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..b9fc0a1 100644
--- a/app-proto/main.css
+++ b/app-proto/main.css
@@ -3,8 +3,7 @@
   --text-bright: white;
   --text-invalid: #f58fc2; /* bright pink */
   --border: #555; /* light gray */
-  --border-focus-dark: #aaa; /* bright gray */
-  --border-focus-light: white;
+  --border-focus: #aaa; /* bright gray */
   --border-invalid: #70495c; /* dusky pink */
   --selection-highlight: #444; /* medium gray */
   --page-background: #222; /* dark gray */
@@ -18,24 +17,13 @@ body {
   font-family: 'Fira Sans', sans-serif;
 }
 
-.invalid {
-  color: var(--text-invalid);
-}
-
-.status {
-  width: 20px;
-  text-align: center;
-  font-family: 'Noto Emoji';
-  font-style: normal;
-}
-
 /* sidebar */
 
 #sidebar {
   display: flex;
   flex-direction: column;
   float: left;
-  width: 500px;
+  width: 450px;
   height: 100vh;
   margin: 0px;
   padding: 0px;
@@ -53,7 +41,9 @@ body {
 }
 
 #add-remove > button {
+  width: 32px;
   height: 32px;
+  font-size: large;
 }
 
 /* KLUDGE */
@@ -62,9 +52,7 @@ body {
   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 */
@@ -89,22 +77,18 @@ summary.selected {
   background-color: var(--selection-highlight);
 }
 
-summary > div, .regulator {
+summary > div, .constraint {
   padding-top: 4px;
   padding-bottom: 4px;
 }
 
-.element, .regulator {
+.element, .constraint {
   display: flex;
   flex-grow: 1;
   padding-left: 8px;
   padding-right: 8px;
 }
 
-.element > input {
-  margin-left: 8px;
-}
-
 .element-switch {
   width: 18px;
   padding-left: 2px;
@@ -123,7 +107,7 @@ details[open]:has(li) .element-switch::after {
   flex-grow: 1;
 }
 
-.regulator-label {
+.constraint-label {
   flex-grow: 1;
 }
 
@@ -139,88 +123,45 @@ details[open]:has(li) .element-switch::after {
   width: 56px;
 }
 
-.regulator {
+.constraint {
   font-style: italic;
 }
 
-.regulator-type {
-  padding: 2px 8px 0px 8px;
-  font-size: 10pt;
+.constraint.invalid {
+  color: var(--text-invalid);
 }
 
-.regulator-input {
-  margin-right: 4px;
+.constraint > input[type=checkbox] {
+  margin: 0px 8px 0px 0px;
+}
+
+.constraint > input[type=text] {
   color: inherit;
   background-color: inherit;
   border: 1px solid var(--border);
   border-radius: 2px;
 }
 
-.regulator-input::placeholder {
-  color: inherit;
-  opacity: 54%;
-  font-style: italic;
-}
-
-.regulator-input.constraint {
-  background-color: var(--display-background);
-}
-
-.regulator-input.invalid {
-  color: var(--text-invalid);
+.constraint.invalid > input[type=text] {
   border-color: var(--border-invalid);
 }
 
-.regulator-input.invalid + .status::after, details:has(.invalid):not([open]) .status::after {
+.status {
+  width: 20px;
+  padding-left: 4px;
+  text-align: center;
+  font-family: 'Noto Emoji';
+  font-style: normal;
+}
+
+.invalid > .status::after, details:has(.invalid):not([open]) .status::after {
   content: '⚠';
   color: var(--text-invalid);
 }
 
-/* diagnostics */
-
-#diagnostics {
-  margin: 10px;
-}
-
-#diagnostics-bar {
-  display: flex;
-}
-
-#realization-status {
-  display: flex;
-  flex-grow: 1;
-}
-
-#realization-status .status {
-  margin-right: 4px;
-}
-
-#realization-status :not(.status) {
-  flex-grow: 1;
-}
-
-#realization-status .status::after {
-  content: '✓';
-}
-
-#realization-status.invalid .status::after {
-  content: '⚠';
-}
-
-.diagnostics-panel {
-  margin-top: 10px;
-  min-height: 180px;
-}
-
-.diagnostics-chart {
-  background-color: var(--display-background);
-  border: 1px solid var(--border);
-  border-radius: 8px;
-}
-
 /* display */
 
