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	<!DOCTYPE html>
	<html lang="en">
	<head>
	<meta charset="utf-8">
	<meta name="viewport" content="width=device-width, initial-scale=1">
	<title>Slapstack Studio — spawn objects, move them, in Gabor space</title>
	<style>
	:root {
	--chassis:#1d222e; --panel:#262c3b; --panel-edge:#333b4f; --well:#10131b;
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	header h1{font-family:var(--cond);font-size:20px;letter-spacing:2.5px;font-weight:700}
	header h1 em{color:var(--phosphor);font-style:normal}
	header .claim{color:var(--muted);font-size:11.5px}
	#state-lamp{margin-left:auto;font-size:11px;letter-spacing:1.5px;padding:3px 10px;
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	#state-lamp.soup{color:var(--outlier);border-color:var(--outlier)}
	#state-lamp.binding{color:var(--entropy);border-color:var(--entropy)}
	#state-lamp.bound{color:var(--go);border-color:var(--go)}
	main{flex:1;display:flex;gap:12px;padding:12px 16px;min-height:0}
	#stage-wrap{flex:1;display:flex;align-items:center;justify-content:center;min-width:0}
	#stage{position:relative;background:var(--well);border:1px solid var(--panel-edge);
	border-radius:6px;box-shadow:inset 0 0 60px rgba(0,0,0,.55)}
	#stage canvas{position:absolute;inset:0;width:100%;height:100%;border-radius:6px}
	#overlay-canvas{cursor:grab}
	#overlay-canvas.dragging{cursor:grabbing}
	#stage .hint{position:absolute;bottom:7px;left:0;right:0;text-align:center;
	color:var(--muted);font-size:10.5px;pointer-events:none;text-shadow:0 1px 3px #000}
	aside{width:330px;flex-shrink:0;display:flex;flex-direction:column;gap:9px;
	overflow-y:auto;padding-right:2px}
	.card{background:var(--panel);border:1px solid var(--panel-edge);border-radius:6px;
	padding:10px 11px}
	.card h2{font-family:var(--cond);font-size:12px;letter-spacing:2px;font-weight:700;
	color:var(--muted);margin-bottom:8px}
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	.row+.row{margin-top:7px}
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	input[type=text]:focus-visible,textarea:focus-visible{outline:2px solid var(--phosphor);border-color:transparent}
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	min-height:13px;white-space:pre-wrap}
	#ledger p{font-size:10.5px;line-height:1.5;color:var(--muted);margin-bottom:6px}
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	details summary{cursor:pointer;font-family:var(--cond);font-size:12px;letter-spacing:2px;color:var(--muted)}
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	input[type=file]{font-size:10.5px;color:var(--muted);max-width:170px}
	@media (max-width:900px){main{flex-direction:column;overflow-y:auto}body{overflow:auto}aside{width:100%}}
	</style>
	</head>
	<body>

	<header>
	<h1>SLAPSTACK <em>STUDIO</em></h1>
	<span class="claim">spawn layers with AI · scramble · bind · grab · stack · every entity is a posterior</span>
	<span id="state-lamp" class="soup">ATOM SOUP</span>
	</header>

	<main>
	<div id="stage-wrap">
	<div id="stage">
	<canvas id="scene-canvas"></canvas>
	<canvas id="overlay-canvas"></canvas>
	<div class="hint">drag = pose clamp · wheel rotate · shift+wheel scale · shift+click = hint · erase tool: brush deletes atoms</div>
	</div>
	</div>

	<aside>
	<div class="card">
	<h2>SCENE</h2>
	<div class="row">
	<button id="btn-scramble">Scramble</button>
	<button id="btn-bind" class="primary">Bind</button>
	<span class="spacer"></span>
	<span class="dim">noise</span>
	<input type="range" id="noise" min="0" max="10" value="1" style="width:60px" aria-label="observation noise">
	</div>
	<div class="row">
	<span class="dim">composite</span>
	<label class="tog"><input type="radio" name="comp" value="field" checked> field</label>
	<label class="tog"><input type="radio" name="comp" value="painter"> painter (depth)</label>
	<span class="spacer"></span>
	<label class="tog"><input type="checkbox" id="auto-occ" checked> depth occlusion</label>
	</div>
	<div id="bind-meter"><div></div></div>
	<div id="metrics">
	<span class="dim">binding vs truth</span><span class="readout" id="m-acc">—</span>
	<span class="dim">mean entropy</span><span class="readout" id="m-ent">—</span>
	<span class="dim">BP iterations</span><span class="readout" id="m-it">—</span>
	<span class="dim">atoms in scene</span><span class="readout" id="m-n">—</span>
	</div>
	</div>

	<div class="card">
	<h2>EDIT & LOOK</h2>
	<div class="row">
	<span class="dim">tool</span>
	<label class="tog"><input type="radio" name="tool" value="pose" checked> pose</label>
	<label class="tog"><input type="radio" name="tool" value="erase"> erase</label>
	<span class="spacer"></span>
	<span class="dim">brush</span>
	<label class="tog"><input type="radio" name="brush" value="0.05"> S</label>
	<label class="tog"><input type="radio" name="brush" value="0.12" checked> M</label>
	<label class="tog"><input type="radio" name="brush" value="0.25"> L</label>
	</div>
	<div class="row">
	<button id="btn-undo-erase" disabled>Undo erase</button>
	<button id="btn-restore-erase" disabled>Restore all</button>
	<label class="tog"><input type="checkbox" id="erase-burn"> burn into template</label>
	</div>
	<div class="row">
	<span class="dim">backdrop</span>
	<input type="color" id="bg-color" value="#808080" title="backdrop color">
	<input type="file" id="bg-file" accept="image/*" style="max-width:46%">
	<button id="btn-bg-clear">clear img</button>
	</div>
	<div class="gain-row"><span class="dim">coarse</span><input type="range" id="g-coarse" min="0" max="200" value="100"><span class="val readout" id="g-coarse-v">1.00</span></div>
	<div class="gain-row"><span class="dim">mid</span><input type="range" id="g-mid" min="0" max="200" value="100"><span class="val readout" id="g-mid-v">1.00</span></div>
	<div class="gain-row"><span class="dim">fine</span><input type="range" id="g-fine" min="0" max="200" value="100"><span class="val readout" id="g-fine-v">1.00</span></div>
	<div class="gain-row"><span class="dim">opacity</span><input type="range" id="g-op" min="0" max="200" value="100"><span class="val readout" id="g-op-v">1.00</span></div>
	<div class="dim" style="font-size:10.5px;margin-top:6px">Erase deletes atoms under the brush (render only, until <b>burn</b> writes it into the layer template; Scramble/Bind rebuild the scene from templates). Undo works until the next Bind. Backdrop is presentation and survives everything. Band gains (coarse<4, mid 4–10, fine>10 c/img) scale atom colors in field mode; opacity blends the whole field over the backdrop.</div>
	</div>

	<div class="card">
	<h2>LAYERS <span class="dim" style="letter-spacing:0">(front is highest)</span></h2>
	<div id="layer-list"></div>
	<div class="dim" style="font-size:10.5px;margin-top:6px">library — place to add to the scene:</div>
	<div id="library"></div>
	</div>

	<div class="card">
	<h2>SPAWN A LAYER</h2>
	<div class="row">
	<input type="text" id="spawn-prompt" placeholder='prompt, e.g. "a red rocket, flat colors"'>
	</div>
	<div class="row">
	<input type="text" id="spawn-token" placeholder="matte token (e.g. rocket)" style="width:55%">
	<button id="btn-spawn-text">Distill (GPU)</button>
	</div>
	<div class="row">
	<input type="file" id="spawn-file" accept="image/*">
	<button id="btn-spawn-img">Fit (CPU)</button>
	</div>
	<div class="row">
	<input type="text" id="spawn-json" placeholder="or paste layer JSON">
	<button id="btn-spawn-json">Add</button>
	</div>
	<div id="spawn-status">Distill runs Stable Diffusion score distillation with a cross-attention matte (GPU Space only, untested — first run is a smoke test). Fit trains atoms to your image on CPU (~1 min; objects on plain mid-gray come out compact).</div>
	</div>

	<div class="card">
	<h2>PROMPT AS INTERVENTION</h2>
	<div class="row">
	<input type="text" id="prompt" placeholder='e.g. "move the boat left, put the star behind the tractor"'>
	<button id="btn-prompt">Do</button>
	</div>
	<div id="prompt-log">Commands become pose clamps and depth moves; BP re-settles. Free-form uses Claude when this runs inside claude.ai; a local grammar otherwise.</div>
	</div>

	<div class="card">
	<h2>OVERLAYS</h2>
	<label class="tog"><input type="checkbox" id="ov-atoms" checked> atoms, colored by belief</label>
	<label class="tog"><input type="checkbox" id="ov-own"> ownership tint</label>
	<label class="tog"><input type="checkbox" id="ov-ent"> entropy border glow</label>
	<label class="tog"><input type="checkbox" id="ov-pose" checked> pose belief (crosshair + covariance)</label>
	<label class="tog"><input type="checkbox" id="ov-hints" checked> semantic hints</label>
	</div>

	<div class="card" id="ledger">
	<details>
	<summary>HONEST LEDGER</summary>
	<p><b>Verified in this build:</b> the BP core matches the SlapstackBet6 Python (transform 2e-16, render MSE 8.6e-8, identical binding); drag = pose clamp + re-settle; identity persists through occlusion; depth occlusion removes evidence honestly (marginals revert toward the prior, coverage releases when moved away); the semantic likelihood factor resolves the twins case (two identical stars: 0.05 acc on geometry alone, 0.99 with location priors) and a mildly wrong prior is overridden by evidence; image→layer fitting runs end to end on CPU. <b>Bet 9:</b> the eraser filters per-atom state (order-free, so undo is re-append), burn edits the template so erases survive rebuilds; the backdrop is pure presentation and persists across Bind/Scramble; band gains exploit render linearity (gain·color &equiv; gain·contribution), verified in tests_edit.js.</p>
	<p><span class="no">Not verified:</span> text→layer (SDS) and cross-attention matte are line-for-line adaptations of the verified Bet-5 GPU loop but have NOT been executed on a GPU — first run is a smoke test; SD attention maps flicker across seeds, which is why they enter BP as a prior with a weight, never as truth. Real-photo scene→atoms remains open. Painter compositing and the alpha matte are presentation choices, not the additive field model.</p>
	</details>
	</div>
	</aside>
	</main>

	<script>
	/* Slapstack Playroom core — faithful JS port of SlapstackBet6 math.
	FIELDS: [x, y, theta, su, sv, f, phase, r, g, b]
	Verified against bet6_open.py / bet6_bp_binding.py / bet6_multimodal.py
	by tests_node.js before being embedded in the playroom. */
	"use strict";

	const TAU = Math.PI * 2;

	function wrapPi(d) {
	return ((d + Math.PI) % TAU + TAU) % TAU - Math.PI;
	}

	function rotApply(rho, x, y) {
	const c = Math.cos(rho), s = Math.sin(rho);
	return [c * x - s * y, s * x + c * y];
	}

	/* Exact Sim(2) action on atom parameters (the Bet 5 algebra):
	xy -> s R xy + t, theta -> theta + rho, sigma -> s sigma, f -> f/s.
	Envelope-relative phase and color are INVARIANT. */
	function transformAtoms(atoms, xi) {
	const [tx, ty, rho, lam] = xi;
	const s = Math.exp(lam);
	const out = new Array(atoms.length);
	for (let i = 0; i < atoms.length; i++) {
	const a = atoms[i];
	const [rx, ry] = rotApply(rho, a[0], a[1]);
	out[i] = [
	s * rx + tx, s * ry + ty,
	a[2] + rho,
	a[3] * s, a[4] * s,
	a[5] / s,
	a[6],
	a[7], a[8], a[9],
	];
	}
	return out;
	}

