/inversive.md
+++ b/notes/inversive.md
@@ -41,25 +41,3 @@ I will have to work out formulas for the Euclidean distance between two entities
 In this vein, it seems as though if J1 and J2 are the reps of two points, then Q(J1,J2) = d^2/2. So then the sphere centered at J1 through J2 is (J1-(2Q(J1,J2),0,0,0,0))/sqrt(2Q(J1,J2)). Ugh has a sqrt in it. Similarly for sphere centered at J3 through J2, (J3-(2Q(J3,J2),0000))/sqrt(2Q(J3,J2)). J1,J2,J3 are collinear if these spheres are tangent, i.e. if those vectors have Q-inner-product 1, which is to say Q(J1,J3) - Q(J1,J2) - Q(J3,J2) = 2sqrt(Q(J1,J2)Q(J2,J3)). But maybe that's not the simplest way of putting it. After all, we can just say that the cross-product of the two differences is 0; that has no square roots in it.
 
 One conceivable way to canonicalize lines is to use the *perpendicular* plane that goes through the origin, that's uniquely defined, and anyway just amounts to I = (0,0,d) where d is the ordinary direction vector of the line; and a point J in that plane that the line goes through, which just amounts to J=(r^2,1,E) with Q(I,J) = 0, i.e. E\dot d = 0. It's also the point on the line closest to the origin. The reason that we don't usually use that point as the companion to the direction vector is that the resulting set of six coordinates is not homogeneous. But here that's not an issue, since we have our standard point coordinates and plane coordinates; and for a plane through the origin, only two of the direction coordinates are really free, and then we have the one dot-product relation, so only two of the point coordinates are really free, giving us the correct dimensionality of 4 for the set of lines. So in some sense this says that we could take naively as coordinates for a line the projection of the unit direction vector to the xy plane and the projection of the line's closest point to the origin to the xy plane. That doesn't seem to have any weird gimbal locks or discontinuities or anything. And with these coordinates, you can test if the point E=x,y,z is on the line (dx,dy,cx,cy) by extending (dx,dy) to d via dz = sqrt(1-dx^2 - dy^2), extending (cx,cy) to c by determining cz via d\dot c = 0, and then checking if d\cross(E-c) = 0. And you can see if two lines are parallel just by checking if they have the same direction vector, and if not, you can see if they are coplanar by projecting both of their closest points perpendicularly onto the line in the direction of the cross product of their directions, and if the projections match they are coplanar.
-
-#### Engine Conventions
-
-The coordinate conventions used in the engine are different from the ones used in these notes. Marking the engine vectors and coordinates with $'$, we have
-$$I' = (x', y', z', b', c'),$$
-where
-$$
-\begin{align*}
-x' & = x & b' & = b/2 \\
-y' & = y & c' & = c/2. \\
-z' & = z
-\end{align*}
-$$
-The engine uses the quadratic form $Q' = -Q$, which is expressed in engine coordinates as
-$$Q'(I'_1, I'_2) = x'_1 x'_2 + y'_1 y'_2 + z'_1 z'_2 - 2(b'_1c'_2 + c'_1 b'_2).$$
-In the `engine` module, the matrix of $Q'$ is encoded in the lazy static variable `Q`.
-
-In the engine's coordinate conventions, a sphere with radius $r > 0$ centered on $P = (P_x, P_y, P_z)$ is represented by the vector
-$$I'_s = \left(\frac{P_x}{r}, \frac{P_y}{r}, \frac{P_z}{r}, \frac1{2r}, \frac{\|P\|^2 - r^2}{2r}\right),$$
-which has the normalization $Q'(I'_s, I'_s) = 1$. The point $P$ is represented by the vector
-$$I'_P = \left(P_x, P_y, P_z, \frac{1}{2}, \frac{\|P\|^2}{2}\right).$$
-In the `engine` module, these formulas are encoded in the `sphere` and `point` functions.
\ No newline at end of file
diff --git a/tools/package-for-deployment.sh b/tools/package-for-deployment.sh
deleted file mode 100644
index fdda434..0000000
--- a/tools/package-for-deployment.sh
+++ /dev/null
@@ -1,16 +0,0 @@
-# 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/." "$DEST"
diff --git a/tools/run-examples.sh b/tools/run-examples.sh
deleted file mode 100644
index 0946d92..0000000
--- a/tools/run-examples.sh
+++ /dev/null
@@ -1,20 +0,0 @@
-# run all Cargo examples, as described here:
-#
-#   Karol Kuczmarski. "Add examples to your Rust libraries"
-#   http://xion.io/post/code/rust-examples.html
-#
-# you should invoke this script by calling `sh` or another interpreter, rather
-# than calling `souce`, to ensure that the script can find the manifest file for
-# the application prototype
-
-# find the manifest file for the application prototype
-MANIFEST="$(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
\ No newline at end of file