-#display {
+canvas {
   float: left;
   margin-left: 20px;
   margin-top: 20px;
@@ -229,12 +170,6 @@ details[open]:has(li) .element-switch::after {
   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: var(--border-focus);
 }
\ 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..f21c2ab
--- /dev/null
+++ b/app-proto/src/add_remove.rs
@@ -0,0 +1,243 @@
+use sycamore::prelude::*;
+use web_sys::{console, wasm_bindgen::JsValue};
+
+use crate::{engine, AppState, assembly::{Assembly, Constraint, Element}};
+
+/* DEBUG */
+// load an example assembly for testing. this code will be removed once we've
+// built a more formal test assembly system
+fn load_gen_assemb(assembly: &Assembly) {
+    let _ = assembly.try_insert_element(
+        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 */
+// load an example assembly for testing. this code will be removed once we've
+// built a more formal test assembly system
+fn load_low_curv_assemb(assembly: &Assembly) {
+    let a = 0.75_f64.sqrt();
+    let _ = assembly.try_insert_element(
+        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());
+            
+            // increment assembly serial number
+            state.assembly_serial.set_fn_silent(|serial| serial.wrapping_add(1));
+            
+            // 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 */ // 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 = state.selection.with(
+                        |sel| {
+                            let subject_vec: Vec<_> = sel.into_iter().collect();
+                            (subject_vec[0].clone(), subject_vec[1].clone())
+                        }
+                    );
+                    let lorentz_prod = create_signal(0.0);
+                    let lorentz_prod_valid = create_signal(false);
+                    let active = create_signal(true);
+                    state.assembly.insert_constraint(Constraint {
+                        subjects: subjects,
+                        lorentz_prod: lorentz_prod,
+                        lorentz_prod_text: create_signal(String::new()),
+                        lorentz_prod_valid: lorentz_prod_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.subjects.0),
+                                &JsValue::from(cst.subjects.1),
+                                &JsValue::from(":"),
+                                &JsValue::from(cst.lorentz_prod.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", subjects.0, subjects.1)
+                        ));
+                        lorentz_prod.track();
+                        if active.get() && lorentz_prod_valid.get() {
+                            state.assembly.realize();
+                        }
+                    });
+                }
+            ) { "🔗" }
+            select(bind:value=assembly_name) { /* DEBUG */ // example assembly chooser
+                option(value="general") { "General" }
+                option(value="low-curv") { "Low-curvature" }
+                option(value="empty") { "Empty" }
+            }
+        }
+    }
+}
\ No newline at end of file
diff --git a/app-proto/src/assembly.rs b/app-proto/src/assembly.rs
index 94e7b3c..35b4417 100644
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@@ -1,592 +1,93 @@
-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};
+
+// the types of the keys we use to access an assembly's elements and constraints
+pub type ElementKey = usize;
+pub type ConstraintKey = usize;
 
 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 constraints: Signal<BTreeSet<ConstraintKey>>,
+    
+    // the configuration matrix column index that was assigned to this element
+    // last time the assembly was realized
+    column_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: DVector<f64>
+    ) -> Element {
+        Element {
+            id: id,
+            label: label,
+            color: color,
             representation: create_signal(representation),
-            ghost: create_signal(false),
-            regulators: create_signal(BTreeSet::new()),
-            serial: Self::next_serial(),
-            column_index: None.into(),
+            constraints: create_signal(BTreeSet::default()),
+            column_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 subjects: (ElementKey, ElementKey),
+    pub lorentz_prod: Signal<f64>,
+    pub lorentz_prod_text: Signal<String>,
+    pub lorentz_prod_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, ElementKey>>
 }
 
 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 +95,36 @@ 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 subjects = constraint.subjects;
+        let key = self.constraints.update(|csts| csts.insert(constraint));
+        let subject_constraints = self.elements.with(
+            |elts| (elts[subjects.0].constraints, elts[subjects.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()
-                            }
-                        }
-                    )
-                );
-            }
-        });
+        subject_constraints.0.update(|csts| csts.insert(key));
+        subject_constraints.1.update(|csts| csts.insert(key));
     }
     
     // --- realization ---
@@ -652,248 +132,79 @@ 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.column_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.lorentz_prod_valid.get_untracked() {
+                        let subjects = cst.subjects;
+                        let row = elts[subjects.0].column_index;
+                        let col = elts[subjects.1].column_index;
+                        gram_to_be.push_sym(row, col, cst.lorentz_prod.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.column_index;
+                gram_to_be.push_sym(index, index, 1.0);
+                guess_to_be.set_column(index, &elt.representation.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.representation.update(
+                    |rep| rep.set_column(0, &config.column(elt.column_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..ee0af47
--- /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.representation.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.representation.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..343b96e 100644
--- a/app-proto/src/engine.rs
+++ b/app-proto/src/engine.rs
@@ -1,9 +1,10 @@
 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 ---
 