	/* Sim(2)-invariant intrinsic signature: identity lives here. */
	function signature(atoms) {
	return atoms.map(a => [
	Math.log(a[3] * a[5]),
	Math.log(a[3] / a[4]),
	Math.cos(a[6]), Math.sin(a[6]),
	a[7], a[8], a[9],
	]);
	}

	/* Two pose-vote hypotheses per correspondence (pi-ambiguity fix):
	H0: rho = d_theta, phi_obs == phi_tmpl
	H1: rho = d_theta + pi, phi_obs == -phi_tmpl */
	function poseVotes2pi(obs, tmpl, sigPhase = 0.35) {
	const s = Math.pow((obs[3] / tmpl[3]) * (obs[4] / tmpl[4]) * (tmpl[5] / obs[5]), 1 / 3);
	const dTheta = obs[2] - tmpl[2];
	const out = [];
	for (let H = 0; H < 2; H++) {
	const rho = wrapPi(dTheta + H * Math.PI);
	const phiExp = H === 0 ? tmpl[6] : -tmpl[6];
	const dphi = wrapPi(obs[6] - phiExp);
	const pc = -0.5 * dphi * dphi / (sigPhase * sigPhase);
	const [rx, ry] = rotApply(rho, tmpl[0], tmpl[1]);
	out.push([[obs[0] - s * rx, obs[1] - s * ry, rho, Math.log(s)], pc]);
	}
	return out;
	}

	/* ------- small dense linear algebra on 4x4 (row-major flat arrays) ------- */
	function mat4Inv(m) {
	// Gauss-Jordan, fine for well-conditioned SPD 4x4s here.
	const a = m.map(r => r.slice());
	const inv = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]];
	for (let col = 0; col < 4; col++) {
	let piv = col;
	for (let r = col + 1; r < 4; r++)
	if (Math.abs(a[r][col]) > Math.abs(a[piv][col])) piv = r;
	[a[col], a[piv]] = [a[piv], a[col]];
	[inv[col], inv[piv]] = [inv[piv], inv[col]];
	const d = a[col][col];
	for (let j = 0; j < 4; j++) { a[col][j] /= d; inv[col][j] /= d; }
	for (let r = 0; r < 4; r++) {
	if (r === col) continue;
	const f = a[r][col];
	for (let j = 0; j < 4; j++) { a[r][j] -= f * a[col][j]; inv[r][j] -= f * inv[col][j]; }
	}
	}
	return inv;
	}
	function mat4Det(m) {
	const a = m.map(r => r.slice());
	let det = 1;
	for (let col = 0; col < 4; col++) {
	let piv = col;
	for (let r = col + 1; r < 4; r++)
	if (Math.abs(a[r][col]) > Math.abs(a[piv][col])) piv = r;
	if (piv !== col) { [a[col], a[piv]] = [a[piv], a[col]]; det = -det; }
	det *= a[col][col];
	if (a[col][col] === 0) return 0;
	for (let r = col + 1; r < 4; r++) {
	const f = a[r][col] / a[col][col];
	for (let j = col; j < 4; j++) a[r][j] -= f * a[col][j];
	}
	}
	return det;
	}
	function mat4Vec(m, v) {
	return [0,1,2,3].map(i => m[i][0]v[0]+m[i][1]v[1]+m[i][2]v[2]+m[i][3]v[3]);
	}
	function matAdd(A, B, wB = 1) {
	return A.map((row, i) => row.map((x, j) => x + wB * B[i][j]));
	}

	/* Greedy mode-seeking init (angle-aware), port of _density_peaks. */
	function densityPeaks(votes, weights, M, radius = 0.45) {
	const scale = [0.15, 0.15, 0.30, 0.20];
	const n = votes.length;
	const dens = new Float64Array(n);
	for (let i = 0; i < n; i++) {
	let acc = 0;
	for (let k = 0; k < n; k++) {
	const d0 = (votes[k][0] - votes[i][0]) / scale[0];
	const d1 = (votes[k][1] - votes[i][1]) / scale[1];
	const d2 = wrapPi(votes[k][2] - votes[i][2]) / scale[2];
	const d3 = (votes[k][3] - votes[i][3]) / scale[3];
	acc += weights[k] * Math.exp(-0.5 * (d0d0 + d1d1 + d2d2 + d3d3));
	}
	dens[i] = acc;
	}
	const peaks = [];
	const alive = new Uint8Array(n).fill(1);
	for (let m = 0; m < M; m++) {
	let best = -1, bestD = -Infinity;
	for (let i = 0; i < n; i++)
	if (alive[i] && dens[i] > bestD) { bestD = dens[i]; best = i; }
	if (best < 0) break;
	peaks.push(votes[best].slice());
	for (let i = 0; i < n; i++) {
	const dxy = Math.hypot(votes[i][0] - votes[best][0], votes[i][1] - votes[best][1]);
	const dr = Math.abs(wrapPi(votes[i][2] - votes[best][2]));
	if (dxy + dr <= radius) alive[i] = 0;
	}
	}
	return peaks;
	}

	/* Loopy BP binding of obs atoms to K templates at unknown poses.
	Port of bet6_open.bp_bind: candidates carry both pi-hypotheses,
	cavity messages, damping, branch-aligned rotation fusion.
	Options: clampPose — array of length K; if clampPose[k] is a pose xi,
	object k's pose is held fixed (conditioning-as-intervention) and only
	the assignment beliefs re-equilibrate around it. */
	function bpBind(templates, obs, opts = {}) {
	const iters = opts.iters ?? 40;
	const damping = opts.damping ?? 0.5;
	const cavity = opts.cavity ?? true;
	const sigVar = opts.sigVar ?? 0.08;
	const outLL = opts.outLL ?? -14.0;
	const clampPose = opts.clampPose ?? null;
	const hiddenMask = opts.hiddenMask ?? null; // per-atom: true = no evidence
	const onIter = opts.onIter ?? null;

	const K = templates.length;
	const sigT = templates.map(signature);
	const sigO = signature(obs);
	const N = obs.length;

	const Vdiag = [0.03 * 0.03, 0.03 * 0.03, 0.05 * 0.05, 0.05 * 0.05];
	const Vinv = [[1/Vdiag[0],0,0,0],[0,1/Vdiag[1],0,0],[0,0,1/Vdiag[2],0],[0,0,0,1/Vdiag[3]]];
	const Vmat = [[Vdiag[0],0,0,0],[0,Vdiag[1],0,0],[0,0,Vdiag[2],0],[0,0,0,Vdiag[3]]];
	const P0inv = [[1e-2,0,0,0],[0,1e-2,0,0],[0,0,1e-2,0],[0,0,0,1e-2]];

	// ---- candidate generation: 3 signature-nearest per template, 2 hypotheses
	const cands = [], votes = [], base = [];
	for (let i = 0; i < N; i++) {
	const c = [], v = [], b = [];
	if (!(hiddenMask && hiddenMask[i])) {
	for (let k = 0; k < K; k++) {
	const d2 = sigT[k].map(st => {
	let acc = 0;
	for (let q = 0; q < 7; q++) { const d = st[q] - sigO[i][q]; acc += d * d; }
	return acc;
	});
	const order = d2.map((d, j) => [d, j]).sort((p, q) => p[0] - q[0]).slice(0, 3);
	for (const [dj, j] of order) {
	for (const [xi, pc] of poseVotes2pi(obs[i], templates[k][j])) {
	c.push([k, j]); v.push(xi); b.push(-0.5 * dj / sigVar + pc);
	}
	}
	}
	}
	cands.push(c); votes.push(v); base.push(b);
	}

	// ---- beliefs seeded from the identity+phase channel
	let B = [];
	for (let i = 0; i < N; i++) {
	const ll = base[i].concat([outLL]);
	const mx = Math.max(...ll);
	let e = ll.map(x => Math.exp(x - mx));
	const s = e.reduce((a, x) => a + x, 0);
	B.push(e.map(x => x / s));
	}

	// ---- pose init: density peak of each object's votes (or the clamp)
	let mu = [];
	for (let k = 0; k < K; k++) {
	if (clampPose && clampPose[k]) { mu.push(clampPose[k].slice()); continue; }
	const vk = [], wk = [];
	for (let i = 0; i < N; i++)
	for (let ci = 0; ci < cands[i].length; ci++)
	if (cands[i][ci][0] === k) { vk.push(votes[i][ci]); wk.push(B[i][ci]); }
	mu.push(vk.length ? densityPeaks(vk, wk, 1)[0] : [0, 0, 0, 0]);
	}
	let Sig = mu.map(() => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]);

	for (let it = 0; it < iters; it++) {
	// pose fusion
	const Lam = [], eta = [];
	for (let k = 0; k < K; k++) { Lam.push(P0inv.map(r => r.slice())); eta.push([0,0,0,0]); }
	for (let i = 0; i < N; i++) {
	for (let ci = 0; ci < cands[i].length; ci++) {
	const k = cands[i][ci][0];
	const v = votes[i][ci].slice();
	v[2] = mu[k][2] + wrapPi(v[2] - mu[k][2]);
	const w = B[i][ci];
	Lam[k] = matAdd(Lam[k], Vinv, w);
	const Vv = mat4Vec(Vinv, v);
	for (let q = 0; q < 4; q++) eta[k][q] += w * Vv[q];
	}
	}
	Sig = Lam.map(mat4Inv);
	for (let k = 0; k < K; k++) {
	if (clampPose && clampPose[k]) {
	mu[k] = clampPose[k].slice();
	Sig[k] = [[1e-6,0,0,0],[0,1e-6,0,0],[0,0,1e-6,0],[0,0,0,1e-6]];
	} else {
	mu[k] = mat4Vec(Sig[k], eta[k]);
	mu[k][2] = wrapPi(mu[k][2]);
	}
	}

	// assignment update with cavity
	const newB = [];
	for (let i = 0; i < N; i++) {
	const nc = cands[i].length;
	const ll = new Array(nc + 1);
	for (let ci = 0; ci < nc; ci++) {
	const k = cands[i][ci][0];
	const v = votes[i][ci].slice();
	v[2] = mu[k][2] + wrapPi(v[2] - mu[k][2]);
	let mC, Sk;
	if (cavity && !(clampPose && clampPose[k])) {
	const Lc = matAdd(Lam[k], Vinv, -B[i][ci]);
	const Vv = mat4Vec(Vinv, v);
	const ecav = [0,1,2,3].map(q => eta[k][q] - B[i][ci] * Vv[q]);
	const Sc = mat4Inv(Lc);
	mC = mat4Vec(Sc, ecav);
	Sk = Sc;
	} else {
	mC = mu[k]; Sk = Sig[k];
	}
	const r = [v[0] - mC[0], v[1] - mC[1], wrapPi(v[2] - mC[2]), v[3] - mC[3]];
	const Cov = matAdd(Sk, Vmat, 1);
	const Ci = mat4Inv(Cov);
	const Cr = mat4Vec(Ci, r);
	const quad = r[0]Cr[0] + r[1]Cr[1] + r[2]Cr[2] + r[3]Cr[3];
	ll[ci] = base[i][ci] - 0.5 * quad - 0.5 * Math.log(mat4Det(Cov));
	}
	ll[nc] = outLL;
	const mx = Math.max(...ll);
	let e = ll.map(x => Math.exp(x - mx));
	const s = e.reduce((a, x) => a + x, 0);
	e = e.map(x => x / s);
	newB.push(e.map((x, q) => damping * x + (1 - damping) * B[i][q]));
	}
	B = newB;
	if (onIter) onIter(it, marginals(), mu, Sig);
	}