+#[cfg(test)]
 pub fn point(x: f64, y: f64, z: f64) -> DVector<f64> {
     DVector::from_column_slice(&[x, y, z, 0.5, 0.5*(x*x + y*y + z*z)])
 }
@@ -16,7 +17,7 @@ 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 +31,112 @@ 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 +146,6 @@ 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 +154,7 @@ 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 +169,25 @@ 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 +196,17 @@ 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 +229,14 @@ 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 +249,85 @@ 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 +336,43 @@ 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 +382,159 @@ 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);
+        }
+    }
+    
+    /* TO DO */
+    // --- new test placed here to avoid merge conflict ---
+    
+    // at the frozen indices, the optimization steps should have exact zeros,
+    // and the realized configuration should match the initial guess
+    #[test]
+    fn frozen_entry_test() {
+        let gram = {
+            let mut gram_to_be = PartialMatrix::new();
+            for j in 0..2 {
+                for k in j..2 {
+                    gram_to_be.push_sym(j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
+                }
+            }
+            gram_to_be
+        };
+        let guess = DMatrix::from_columns(&[
+            point(0.0, 0.0, 2.0),
+            sphere(0.0, 0.0, 0.0, 1.0)
+        ]);
+        let frozen = [(3, 0), (3, 1)];
+        println!();
+        let (config, success, history) = realize_gram(
+            &gram, guess.clone(), &frozen,
+            1.0e-12, 0.5, 0.9, 1.1, 200, 110
+        );
+        assert_eq!(success, true);
+        for base_step in history.base_step.into_iter() {
+            for index in frozen {
+                assert_eq!(base_step[index], 0.0);
+            }
+        }
+        for index in frozen {
+            assert_eq!(config[index], guess[index]);
+        }
     }
 }
\ 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..d916a81 100644
--- a/app-proto/src/main.rs
+++ b/app-proto/src/main.rs
@@ -1,67 +1,42 @@
+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, ElementKey};
+use display::Display;
+use outline::Outline;
 
 #[derive(Clone)]
 struct AppState {
     assembly: Assembly,
-    selection: Signal<BTreeSet<Rc<dyn Element>>>,
+    assembly_serial: Signal<u32>,
+    selection: Signal<FxHashSet<ElementKey>>
 }
 
 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());
-            });
+            assembly_serial: create_signal(0),
+            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..39247fa
--- /dev/null
+++ b/app-proto/src/outline.rs
@@ -0,0 +1,211 @@
+use itertools::Itertools;
+use sycamore::prelude::*;
+use web_sys::{
+    Event,
+    HtmlInputElement,
+    KeyboardEvent,
+    MouseEvent,
+    wasm_bindgen::JsCast
+};
+
+use crate::{AppState, assembly, assembly::{Constraint, ConstraintKey, ElementKey}};
+
+// 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.lorentz_prod_text,
+            on:change=move |event: Event| {
+                let target: HtmlInputElement = event.target().unwrap().unchecked_into();
+                match target.value().parse::<f64>() {
+                    Ok(lorentz_prod) => batch(|| {
+                        constraint.lorentz_prod.set(lorentz_prod);
+                        constraint.lorentz_prod_valid.set(true);
+                    }),
+                    Err(_) => constraint.lorentz_prod_valid.set(false)
+                };
+            }
+        )
+    }
+}
+
+// a list item that shows a constraint in an outline view of an element
+#[component(inline_props)]
+fn ConstraintOutlineItem(constraint_key: ConstraintKey, element_key: ElementKey) -> View {
+    let state = use_context::<AppState>();
+    let assembly = &state.assembly;
+    let constraint = assembly.constraints.with(|csts| csts[constraint_key].clone());
+    let other_subject = if constraint.subjects.0 == element_key {
+        constraint.subjects.1
+    } else {
+        constraint.subjects.0
+    };
+    let other_subject_label = assembly.elements.with(|elts| elts[other_subject].label.clone());
+    let class = constraint.lorentz_prod_valid.map(
+        |&lorentz_prod_valid| if lorentz_prod_valid { "constraint" } else { "constraint invalid" }
+    );
+    view! {
+        li(class=class.get()) {
+            input(r#type="checkbox", bind:checked=constraint.active)
+            div(class="constraint-label") { (other_subject_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: ElementKey, 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.representation.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="element-switch",
+                        on:click=|event: MouseEvent| event.stop_propagation()
+                    )
+                    div(
+                        class="element",
+                        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="element-label") { (label) }
+                        div(class="element-representation") {
+                            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(
+        move |elts| {
+            let asm_serial = state.assembly_serial.get_untracked();
+            elts
+                .clone()
+                .into_iter()
+                .sorted_by_key(|(_, elt)| elt.id.clone())
+                .map(|(key, elt)| (asm_serial, key, elt))
+                .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=|(asm_serial, key, _)| (asm_serial.clone(), 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/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