	function marginals() {
	const marg = [];
	for (let i = 0; i < N; i++) {
	if (cands[i].length === 0) {
	// no evidence: assignment belief reverts to the prior (uniform),
	// not to a confident "outlier" — this is what permanence means.
	marg.push(new Array(K + 1).fill(1 / (K + 1)));
	continue;
	}
	const m = new Array(K + 1).fill(0);
	for (let ci = 0; ci < cands[i].length; ci++) m[cands[i][ci][0]] += B[i][ci];
	m[K] = B[i][cands[i].length];
	marg.push(m);
	}
	return marg;
	}

	return { marg: marginals(), mu, Sig, cands, votes, B };
	}

	/* Numpy-matching reference render (verification + full-res compositor).
	pre[c] += color_c * env * carrier ; out = sigmoid(2 * pre).
	Returns {pre: Float32Array(3HH)} pre-sigmoid field. */
	function renderPre(atoms, H, pre) {
	pre = pre \|\| new Float32Array(3 * H * H);
	const lim = 3.2; // envelope support cut, in sigmas
	for (const a of atoms) {
	const [ax, ay, th, su, sv, f, ph, r, g, b] = a;
	const ct = Math.cos(th), st = Math.sin(th);
	const rad = lim * Math.max(su, sv);
	// pixel bbox: x in [-1,1] maps to col (H-1)*(x+1)/2
	const x0 = Math.max(0, Math.floor((ax - rad + 1) / 2 * (H - 1)));
	const x1 = Math.min(H - 1, Math.ceil((ax + rad + 1) / 2 * (H - 1)));
	const y0 = Math.max(0, Math.floor((ay - rad + 1) / 2 * (H - 1)));
	const y1 = Math.min(H - 1, Math.ceil((ay + rad + 1) / 2 * (H - 1)));
	for (let py = y0; py <= y1; py++) {
	const Y = -1 + 2 * py / (H - 1);
	const dy = Y - ay;
	for (let px = x0; px <= x1; px++) {
	const X = -1 + 2 * px / (H - 1);
	const dx = X - ax;
	const u = ct * dx + st * dy;
	const v = -st * dx + ct * dy;
	const eArg = 0.5 * ((u / su) * (u / su) + (v / sv) * (v / sv));
	if (eArg > lim * lim / 2 * 1.6) continue;
	const env = Math.exp(-eArg);
	const car = Math.cos(TAU * f * u + ph);
	const ec = env * car;
	const idx = py * H + px;
	pre[idx] += r * ec;
	pre[H * H + idx] += g * ec;
	pre[2 * H * H + idx] += b * ec;
	}
	}
	}
	return pre;
	}

	function sigmoidField(pre, H, out) {
	out = out \|\| new Uint8ClampedArray(4 * H * H);
	const n = H * H;
	for (let i = 0; i < n; i++) {
	out[4 * i] = 255 / (1 + Math.exp(-2 * pre[i]));
	out[4 * i + 1] = 255 / (1 + Math.exp(-2 * pre[n + i]));
	out[4 * i + 2] = 255 / (1 + Math.exp(-2 * pre[2 * n + i]));
	out[4 * i + 3] = 255;
	}
	return out;
	}

	/* Ownership field: P(k\|pixel) through the atoms' actual envelopes,
	energy-weighted. Port of bet6_open.ownership_field. */
	function ownershipField(obs, marg, K, H) {
	const O = [];
	for (let k = 0; k <= K; k++) O.push(new Float32Array(H * H));
	const lim = 3.2;
	for (let i = 0; i < obs.length; i++) {
	const a = obs[i];
	const energy = Math.hypot(a[7], a[8], a[9]);
	const ct = Math.cos(a[2]), st = Math.sin(a[2]);
	const rad = lim * Math.max(a[3], a[4]);
	const x0 = Math.max(0, Math.floor((a[0] - rad + 1) / 2 * (H - 1)));
	const x1 = Math.min(H - 1, Math.ceil((a[0] + rad + 1) / 2 * (H - 1)));
	const y0 = Math.max(0, Math.floor((a[1] - rad + 1) / 2 * (H - 1)));
	const y1 = Math.min(H - 1, Math.ceil((a[1] + rad + 1) / 2 * (H - 1)));
	for (let py = y0; py <= y1; py++) {
	const Y = -1 + 2 * py / (H - 1);
	const dy = Y - a[1];
	for (let px = x0; px <= x1; px++) {
	const X = -1 + 2 * px / (H - 1);
	const dx = X - a[0];
	const u = ct * dx + st * dy;
	const v = -st * dx + ct * dy;
	const env = Math.exp(-0.5 * ((u / a[3]) 2 + (v / a[4]) 2));
	const idx = py * H + px;
	for (let k = 0; k <= K; k++) O[k][idx] += marg[i][k] * energy * env;
	}
	}
	}
	const P = O.map(() => new Float32Array(H * H));
	const ent = new Float32Array(H * H);
	const support = new Uint8Array(H * H);
	for (let idx = 0; idx < H * H; idx++) {
	let tot = 0;
	for (let k = 0; k <= K; k++) tot += O[k][idx];
	support[idx] = tot > 0.05 ? 1 : 0;
	let e = 0;
	for (let k = 0; k <= K; k++) {
	const p = O[k][idx] / (tot + 1e-6);
	P[k][idx] = p;
	e -= p * Math.log2(p + 1e-12);
	}
	ent[idx] = e;
	}
	return { P, ent, support };
	}

	/* Assignment entropy per atom, in bits. */
	function atomEntropy(marg) {
	return marg.map(m => {
	let e = 0;
	for (const p of m) e -= p * Math.log2(p + 1e-12);
	return e;
	});
	}


	</script>
	<script>
	/* Slapstack Studio layer math — NEW mechanics on top of the verified core.
	core.js is untouched; everything here is presentation-adjacent inference
	plumbing, tested by tests_studio.js:
	renderEnv per-layer envelope-energy buffer (for alpha + coverage)
	coverageOf how much front-stack mass sits on each atom center
	autoHidden coverage -> per-atom evidence mask (depth occlusion)
	compositePainter back-to-front alpha compositing of layer buffers
	composePose Sim(2) composition in vote coordinates [tx,ty,rho,lam]
	*/
	"use strict";

	const ALPHA_C = 2.0; // alpha = 1 - exp(-ALPHA_C * bounded envelope energy)
	const COVER_THRESH = 0.55; // atom loses evidence when this covered

	/* Opacity of a layer = where it actually PAINTS: per-pixel deviation of
	the pre-sigmoid field from neutral. Cancelling atom pairs (high energy,
	zero sum) are correctly transparent — envelope-based opacity is not used
	because it saturates on exactly those invisible pairs.
	a = 1 - exp(-ALPHA_C * max(0, \|preR\|+\|preG\|+\|preB\| - FLOOR)). */
	const ALPHA_FLOOR = 0.08;
	function alphaFromPre(pre, H, out) {
	out = out \|\| new Float32Array(H * H);
	const n = H * H;
	for (let i = 0; i < n; i++) {
	const m = Math.abs(pre[i]) + Math.abs(pre[n + i]) + Math.abs(pre[2 * n + i]);
	out[i] = m > ALPHA_FLOOR ? 1 - Math.exp(-ALPHA_C * (m - ALPHA_FLOOR)) : 0;
	}
	return out;
	}

	/* coverage of each atom center by a front stack of alpha buffers:
	cov_i = 1 - prod_front (1 - a_m(x_i)). */
	function coverageOf(atoms, frontAlphaBufs, H) {
	const out = new Float32Array(atoms.length);
	for (let i = 0; i < atoms.length; i++) {
	const px = Math.max(0, Math.min(H - 1, Math.round((atoms[i][0] + 1) / 2 * (H - 1))));
	const py = Math.max(0, Math.min(H - 1, Math.round((atoms[i][1] + 1) / 2 * (H - 1))));
	let keep = 1;
	for (const buf of frontAlphaBufs) keep = 1 - buf[py H + px];
	out[i] = 1 - keep;
	}
	return out;
	}

	/* Per-atom evidence mask from the depth stack.
	alphaBufs aligned with layers. An atom of layer k is evidence-free if the
	strictly-in-front stack covers it beyond COVER_THRESH, or its layer is
	user-hidden. */
	function autoHidden(obs, layerOf, layers, alphaBufs, H) {
	const mask = new Array(obs.length).fill(false);
	const covFrac = layers.map(() => 0);
	const counts = layers.map(() => 0);
	for (let i = 0; i < obs.length; i++) {
	const k = layerOf[i];
	if (k < 0) continue; // clutter: always evidenced
	counts[k]++;
	if (layers[k].hidden) { mask[i] = true; covFrac[k]++; continue; }
	const front = [];
	for (let m = 0; m < layers.length; m++)
	if (m !== k && !layers[m].hidden && layers[m].depth > layers[k].depth)
	front.push(alphaBufs[m]);
	if (!front.length) continue;
	const cov = coverageOf([obs[i]], front, H)[0];
	if (cov > COVER_THRESH) { mask[i] = true; covFrac[k]++; }
	}
	for (let k = 0; k < layers.length; k++)
	covFrac[k] = counts[k] ? covFrac[k] / counts[k] : 0;
	return { mask, covFrac };
	}

	/* Painter compositing: layers back-to-front by depth.
	rgbBufs[k]: Float32Array(3HH) pre-sigmoid; alphaBufs[k]: from
	alphaFromPre. Base is mid-gray (sigmoid(0)). */
	function compositePainter(order, rgbBufs, alphaBufs, H, out) {
	out = out \|\| new Uint8ClampedArray(4 * H * H);
	const n = H * H;
	const acc = new Float32Array(3 * n);
	for (let i = 0; i < n; i++) { acc[i] = 127.5; acc[n + i] = 127.5; acc[2 * n + i] = 127.5; }
	for (const k of order) {
	const pre = rgbBufs[k], al = alphaBufs[k];
	for (let i = 0; i < n; i++) {
	const a = al[i];
	if (a < 1e-3) continue;
	acc[i] += a * (255 / (1 + Math.exp(-2 * pre[i])) - acc[i]);
	acc[n + i] += a * (255 / (1 + Math.exp(-2 * pre[n + i])) - acc[n + i]);
	acc[2 * n + i] += a * (255 / (1 + Math.exp(-2 * pre[2 * n + i])) - acc[2 * n + i]);
	}
	}
	for (let i = 0; i < n; i++) {
	out[4 * i] = acc[i]; out[4 * i + 1] = acc[n + i];
	out[4 * i + 2] = acc[2 * n + i]; out[4 * i + 3] = 255;
	}
	return out;
	}

	/* Backdrop trim: whole-image fits carry large-sigma background pads that
	cover the full frame; for OBJECT layers, drop atoms whose envelope is
	wider than sigMax. HEURISTIC, honestly: it also kills any genuinely
	large object parts. The untrimmed layer is kept in the library. */
	function trimAtoms(atoms, sigMax = 0.35) {
	const kept = atoms.filter(a => Math.max(a[3], a[4]) <= sigMax);
	if (!kept.length) return atoms.slice();
	// re-center xy so the trimmed set is a canonical template again
	let mx = 0, my = 0;
	for (const a of kept) { mx += a[0]; my += a[1]; }
	mx /= kept.length; my /= kept.length;
	return kept.map(a => { const b = a.slice(); b[0] -= mx; b[1] -= my; return b; });
	}

	/* ---- Bet 9 additions: eraser + backdrop + band gains (pure, testable) ---- */

	/* Frequency band of an atom. f is cycles/unit; the frame spans 2 units, so
	cycles-per-image = 2f. Bands follow the original splatstack dials:
	coarse < 4 c/img, mid 4–10, fine > 10. Returns 0\|1\|2. */
	const BAND_EDGES = [2.0, 5.0];
	function bandOf(f) { return f < BAND_EDGES[0] ? 0 : f < BAND_EDGES[1] ? 1 : 2; }

	/* Erase mask: true for atoms whose center falls inside the brush circle.
	skip(i) can veto (e.g. atoms of hidden layers stay untouched). */
	function eraseMask(obs, wx, wy, r, skip) {
	const r2 = r * r;
	return obs.map((a, i) => {
	if (skip && skip(i)) return false;
	const dx = a[0] - wx, dy = a[1] - wy;
	return dx * dx + dy * dy < r2;
	});
	}

	/* Composite an already-sigmoided field over a backdrop.
	img: Uint8ClampedArray RGBA from sigmoidField/compositePainter (mutated).
	alpha: Float32Array(H*H) from alphaFromPre of the (band-gained) pre field.
	opacity: global gain on alpha, clamped to [0,1] per pixel.
	bg: either [r,g,b] flat color or a Uint8ClampedArray(4HH) RGBA image.
	Identity check: with alpha==1 everywhere or bg==the field itself the
	output is unchanged; with opacity such that a==1 the field wins. */
	function blendOverBackdrop(img, alpha, opacity, bg, H) {
	const n = H * H;
	const flat = !(bg && bg.length === 4 * n);
	for (let i = 0; i < n; i++) {
	const a = Math.min(1, alpha[i] * opacity);
	const br = flat ? bg[0] : bg[4 * i],
	bgr = flat ? bg[1] : bg[4 * i + 1],
	bb = flat ? bg[2] : bg[4 * i + 2];
	img[4 * i] = br + a * (img[4 * i] - br);
	img[4 * i + 1] = bgr + a * (img[4 * i + 1] - bgr);
	img[4 * i + 2] = bb + a * (img[4 * i + 2] - bb);
	}
	return img;
	}

	/* Sim(2) composition in vote coordinates: (g2 ∘ g1). */
	function composePose(g2, g1) {
	const s2 = Math.exp(g2[3]);
	const c = Math.cos(g2[2]), s = Math.sin(g2[2]);
	const wrap = d => ((d + Math.PI) % (2 * Math.PI) + 2 * Math.PI) % (2 * Math.PI) - Math.PI;
	return [s2 * (c * g1[0] - s * g1[1]) + g2[0],
	s2 * (s * g1[0] + c * g1[1]) + g2[1],
	wrap(g1[2] + g2[2]), g1[3] + g2[3]];
	}
	function gestureTranslate(dx, dy) { return [dx, dy, 0, 0]; }
	function gestureRotateAbout(c, drho) {
	const co = Math.cos(drho), si = Math.sin(drho);
	return [c[0] - (co * c[0] - si * c[1]), c[1] - (si * c[0] + co * c[1]), drho, 0];
	}
	function gestureScaleAbout(c, ds) {
	const s = Math.exp(ds);
	return [c[0] - s * c[0], c[1] - s * c[1], 0, ds];
	}


	</script>
	<script>
	const BUILTINS = {"tractor": [[-0.6824, -0.45011, 2.66975, 0.70848, 0.92606, 0.44334, 5.19345, -0.09237, 0.04058, -0.01663], [-0.08584, -0.04802, 0.61626, 0.49888, 0.51436, 0.28444, 2.98078, -0.10011, 0.19875, 0.39398], [0.74864, 0.1407, 2.20893, 0.54502, 0.36724, 0.58724, 1.0072, 0.08821, 0.17557, 0.02929], [0.16677, -0.78973, 0.94754, 0.31915, 0.39057, 0.59383, 1.7488, 0.04293, 0.29863, 0.19046], [0.13943, -0.4621, 0.34775, 0.43809, 0.50801, 0.30553, 2.8646, -0.17673, 0.21056, 0.20304], [-0.05499, 0.43338, 1.6514, 0.61284, 0.45687, 0.32725, 1.11694, 0.16899, -0.3567, -0.20526], [-0.34716, 0.78101, 1.2311, 0.74696, 0.43588, 0.47387, 4.34096, 0.2865, 0.32634, 0.40835], [0.38634, 0.15072, 1.59185, 0.38671, 0.80153, 0.2006, 3.93334, -0.038, 0.2346, 0.21658], [-0.24576, -0.6867, 1.53196, 0.713, 0.38647, 0.52652, 3.95442, 0.02936, -0.05187, 0.00121], [0.35205, 0.08337, 0.53545, 0.47834, 0.43423, 0.76246, 4.15911, -0.20329, -0.08114, 0.10186], [0.35364, -0.86473, 2.06911, 1.01878, 0.6701, 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1.84332, 5.30456, -0.43615, -0.27265, -0.47339], [0.14923, 0.43003, 1.26489, 0.25233, 0.08449, 2.11129, 2.12432, -0.07108, -0.0937, -0.14313], [-0.79014, 0.61709, 1.90558, 0.37037, 0.11136, 1.64229, 5.18906, -0.13822, 0.16428, 0.3693], [-0.12659, 0.30183, 1.57897, 0.03235, 0.65149, 3.35957, 4.83163, 0.62631, -1.09254, -2.34957], [0.74631, -0.27895, 2.57092, 0.32236, 0.22899, 1.70782, 4.40745, -0.10511, -0.11866, -0.0974], [-0.4706, -1.01786, 1.562, 0.11467, 0.13857, 1.21133, 5.87333, 0.02135, -0.01299, 0.02737], [-0.05836, 0.04774, 0.62651, 0.22665, 0.15889, 1.20993, 2.69819, -0.14953, -0.32859, -0.33054], [0.48753, 0.18505, 1.40111, 0.09815, 0.21416, 1.35927, 0.28737, -0.22569, -0.15438, -0.10252], [0.19376, 0.78175, 0.86577, 0.232, 0.101, 1.39569, 2.35936, 0.06397, 0.01969, -0.15017], [-0.32573, 0.28337, 1.44029, 0.10177, 0.09071, 2.11344, 1.90905, -0.0877, 0.22625, 0.5373], [-0.10059, 0.20726, -0.15807, 0.04677, 0.10242, 1.83554, 3.26912, -2.11536, -1.82547, -1.57415], [0.84624, -0.47251, 1.47539, 0.20866, 0.22456, 1.01765, 2.08865, 0.01409, 0.01689, 0.01502], [0.50083, -0.29505, 1.39077, 0.08953, 0.07203, 1.88329, 0.12959, -0.05621, -0.08363, -0.1078], [-0.1445, -0.95257, 2.90764, 0.07775, 0.01977, 2.03443, 3.97165, 0.97008, 0.86927, 0.57117], [-0.47625, -0.61653, 2.43245, 0.11514, 0.11414, 1.41168, 3.49398, 0.02675, 0.04917, 0.00409], [0.15157, 0.15012, 1.47682, 0.03508, 0.16766, 3.63825, 3.18341, 0.92059, 0.83145, 0.42329], [0.14193, 0.25131, 2.49569, 0.17593, 0.13607, 2.08532, 0.75981, -0.11116, 0.00501, 0.01148], [-0.66478, 0.65038, 1.19491, 0.35746, 0.06058, 2.73093, 5.53523, 0.11769, -0.16289, -0.3357], [0.61342, 0.56992, 3.7336, 0.02526, 0.21197, 4.26954, 1.86086, -0.6535, 0.93151, 2.24838], [0.6787, -0.92989, 0.41269, 0.25026, 0.38995, 1.63202, 5.8353, -0.00703, -0.02194, -0.01415], [0.04638, -0.55831, 2.42571, 0.12093, 0.16263, 0.73856, 6.14543, 0.36226, 0.49601, 0.35012], [-0.21198, -0.14439, 1.58812, 0.15066, 0.05129, 0.70131, 6.16365, -0.33509, -0.32551, -0.12919], [-0.2144, 0.03032, 2.91624, 0.05753, 0.07852, 1.87215, 0.1741, -0.39673, -0.36386, -0.22987], [-0.13844, -0.71483, 0.07072, 0.07635, 0.33219, 2.26688, 4.82888, 0.2467, 0.18457, 0.16929], [0.15999, -0.29622, 2.69916, 0.20213, 0.24233, 1.002, 5.81437, 1.45309, 1.05946, 0.17348], [-0.07523, 0.37701, 0.46661, 0.06141, 0.03343, 1.56853, 0.70886, -1.05117, -1.23321, -0.96933], [-0.16682, -0.99045, 1.12432, 0.05948, 0.2007, 1.9382, 3.04478, 0.1796, 0.16536, 0.09781], [0.80351, -0.49286, 1.98354, 0.17694, 0.25954, 1.03301, 1.10691, 0.00779, 0.03798, 0.06703], [0.82117, 0.6799, 1.03574, 0.09622, 0.19606, 0.89922, 4.38744, 0.08018, -0.11594, -0.18364], [-0.13149, -0.81441, 0.15398, 0.07111, 0.12125, 1.76403, 2.42052, -0.97914, -1.07737, -0.75186], [-0.61828, -0.31465, 0.80308, 0.12261, 0.14744, 0.48786, 2.49841, -0.08821, -0.04903, 0.05376], [0.39459, -0.10493, 2.5056, 0.09057, 0.16075, 1.27382, 3.16278, -2.35689, -1.60934, -0.60862], [-0.09579, 0.81222, 1.57241, 0.01623, 0.37915, 5.3683, 1.47924, 0.88204, -1.30361, -2.71795], [-0.28004, 0.49948, 1.65494, 0.17664, 0.2661, 0.75148, 0.10037, 0.22502, -0.18689, -0.88598], [0.24841, -0.53404, 2.51898, 0.01783, 0.41616, 3.90649, 2.67916, 1.43219, 1.213, 0.7207], [0.11963, -0.67874, 0.9541, 0.60554, 0.00669, 0.856, 0.23229, -1.54654, -1.29281, -0.86237], [-0.52329, 0.77623, 1.58572, 0.03163, 0.13249, 1.86478, 3.20299, -0.22208, 0.35925, 0.72493], [0.0299, 0.77708, 1.54304, 0.06955, 0.29003, 2.61709, 3.92385, -0.28405, 0.4157, 1.04792], [-0.17194, 0.06405, 2.53053, 0.20492, 0.08149, 1.43345, 5.17384, -0.2267, 0.02543, 0.00314], [0.55317, 0.66661, 1.90108, 0.42554, 0.21636, 1.83571, 6.12928, -0.07583, 0.08871, 0.17245], [-0.44615, 0.12555, 3.12824, 0.23051, 0.18191, 1.53885, 4.09845, 0.04691, 0.01757, 0.05995], [-0.24918, -0.17663, 0.32413, 0.05639, 0.06614, 0.86147, 1.95925, 0.19675, 0.15027, 0.25504], [0.29911, 0.60437, 0.50524, 0.14357, 0.11689, 0.9624, 2.34493, -0.14827, 0.15435, 0.16659], [-0.41892, 0.7034, 1.53665, 0.09705, 0.16946, 1.9209, 3.17691, -0.1839, 0.26102, 0.75296], [-0.79271, 0.58647, 2.62031, 0.05162, 0.19227, 2.43745, 1.26147, 0.4843, -0.74477, -1.61327], [-0.60484, 0.03067, 1.28536, 0.17084, 0.14292, 1.52045, 3.6335, -0.04817, 0.02099, 0.0977], [-0.34671, 0.04527, 3.40945, 0.07248, 0.08656, 1.07657, 2.47549, 0.04936, 0.10153, 0.02661], [-0.22547, 0.15271, 0.20253, 0.16391, 0.13752, 1.71726, 4.2191, -0.02961, 0.15912, 0.14774], [-0.00687, -0.73161, 2.5028, 0.07599, 0.1783, 3.06414, 0.4712, 1.32528, 1.34062, 0.86031], [-0.15703, -0.95468, 3.25628, 0.1045, 0.01257, 2.11908, 1.13725, -0.45612, -0.42957, -0.29404], [-0.05372, 0.24665, 0.22127, 0.08319, 0.07884, 2.87674, 4.38322, -0.70704, -0.72359, -0.67824], [0.24342, 0.81571, 1.44644, 0.29137, 0.25659, 0.76395, 1.4982, 0.29314, -0.19535, -0.53801], [-0.68747, 0.54977, 0.22252, 0.25197, 0.1895, 0.88591, 2.94688, -0.12023, 0.23612, 0.56521], [0.47923, 0.30185, 1.57186, 0.00961, 0.2431, 1.65118, 0.45513, 0.60631, -0.81851, -1.97919], [0.04753, -0.49167, 2.745, 0.17775, 0.21465, 1.05867, 0.09611, 0.74664, 0.67871, 0.72987], [-0.91372, 0.37551, 2.54913, 0.04007, 0.06297, 3.36503, 3.85676, -0.40663, 0.58702, 1.40486], [0.409, 0.69172, 1.80022, 0.23277, 0.04852, 2.95077, 6.09774, 0.09222, -0.18616, -0.43305], [-0.96688, 0.90454, 1.94801, 0.08507, 0.17094, 1.69168, 6.06099, -0.06892, 0.06249, 0.09266], [-0.44291, -0.08531, -0.15556, 0.15896, 0.14925, 2.22345, 4.15054, -0.02685, -0.03191, -0.01925], [-0.22339, 0.07173, 0.92299, 0.05924, 0.04536, 1.11415, 5.24568, -0.18604, -0.34506, -0.07539], [0.56561, -0.04271, -0.6544, 0.02191, 0.16757, 3.69071, 4.20103, -4.09617, -4.05649, -2.88399], [0.35068, -0.35148, 2.51338, 0.05881, 0.30758, 2.72514, 1.79961, -1.26945, -1.30986, -1.07607], [-0.18379, -0.3334, 0.0015, 0.01045, 0.44674, 3.65024, 2.58839, 1.95094, 1.62632, 1.11477], [0.55417, 0.01449, 2.11492, 0.08191, 0.07838, 2.38535, 2.59567, -1.26342, -1.06981, -0.79691], [0.32377, 0.11651, 1.57898, 0.0271, 0.21155, 4.63407, 3.87996, -6.17162, -5.12337, -3.60569]]};
	</script>
	<script>
	"use strict";
	/* ============================ studio app ============================ */

	const PALETTE = [
	["#ff6b5e",[255,107,94]], ["#5ec8ff",[94,200,255]], ["#ffd35e",[255,211,94]],
	["#7fd98a",[127,217,138]], ["#c86bff",[200,107,255]], ["#5effd0",[94,255,208]],
	["#ff8fc7",[255,143,199]], ["#b0b8ff",[176,184,255]],
	];
	const OUTLIER_RGB = [120,128,143];
	const RES = 192, OWN_RES = 128;
	const NOISE_SCALE = [1,1,1,.3,.3,20,3,.5,.5,.5];
	const HINT_W = 6.0, HINT_SIG = 0.4;

	/* ------------- state ------------- */
	const S = {
	phase: "soup",
	layers: [], // {id,name,color,rgb,template,placed,pose,hidden,depth,hints:[]}
	selected: -1, // index into layers
	obs: [], gt: [], // gt = placed-order index, -1 clutter
	placed: [], // layer indices in placed order (BP object order)
	marg: null, mu: null, Sig: null, assign: null,
	evid: [], covFrac: [],
	groupPre: [], groupAlpha: [], // per placed group + clutter last
	ownField: null, coastT: [],
	};
	let nextDepth = 1, nextId = 1;

	/* ---- Bet 9: eraser / backdrop / band-gain state ---- */
	const GAINS = { band: [1, 1, 1], opacity: 1 };
	const backdrop = { custom: false, rgb: [128, 128, 128], img: null }; // img: RGBA RES*RES
	let bandPre = null, bandDirty = true;
	const fieldAlpha = new Float32Array(RES * RES);
	let eraseStack = [], lastCursor = null;
	function toolMode(){ return document.querySelector('input[name=tool]:checked').value; }
	function brushR(){ return +document.querySelector('input[name=brush]:checked').value; }
	function updateEraseButtons(){
	document.getElementById("btn-undo-erase").disabled = !eraseStack.length;
	document.getElementById("btn-restore-erase").disabled = !eraseStack.length;
	}

	function addLayer(name, template, autoPlace) {
	const [color, rgb] = PALETTE[(S.layers.length) % PALETTE.length];
	const L = { id: nextId++, name, color, rgb, template, placed: false,
	pose: [0,0,0,Math.log(0.5)], hidden: false, depth: 0, hints: [] };
	S.layers.push(L);
	if (autoPlace) placeLayer(S.layers.length - 1);
	else { renderLibrary(); }
	return L;
	}
	function placeLayer(li) {
	const L = S.layers[li];
	L.placed = true; L.hidden = false; L.depth = nextDepth++;
	L.pose = [ -0.3 + 0.6rand(), -0.3 + 0.6rand(), -Math.PI + TAU*rand(),
	Math.log(0.45 + 0.2*rand()) ];
	rebuildScene();
	}
	function removeLayer(li) {
	S.layers[li].placed = false;
	rebuildScene();
	}

	/* ------------- scene construction ------------- */
	let rngState = 22222;
	function rand(){ rngState=(rngState*1103515245+12345)&0x7fffffff; return rngState/0x7fffffff; }

	function rebuildScene() {
	S.placed = S.layers.map((L,i)=>L.placed?i:-1).filter(i=>i>=0);
	const noiseAmt = 0.006 * Math.pow(3, +document.getElementById("noise").value / 3);
	S.obs = []; S.gt = []; S.src = [];
	S.placed.forEach((li,k)=>{
	const tmpl = S.layers[li].template;
	const tr = transformAtoms(tmpl, S.layers[li].pose);
	for (let j = 0; j < tr.length; j++) {
	S.obs.push(tr[j]); S.gt.push(k); S.src.push({ li, ref: tmpl[j] });
	}
	});
	for (let i=0;i<12;i++){
	const su=0.04+0.08*rand();
	S.obs.push([-0.95+1.9rand(),-0.95+1.9rand(),-Math.PI/2+Math.PI*rand(),
	su,su(0.4+0.5rand()),4+10rand(),TAUrand(),rand(),rand(),rand()]);
	S.gt.push(-1); S.src.push(null);
	}
	for (const a of S.obs) for(let q=0;q<10;q++){
	const g=Math.sqrt(-2Math.log(rand()+1e-9))Math.cos(TAU*rand());
	a[q]+=gnoiseAmtNOISE_SCALE[q];
	}
	for (const a of S.obs){a[3]=Math.max(a[3],.012);a[4]=Math.max(a[4],.008);a[5]=Math.max(a[5],.5);}
	S.marg=null; S.mu=null; S.Sig=null; S.assign=null;
	S.evid=S.obs.map(()=>true);
	S.covFrac=S.placed.map(()=>0);
	S.coastT=S.placed.map(()=>0);
	S.ownField=null;
	eraseStack=[]; updateEraseButtons();
	setPhase("soup");
	rebuildGroupBuffers();
	renderScene(); drawOverlay(); renderLayerList(); renderLibrary(); updatePanels();
	}
	function scramble(){
	for (const li of S.placed){
	S.layers[li].pose=[-0.35+0.7rand(),-0.35+0.7rand(),-Math.PI+TAU*rand(),
	Math.log(0.4+0.25*rand())];
	}
	rebuildScene();
	}

	/* ------------- believed grouping (persistent through occlusion) ------------- */
	function believedGroup(i){ return S.assign ? S.assign[i] : -2; }
	function updateAssign(){
	if(!S.marg){S.assign=null;return;}
	const K=S.placed.length;
	if(!S.assign) S.assign=new Array(S.obs.length).fill(-1);
	for(let i=0;i<S.obs.length;i++){
	if(S.assign[i]>=0 && !S.evid[i]) continue; // no evidence: identity persists
	const m=S.marg[i]; let b=0;
	for(let k=1;k<=K;k++) if(m[k]>m[b]) b=k;
	S.assign[i]= b===K ? -1 : b;
	}
	}
	function groupAtomIdx(k){
	const out=[];
	for(let i=0;i<S.obs.length;i++) if(believedGroup(i)===k) out.push(i);
	return out;
	}

	/* ------------- rendering ------------- */
	const stage=document.getElementById("stage");
	const sceneC=document.getElementById("scene-canvas");
	const overC=document.getElementById("overlay-canvas");
	sceneC.width=sceneC.height=RES;
	let CSS=600;
	function fitStage(){
	const wrap=document.getElementById("stage-wrap");
	CSS=Math.max(280,Math.floor(Math.min(wrap.clientWidth,wrap.clientHeight)-8));
	stage.style.width=stage.style.height=CSS+"px";
	overC.width=overC.height=CSS*(window.devicePixelRatio\|\|1);
	drawOverlay();
	}
	window.addEventListener("resize",fitStage);

	function rebuildGroupBuffers(){
	const K=S.placed.length;
	S.groupPre=[]; S.groupAlpha=[];
	for(let g=0;g<=K;g++) S.groupPre.push(new Float32Array(3RESRES));
	const groupOf=i=>{ const g=S.marg?believedGroup(i):S.gt[i]; return g>=0?g:K; };
	for(let i=0;i<S.obs.length;i++){
	const g=groupOf(i);
	if(g<K && S.layers[S.placed[g]].hidden) continue;
	renderPre([S.obs[i]],RES,S.groupPre[g]);
	}
	for(let g=0;g<=K;g++) S.groupAlpha.push(alphaFromPre(S.groupPre[g],RES));
	bandDirty=true;
	}
	function rebuildOneGroup(k){
	S.groupPre[k]=new Float32Array(3RESRES);
	if(!S.layers[S.placed[k]].hidden)
	renderPre(groupAtomIdx(k).map(i=>S.obs[i]),RES,S.groupPre[k]);
	S.groupAlpha[k]=alphaFromPre(S.groupPre[k],RES);
	bandDirty=true;
	}
	/* frequency-band buffers, built lazily only when a band gain != 1.
	Same visibility rule as the group buffers; render is linear in atom color,
	so gaincolor == gaincontribution and Σ_b gain_b·bandPre_b is exact. */
	function rebuildBandBuffers(){
	const K=S.placed.length;
	bandPre=[new Float32Array(3RESRES),new Float32Array(3RESRES),new Float32Array(3RESRES)];
	const groupOf=i=>{ const g=S.marg?believedGroup(i):S.gt[i]; return g>=0?g:K; };
	for(let i=0;i<S.obs.length;i++){
	const g=groupOf(i);
	if(g<K && S.layers[S.placed[g]].hidden) continue;
	renderPre([S.obs[i]],RES,bandPre[bandOf(S.obs[i][5])]);
	}
	bandDirty=false;
	}
	const sceneCtx=sceneC.getContext("2d");
	const compositePre=new Float32Array(3RESRES);
	const sceneImg=new ImageData(RES,RES);
	function compMode(){ return document.querySelector('input[name=comp]:checked').value; }
	function renderScene(){
	const K=S.placed.length;
	const gb=GAINS.band, gainsOn=gb[0]!==1\|\|gb[1]!==1\|\|gb[2]!==1;
	const bgOn=backdrop.custom\|\|backdrop.img\|\|GAINS.opacity!==1;
	if(compMode()==="field"){
	compositePre.fill(0);
	if(gainsOn){
	if(bandDirty) rebuildBandBuffers();
	for(let b=0;b<3;b++){
	const g=gb[b]; if(!g) continue;
	const buf=bandPre[b];
	for(let i=0;i<compositePre.length;i++) compositePre[i]+=g*buf[i];
	}
	} else {
	for(const buf of S.groupPre)
	for(let i=0;i<compositePre.length;i++) compositePre[i]+=buf[i];
	}
	sigmoidField(compositePre,RES,sceneImg.data);
	if(bgOn){
	alphaFromPre(compositePre,RES,fieldAlpha);
	blendOverBackdrop(sceneImg.data,fieldAlpha,GAINS.opacity,backdrop.img\|\|backdrop.rgb,RES);
	}
	} else {
	// painter: clutter at the back, then placed layers by depth
	const order=[K, ...S.placed.map((li,k)=>k)
	.sort((a,b)=>S.layers[S.placed[a]].depth-S.layers[S.placed[b]].depth)];
	compositePainter(order,S.groupPre,S.groupAlpha,RES,sceneImg.data);
	if(bgOn){
	// union alpha of everything rendered (band gains are field-mode only)
	for(let i=0;i<RES*RES;i++){
	let keep=1;
	for(let q=0;q<=K;q++) keep*=1-S.groupAlpha[q][i];
	fieldAlpha[i]=1-keep;
	}
	blendOverBackdrop(sceneImg.data,fieldAlpha,GAINS.opacity,backdrop.img\|\|backdrop.rgb,RES);
	}
	}
	sceneCtx.putImageData(sceneImg,0,0);
	}

	function w2p(x){return (x+1)/2*overC.width;}
	function p2w(px){return px/overC.width*2-1;}

	const ovAtoms=document.getElementById("ov-atoms"),ovOwn=document.getElementById("ov-own"),
	ovEnt=document.getElementById("ov-ent"),ovPose=document.getElementById("ov-pose"),
	ovHints=document.getElementById("ov-hints");
	for(const el of [ovAtoms,ovOwn,ovEnt,ovPose,ovHints]) el.addEventListener("change",drawOverlay);
	document.querySelectorAll('input[name=comp]').forEach(el=>
	el.addEventListener("change",()=>{renderScene();}));

	function drawOverlay(){
	const ctx=overC.getContext("2d");
	ctx.clearRect(0,0,overC.width,overC.height);
	const px1=overC.width/CSS;
	const K=S.placed.length;
	const colOf=k=>S.layers[S.placed[k]];

	if(S.ownField && (ovOwn.checked\|\|ovEnt.checked)){
	const {P,ent,support}=S.ownField;
	const im=ctx.createImageData(OWN_RES,OWN_RES);
	for(let i=0;i<OWN_RES*OWN_RES;i++){
	if(!support[i]) continue;
	let r=0,g=0,b=0,a=0;
	if(ovOwn.checked){
	let best=0;
	for(let k=1;k<=K;k++) if(P[k][i]>P[best][i]) best=k;
	const rgb=best===K?OUTLIER_RGB:colOf(best).rgb;
	r=rgb[0];g=rgb[1];b=rgb[2];a=90*P[best][i];
	}
	if(ovEnt.checked){
	const maxE=Math.log2(K+1);
	const e=Math.min(1,ent[i]/maxE), ea=160ee;
	if(ea>a){r=200;g=107;b=255;a=ea;}
	}
	im.data[4i]=r;im.data[4i+1]=g;im.data[4i+2]=b;im.data[4i+3]=a;
	}
	const tmp=document.createElement("canvas");
	tmp.width=tmp.height=OWN_RES;
	tmp.getContext("2d").putImageData(im,0,0);
	ctx.imageSmoothingEnabled=true;
	ctx.drawImage(tmp,0,0,overC.width,overC.height);
	}

	if(ovAtoms.checked){
	for(let i=0;i<S.obs.length;i++){
	const a=S.obs[i], g=believedGroup(i);
	if(g>=0 && S.layers[S.placed[g]].hidden) continue;
	let rgb=OUTLIER_RGB, alpha=0.5;
	if(g===-2){rgb=[150,155,168];alpha=0.55;}
	else if(g>=0){rgb=colOf(g).rgb;alpha=S.evid[i]?0.25+0.75*S.marg[i][g]:0.35;}
	else if(S.marg){alpha=0.25+0.55*S.marg[i][K];}
	const len=Math.max(3px1,a[3]overC.width*0.5);
	const cx=w2p(a[0]),cy=w2p(a[1]);
	const dx=Math.cos(a[2])len/2,dy=Math.sin(a[2])len/2;
	ctx.strokeStyle=`rgba(${rgb[0]},${rgb[1]},${rgb[2]},${alpha})`;
	ctx.lineWidth=1.6*px1;
	ctx.setLineDash(g>=0&&!S.evid[i]?[3px1,3px1]:[]);
	ctx.beginPath();ctx.moveTo(cx-dx,cy-dy);ctx.lineTo(cx+dx,cy+dy);ctx.stroke();
	}
	ctx.setLineDash([]);
	}

	if(ovHints.checked){
	for(let k=0;k<K;k++){
	const L=colOf(k);
	for(const h of L.hints){
	ctx.strokeStyle=L.color; ctx.lineWidth=1.2px1; ctx.setLineDash([2px1,3*px1]);
	ctx.beginPath();ctx.arc(w2p(h[0]),w2p(h[1]),HINT_SIG*overC.width/2,0,TAU);ctx.stroke();
	ctx.setLineDash([]);
	ctx.beginPath();ctx.arc(w2p(h[0]),w2p(h[1]),3*px1,0,TAU);
	ctx.fillStyle=L.color;ctx.fill();
	}
	}
	}

	if(ovPose.checked && S.mu){
	for(let k=0;k<K;k++){
	const mu=S.mu[k],Sg=S.Sig[k],L=colOf(k);
	const cx=w2p(mu[0]),cy=w2p(mu[1]);
	ctx.strokeStyle=L.color;ctx.lineWidth=1.2*px1;
	ctx.beginPath();
	ctx.moveTo(cx-7px1,cy);ctx.lineTo(cx+7px1,cy);
	ctx.moveTo(cx,cy-7px1);ctx.lineTo(cx,cy+7px1);ctx.stroke();
	const Ln=26px1Math.exp(mu[3]);
	ctx.beginPath();ctx.moveTo(cx,cy);
	ctx.lineTo(cx+Math.cos(mu[2])Ln,cy+Math.sin(mu[2])Ln);ctx.stroke();
	const coast=S.coastT[k], q=coastcoast0.0012;
	const a11=Sg[0][0]+q,a12=Sg[0][1],a22=Sg[1][1]+q;
	const tr=a11+a22,det=a11a22-a12a12;
	const disc=Math.sqrt(Math.max(0,tr*tr/4-det));
	const l1=tr/2+disc,l2=Math.max(1e-12,tr/2-disc);
	const ang=Math.atan2(l1-a11,a12\|\|1e-12);
	const ghost=L.hidden\|\|S.covFrac[k]>0.7;
	ctx.save();ctx.translate(cx,cy);ctx.rotate(-ang+Math.PI/2);
	ctx.setLineDash(ghost?[5px1,4px1]:[]);
	ctx.beginPath();
	ctx.ellipse(0,0,2Math.sqrt(l1)overC.width/2,2Math.sqrt(l2)overC.width/2,0,0,TAU);
	ctx.stroke();ctx.restore();ctx.setLineDash([]);
	if(ghost){
	ctx.fillStyle=L.color;
	ctx.font=`${11*px1}px ${getComputedStyle(document.body).fontFamily}`;
	ctx.fillText("believed, unseen",cx+10px1,cy-10px1);
	}
	}
	}

	if(toolMode()==="erase"&&lastCursor){ // eraser brush cursor
	ctx.strokeStyle="rgba(255,120,110,0.9)";
	ctx.lineWidth=1.4px1;ctx.setLineDash([4px1,3*px1]);
	ctx.beginPath();
	ctx.arc(w2p(lastCursor[0]),w2p(lastCursor[1]),brushR()*overC.width/2,0,TAU);
	ctx.stroke();ctx.setLineDash([]);
	}
	}

	/* ------------- semantic factor from hints ------------- */
	function makeSemLL(){
	const K=S.placed.length;
	let any=false;
	for(const li of S.placed) if(S.layers[li].hints.length) any=true;
	if(!any) return null;
	return (i,k)=>{
	const hs=S.layers[S.placed[k]].hints;
	if(!hs.length) return 0;
	let best=0;
	for(const h of hs){
	const d2=(S.obs[i][0]-h[0])2+(S.obs[i][1]-h[1])2;
	best=Math.max(best,Math.exp(-0.5d2/(HINT_SIGHINT_SIG)));
	}
	return HINT_W*(best-0.5);
	};
	}

	/* ------------- BP wiring + depth occlusion ------------- */
	function currentTemplates(){ return S.placed.map(li=>S.layers[li].template); }

	function computeEvidence(){
	const K=S.placed.length;
	if(!document.getElementById("auto-occ").checked \|\| !S.assign){
	S.evid=S.obs.map((_,i)=>{
	const g=believedGroup(i);
	return !(g>=0 && S.layers[S.placed[g]].hidden);
	});
	S.covFrac=S.placed.map((li,k)=>S.layers[li].hidden?1:0);
	return;
	}
	const layersMeta=S.placed.map(li=>({depth:S.layers[li].depth,hidden:S.layers[li].hidden}));
	const {mask,covFrac}=autoHidden(S.obs,S.assign,layersMeta,S.groupAlpha,RES);
	S.evid=mask.map(m=>!m);
	S.covFrac=covFrac;
	}

	function runBind(opts={}){
	const hiddenMask=S.evid.map(e=>!e);
	const frames=[];
	const res=bpBind(currentTemplates(),S.obs,{
	iters:opts.iters??40,
	clampPose:opts.clampPose??null,
	hiddenMask,
	semLL:makeSemLL(),
	onIter:(it,marg,mu,Sig)=>{ if(opts.animate) frames.push({
	marg,mu:mu.map(m=>m.slice()),Sig:Sig.map(M=>M.map(r=>r.slice()))}); },
	});
	return {res,frames};
	}

	function bind(animate=true){
	if(S.phase==="binding"\|\|!S.placed.length) return;
	S.assign=null;
	eraseStack=[]; updateEraseButtons(); // erase history is stale once BP re-runs
	S.evid=S.obs.map(()=>true); // full re-bind: everything is evidence again
	for(const li of S.placed) if(S.layers[li].hidden){
	// user-hidden layers stay evidence-free
	// (their atoms are excluded per-atom below via gt at soup time)
	}
	setPhase("binding");
	setTimeout(()=>{
	const {res,frames}=runBind({iters:40,animate});
	if(!animate){finishBind(res);return;}
	let f=0;
	const meter=document.querySelector("#bind-meter > div");
	const step=()=>{
	if(f<frames.length){
	S.marg=frames[f].marg;S.mu=frames[f].mu;S.Sig=frames[f].Sig;
	updateAssign();
	meter.style.width=(100*(f+1)/frames.length)+"%";
	document.getElementById("m-it").textContent=(f+1);
	drawOverlay();updatePanels();
	f++;requestAnimationFrame(step);
	} else finishBind(res);
	};
	step();
	},30);
	}
	function finishBind(res){
	S.marg=res.marg;S.mu=res.mu;S.Sig=res.Sig;
	updateAssign();
	rebuildGroupBuffers();
	occlusionRefresh(true);
	renderScene();refreshOwnership();
	setPhase("bound");
	drawOverlay();updatePanels();renderLayerList();
	}

	/* recompute evidence from the depth stack; if it changed, refresh marginals
	with all poses clamped (occlusion changes evidence, not where things are) */
	function occlusionRefresh(silent){
	const before=S.evid.join("");
	computeEvidence();
	if(S.evid.join("")===before) return;
	const clamp=S.mu.map(m=>m.slice());
	const {res}=runBind({iters:8,clampPose:clamp});
	S.marg=res.marg;
	updateAssign();
	// coasting for heavily covered layers
	for(let k=0;k<S.placed.length;k++)
	S.coastT[k]=(S.covFrac[k]>0.7\|\|S.layers[S.placed[k]].hidden)?S.coastT[k]+1:0;
	if(!silent){drawOverlay();updatePanels();renderLayerList();}
	}

	function refreshOwnership(){
	if(!S.marg){S.ownField=null;return;}
	const K=S.placed.length;
	const vis=[],visMarg=[];
	for(let i=0;i<S.obs.length;i++){
	const g=believedGroup(i);
	if(g>=0&&S.layers[S.placed[g]].hidden) continue;
	vis.push(S.obs[i]);visMarg.push(S.marg[i]);
	}
	S.ownField=ownershipField(vis,visMarg,K,OWN_RES);
	}

	function resettle(k,clampXi){
	const clamp=S.placed.map(()=>null);clamp[k]=clampXi;
	const {res}=runBind({iters:10,clampPose:clamp});
	S.marg=res.marg;S.mu=res.mu;S.Sig=res.Sig;
	S.mu[k]=clampXi.slice();
	updateAssign();
	rebuildGroupBuffers();
	occlusionRefresh(true);
	renderScene();refreshOwnership();
	drawOverlay();updatePanels();renderLayerList();
	document.getElementById("m-it").textContent="10 (re-settle)";
	}

	/* ------------- interventions ------------- */
	function applyGesture(k,g){
	for(const i of groupAtomIdx(k)) S.obs[i]=transformAtoms([S.obs[i]],g)[0];
	S.mu[k]=composePose(g,S.mu[k]);
	rebuildOneGroup(k);
	renderScene();drawOverlay();updatePanels();
	}

	/* ------------- eraser (Bet 9) -------------
	Deleting an atom = filtering every per-atom parallel array by the brush
	mask. Order of atoms carries no meaning anywhere (additive render, per-atom
	marginals), so undo can simply re-append the removed records.
	Undo is valid until the next Bind/Scramble/place/remove (those rebuild or
	re-infer the per-atom state). "Burn" additionally removes the source atom
	from the layer TEMPLATE, so the erase survives scene rebuilds. */
	function eraseAt(wx,wy,stroke){
	const skip=i=>{ const g=believedGroup(i); return g>=0&&S.layers[S.placed[g]].hidden; };
	const mask=eraseMask(S.obs,wx,wy,brushR(),skip);
	let any=false; for(const m of mask) if(m){any=true;break;}
	if(!any) return;
	const kObs=[],kGt=[],kSrc=[],kEvid=[],
	kAssign=S.assign?[]:null, kMarg=S.marg?[]:null;
	for(let i=0;i<S.obs.length;i++){
	if(mask[i]){
	stroke.atoms.push({a:S.obs[i],gt:S.gt[i],src:S.src[i],evid:S.evid[i],
	assign:S.assign?S.assign[i]:null, marg:S.marg?S.marg[i]:null});
	} else {
	kObs.push(S.obs[i]);kGt.push(S.gt[i]);kSrc.push(S.src[i]);kEvid.push(S.evid[i]);
	if(kAssign)kAssign.push(S.assign[i]);
	if(kMarg)kMarg.push(S.marg[i]);
	}
	}
	S.obs=kObs;S.gt=kGt;S.src=kSrc;S.evid=kEvid;
	if(kAssign)S.assign=kAssign;
	if(kMarg)S.marg=kMarg;
	rebuildGroupBuffers();renderScene();drawOverlay();updatePanels();
	}
	function commitStroke(stroke){
	if(!stroke.atoms.length) return;
	if(document.getElementById("erase-burn").checked){
	for(const rec of stroke.atoms){
	if(!rec.src) continue; // clutter has no template
	const L=S.layers[rec.src.li];
	const idx=L.template.indexOf(rec.src.ref);
	if(idx>=0){L.template.splice(idx,1);stroke.tmpl.push(rec.src);}
	}
	}
	eraseStack.push(stroke);
	updateEraseButtons();
	refreshOwnership();drawOverlay();renderLayerList();renderLibrary();
	}
	function undoErase(redraw=true){
	const stroke=eraseStack.pop();
	if(!stroke) return;
	for(const t of stroke.tmpl) S.layers[t.li].template.push(t.ref);
	for(const rec of stroke.atoms){
	S.obs.push(rec.a);S.gt.push(rec.gt);S.src.push(rec.src);S.evid.push(rec.evid);
	if(S.assign)S.assign.push(rec.assign??-1);
	if(S.marg)S.marg.push(rec.marg);
	}
	updateEraseButtons();
	if(redraw){
	rebuildGroupBuffers();renderScene();refreshOwnership();
	drawOverlay();updatePanels();renderLayerList();renderLibrary();
	}
	}
	function restoreAllErases(){
	while(eraseStack.length) undoErase(false);
	rebuildGroupBuffers();renderScene();refreshOwnership();
	drawOverlay();updatePanels();renderLayerList();renderLibrary();
	}

	/* ------------- pointer interaction ------------- */
	let drag=null;
	overC.addEventListener("pointerdown",e=>{
	const rect=overC.getBoundingClientRect();
	const wx=p2w((e.clientX-rect.left)*overC.width/rect.width);
	const wy=p2w((e.clientY-rect.top)*overC.width/rect.width);
	if(e.shiftKey){ // semantic hint for the selected layer
	const li=S.selected;
	if(li>=0&&S.layers[li].placed){
	S.layers[li].hints.push([wx,wy]);
	drawOverlay();renderLayerList();
	document.getElementById("prompt-log").textContent=
	`hint added for ${S.layers[li].name} — Bind applies it as a location prior.`;
	}
	return;
	}
	if(toolMode()==="erase"){ // erase works in soup AND bound
	drag={erase:true,stroke:{atoms:[],tmpl:[]}};
	overC.setPointerCapture(e.pointerId);
	lastCursor=[wx,wy];
	eraseAt(wx,wy,drag.stroke);
	return;
	}
	if(S.phase!=="bound") return;
	let best=-1,bd=0.12*0.12;
	for(let i=0;i<S.obs.length;i++){
	const g=believedGroup(i);
	if(g<0) continue;
	if(S.layers[S.placed[g]].hidden) continue;
	const d=(S.obs[i][0]-wx)2+(S.obs[i][1]-wy)2;
	if(d<bd){bd=d;best=i;}
	}
	let k=best>=0?believedGroup(best):-1;
	if(k<0) for(let kk=0;kk<S.placed.length;kk++)
	if((S.layers[S.placed[kk]].hidden\|\|S.covFrac[kk]>0.7)&&
	(S.mu[kk][0]-wx)2+(S.mu[kk][1]-wy)2<0.05*0.05) k=kk;
	if(k<0) return;
	drag={k,lx:wx,ly:wy,moved:false};
	overC.classList.add("dragging");
	overC.setPointerCapture(e.pointerId);
	});
	overC.addEventListener("pointermove",e=>{
	const rect=overC.getBoundingClientRect();
	const wx=p2w((e.clientX-rect.left)*overC.width/rect.width);
	const wy=p2w((e.clientY-rect.top)*overC.width/rect.width);
	if(toolMode()==="erase") lastCursor=[wx,wy];
	if(!drag){ if(toolMode()==="erase") drawOverlay(); return; }
	if(drag.erase){ eraseAt(wx,wy,drag.stroke); return; }
	const dx=wx-drag.lx,dy=wy-drag.ly;
	if(dx\|\|dy){applyGesture(drag.k,gestureTranslate(dx,dy));drag.lx=wx;drag.ly=wy;drag.moved=true;}
	});
	overC.addEventListener("pointerup",e=>{
	if(!drag) return;
	if(drag.erase){ commitStroke(drag.stroke); drag=null; return; }
	overC.classList.remove("dragging");
	if(drag.moved) resettle(drag.k,S.mu[drag.k]);
	drag=null;
	});
	overC.addEventListener("pointerleave",()=>{
	if(lastCursor){ lastCursor=null; drawOverlay(); }
	});
	overC.addEventListener("wheel",e=>{
	if(S.phase!=="bound") return;
	const rect=overC.getBoundingClientRect();
	const wx=p2w((e.clientX-rect.left)*overC.width/rect.width);
	const wy=p2w((e.clientY-rect.top)*overC.width/rect.width);
	let k=-1,bd=0.16*0.16;
	for(let kk=0;kk<S.placed.length;kk++){
	const d=(S.mu[kk][0]-wx)2+(S.mu[kk][1]-wy)2;
	if(d<bd){bd=d;k=kk;}
	}
	if(k<0) return;
	e.preventDefault();
	const c=[S.mu[k][0],S.mu[k][1]];
	const g=e.shiftKey?gestureScaleAbout(c,e.deltaY>0?-0.05:0.05)
	:gestureRotateAbout(c,e.deltaY>0?0.08:-0.08);
	applyGesture(k,g);
	clearTimeout(overC._wt);
	overC._wt=setTimeout(()=>resettle(k,S.mu[k]),350);
	},{passive:false});

	/* ------------- panels ------------- */
	function setPhase(p){
	S.phase=p;
	const lamp=document.getElementById("state-lamp");
	lamp.className=p==="soup"?"soup":p==="binding"?"binding":"bound";
	lamp.textContent=p==="soup"?"ATOM SOUP":p==="binding"?"BELIEFS SETTLING":"BOUND — GRABBABLE";
	document.getElementById("btn-bind").disabled=p==="binding"\|\|!S.placed.length;
	}

	function renderLayerList(){
	const el=document.getElementById("layer-list");
	el.innerHTML="";
	const byDepth=[...S.placed].map((li,k)=>({li,k}))
	.sort((a,b)=>S.layers[b.li].depth-S.layers[a.li].depth);
	for(const {li,k} of byDepth){
	const L=S.layers[li];
	const idx=S.assign?groupAtomIdx(k):[];
	const conf=idx.length?idx.reduce((a,i)=>a+(S.evid[i]?S.marg[i][k]:0),0)/Math.max(1,idx.filter(i=>S.evid[i]).length):0;
	const cov=S.covFrac[k]\|\|0;
	const d=document.createElement("div");
	d.className="layer"+(S.selected===li?" sel":"");
	d.innerHTML=`
	<div class="name" data-li="${li}">
	<span class="swatch" style="background:${L.color}"></span>
	<span>${L.name}</span>
	<span class="dim">${idx.length\|\|L.template.length} atoms${L.hints.length?` · ${L.hints.length} hint${L.hints.length>1?"s":""}`:""}</span>
	<span class="spacer"></span>
	<div class="belief-bar"><div style="width:${100*conf}%"></div></div>
	</div>
	<div class="pose">${S.mu?`t=(${S.mu[k][0].toFixed(2)}, ${S.mu[k][1].toFixed(2)}) \u03c1=${(S.mu[k][2]180/Math.PI).toFixed(0)}\u00b0 s=${Math.exp(S.mu[k][3]).toFixed(2)}`:"pose: unbound"}${cov>0.05?` · <span style="color:var(--entropy)">${(100cov).toFixed(0)}% occluded${S.coastT[k]?`, coasting ${S.coastT[k]}`:""}</span>`:""}</div>
	<div class="ctl">
	<button data-li="${li}" data-op="rotl">↺</button>
	<button data-li="${li}" data-op="rotr">↻</button>
	<button data-li="${li}" data-op="grow">+</button>
	<button data-li="${li}" data-op="shrink">−</button>
	<button data-li="${li}" data-op="front">front</button>
	<button data-li="${li}" data-op="back">back</button>
	<button data-li="${li}" data-op="hide">${L.hidden?"reveal":"hide"}</button>
	${L.hints.length?`<button data-li="${li}" data-op="clearhints">hints ✕</button>`:""}
	<button data-li="${li}" data-op="remove">✕</button>
	</div>`;
	el.appendChild(d);
	}
	if(!byDepth.length)
	el.innerHTML='<div class="dim" style="font-size:11px">no layers placed — place from the library or spawn one</div>';
	}
	document.getElementById("layer-list").addEventListener("click",e=>{
	const nm=e.target.closest(".name");
	if(nm&&!e.target.closest("button")){
	S.selected=+nm.dataset.li===S.selected?-1:+nm.dataset.li;
	renderLayerList();return;
	}
	const b=e.target.closest("button");if(!b)return;
	const li=+b.dataset.li,op=b.dataset.op;
	const k=S.placed.indexOf(li);
	if(op==="remove"){removeLayer(li);return;}
	if(op==="clearhints"){S.layers[li].hints=[];drawOverlay();renderLayerList();return;}
	if(op==="front"\|\|op==="back"){
	S.layers[li].depth=op==="front"?nextDepth++:(Math.min(...S.placed.map(x=>S.layers[x].depth))-1);
	if(S.phase==="bound"){rebuildGroupBuffers();occlusionRefresh(false);renderScene();refreshOwnership();}
	renderLayerList();return;
	}
	if(S.phase!=="bound")return;
	if(op==="hide"){
	S.layers[li].hidden=!S.layers[li].hidden;
	rebuildGroupBuffers();occlusionRefresh(false);renderScene();refreshOwnership();drawOverlay();renderLayerList();
	return;
	}
	const c=[S.mu[k][0],S.mu[k][1]];
	if(op==="rotl"){applyGesture(k,gestureRotateAbout(c,-Math.PI/12));resettle(k,S.mu[k]);}
	if(op==="rotr"){applyGesture(k,gestureRotateAbout(c,Math.PI/12));resettle(k,S.mu[k]);}
	if(op==="grow"){applyGesture(k,gestureScaleAbout(c,0.12));resettle(k,S.mu[k]);}
	if(op==="shrink"){applyGesture(k,gestureScaleAbout(c,-0.12));resettle(k,S.mu[k]);}
	});

	function renderLibrary(){
	const el=document.getElementById("library");
	el.innerHTML="";
	S.layers.forEach((L,li)=>{
	if(L.placed) return;
	const c=document.createElement("span");
	c.className="chip";
	c.innerHTML=`<span class="swatch" style="background:${L.color}"></span>${L.name}
	<span class="dim">${L.template.length}</span>
	<button data-li="${li}" data-op="place" title="place">+</button>`;
	el.appendChild(c);
	});
	}
	document.getElementById("library").addEventListener("click",e=>{
	const b=e.target.closest("button");if(!b)return;
	placeLayer(+b.dataset.li);
	});

	function updatePanels(){
	document.getElementById("m-n").textContent=S.obs.length;
	const K=S.placed.length;
	if(!S.marg){
	document.getElementById("m-acc").textContent="—";
	document.getElementById("m-ent").textContent="—";
	return;
	}
	let correct=0;
	for(let i=0;i<S.gt.length;i++) if(believedGroup(i)===S.gt[i]) correct++;
	document.getElementById("m-acc").textContent=(100*correct/S.gt.length).toFixed(1)+"%";
	const ent=atomEntropy(S.marg);
	document.getElementById("m-ent").textContent=
	(ent.reduce((a,x)=>a+x,0)/ent.length).toFixed(2)+" bits";
	}

	/* ------------- spawn: server endpoints ------------- */
	const spawnStatus=document.getElementById("spawn-status");
	async function gradioCall(name,data){
	const base=location.pathname.includes("/studio/")?"..":"";
	const r=await fetch(`${base}/gradio_api/call/${name}`,{
	method:"POST",headers:{"Content-Type":"application/json"},
	body:JSON.stringify({data})});
	const {event_id}=await r.json();
	const resp=await fetch(`${base}/gradio_api/call/${name}/${event_id}`);
	const text=await resp.text();
	const lines=text.split("\n").filter(l=>l.startsWith("data:"));
	if(!lines.length) throw new Error("no data from server");
	const payload=JSON.parse(lines[lines.length-1].slice(5));
	if(payload==null\|\|payload.error) throw new Error(payload?.error\|\|"server error");
	return JSON.parse(payload[0]);
	}
	function addGenerated(layer,fallbackName){
	const name=(layer.ledger&&layer.ledger.prompt)
	? (layer.ledger.attention&&layer.ledger.attention.token!=="(all content tokens)"
	? layer.ledger.attention.token : layer.ledger.prompt.split(/[ ,]/)[1]\|\|fallbackName)
	: fallbackName;
	addLayer(name,layer.atoms,true);
	spawnStatus.textContent=`layer "${name}": ${layer.atoms.length} atoms · ${layer.ledger.status}`+
	(layer.ledger.attention?` · matte kept ${layer.ledger.attention.atoms_after_matte}/${layer.ledger.attention.atoms_before_matte}`:"");
	}
	document.getElementById("btn-spawn-text").addEventListener("click",async()=>{
	const prompt=document.getElementById("spawn-prompt").value.trim();
	const token=document.getElementById("spawn-token").value.trim();
	if(!prompt){spawnStatus.textContent="write a prompt first";return;}
	spawnStatus.textContent="distilling on the server (GPU, minutes)\u2026";
	try{
	const layer=await gradioCall("layer_from_text",[prompt,"",192,900,30,token,0.35]);
	addGenerated(layer,"generated");
	}catch(err){spawnStatus.textContent="distill failed: "+err.message+
	" (needs a GPU Space; on CPU use Fit or paste JSON)";}
	});
	document.getElementById("btn-spawn-img").addEventListener("click",async()=>{
	const f=document.getElementById("spawn-file").files[0];
	if(!f){spawnStatus.textContent="choose an image first";return;}
	spawnStatus.textContent="fitting atoms to the image (CPU, ~1 min)\u2026";
	try{
	const b64=await new Promise((res,rej)=>{
	const img=new Image();
	img.onload=()=>{
	const c=document.createElement("canvas");
	const s=Math.min(1,160/Math.max(img.width,img.height));
	c.width=Math.round(img.widths);c.height=Math.round(img.heights);
	c.getContext("2d").drawImage(img,0,0,c.width,c.height);
	res(c.toDataURL("image/png").split(",")[1]);
	};
	img.onerror=rej;
	img.src=URL.createObjectURL(f);
	});
	const layer=await gradioCall("layer_from_image_b64",[b64,140,400]);
	addGenerated(layer,f.name.replace(/\.[^.]+$/,""));
	}catch(err){spawnStatus.textContent="fit failed: "+err.message+
	" (is this page running from the Space? standalone files can only paste JSON)";}
	});
	document.getElementById("btn-spawn-json").addEventListener("click",()=>{
	try{
	const raw=JSON.parse(document.getElementById("spawn-json").value);
	const atoms=raw.atoms\|\|raw;
	if(!Array.isArray(atoms)\|\|atoms[0].length!==10) throw new Error("expect [[10 fields]...]");
	addLayer("pasted-"+nextId,atoms,true);
	spawnStatus.textContent=`pasted layer: ${atoms.length} atoms`;
	document.getElementById("spawn-json").value="";
	}catch(err){spawnStatus.textContent="bad JSON: "+err.message;}
	});

	/* ------------- prompt as intervention ------------- */
	const promptLog=document.getElementById("prompt-log");
	function layerByName(part){
	for(let k=0;k<S.placed.length;k++)
	if(part.includes(S.layers[S.placed[k]].name.toLowerCase())) return k;
	return -1;
	}
	function localParse(text){
	const t=text.toLowerCase(),ops=[];
	for(const part of t.split(/,\|;\| and /)){
	const k=layerByName(part);
	if(k<0) continue;
	if(/hide\|occlude/.test(part)){ops.push({op:"hide",k});continue;}
	if(/show\|reveal\|unhide/.test(part)){ops.push({op:"show",k});continue;}
	if(/front\|top\|forward/.test(part)&&/bring\|put\|move\|send/.test(part)){ops.push({op:"front",k});continue;}
	if(/back\|behind\|bottom/.test(part)&&/send\|put\|move\|push/.test(part)){ops.push({op:"back",k});continue;}
	const deg=part.match(/(-?\d+)\s*(deg\|\u00b0)?/);
	if(/rotate\|turn\|spin/.test(part))
	ops.push({op:"rotate",k,deg:deg?+deg[1]:30*(/left\|counter\|ccw/.test(part)?-1:1)});
	if(/scale\|grow\|bigger\|larger\|shrink\|smaller/.test(part))
	ops.push({op:"scale",k,ds:/shrink\|smaller/.test(part)?-0.15:0.15});
	if(/move\|push\|slide\|put\|drag/.test(part)){
	let dx=0,dy=0;const step=0.22;
	if(/left/.test(part))dx-=step;
	if(/right/.test(part))dx+=step;
	if(/up\|top/.test(part))dy-=step;
	if(/down\|bottom/.test(part))dy+=step;
	if(/center\|middle/.test(part))ops.push({op:"moveto",k,x:0,y:0});
	else if(dx\|\|dy)ops.push({op:"move",k,dx,dy});
	}
	}
	return ops;
	}
	async function claudeParse(text){
	const names=S.placed.map(li=>S.layers[li].name);
	const sceneDesc=S.placed.map((li,k)=>
	`${S.layers[li].name}: t=(${S.mu[k][0].toFixed(2)},${S.mu[k][1].toFixed(2)}) rho=${S.mu[k][2].toFixed(2)} scale=${Math.exp(S.mu[k][3]).toFixed(2)} depth=${S.layers[li].depth} hidden=${S.layers[li].hidden}`).join("; ");
	const resp=await fetch("https://api.anthropic.com/v1/messages",{
	method:"POST",headers:{"Content-Type":"application/json"},
	body:JSON.stringify({model:"claude-sonnet-4-6",max_tokens:1000,
	messages:[{role:"user",content:
	`You control a probabilistic layered scene editor. Coordinates x,y in [-1,1], y grows DOWNWARD. Higher depth = in front. Layers: ${sceneDesc}.
	User command: "${text}"
	Respond ONLY with a JSON array (no prose, no fences) of ops:
	{"op":"move","object":<name>,"dx":n,"dy":n} {"op":"moveto","object":<name>,"x":n,"y":n}
	{"op":"rotate","object":<name>,"deg":n} {"op":"scale","object":<name>,"factor":n}
	{"op":"front","object":<name>} {"op":"back","object":<name>}
	{"op":"hide","object":<name>} {"op":"show","object":<name>}
	Valid names: ${JSON.stringify(names)}`}]})});
	const data=await resp.json();
	const txt=data.content.filter(c=>c.type==="text").map(c=>c.text).join("");
	const arr=JSON.parse(txt.replace(/```json\|```/g,"").trim());
	return arr.map(o=>{
	const k=S.placed.findIndex(li=>S.layers[li].name===o.object);
	if(k<0)return null;
	if(o.op==="move")return{op:"move",k,dx:o.dx,dy:o.dy};
	if(o.op==="moveto")return{op:"moveto",k,x:o.x,y:o.y};
	if(o.op==="rotate")return{op:"rotate",k,deg:o.deg};
	if(o.op==="scale")return{op:"scale",k,ds:Math.log(o.factor)};
	return{op:o.op,k};
	}).filter(Boolean);
	}
	function execOps(ops){
	if(!ops.length){promptLog.textContent="Parsed no intervention. Layers: "+
	S.placed.map(li=>S.layers[li].name).join(", ")+". Verbs: move/rotate/scale/hide/show/front/back.";return;}
	const touched=new Set();
	for(const o of ops){
	const li=S.placed[o.k];
	if(o.op==="hide"&&!S.layers[li].hidden){S.layers[li].hidden=true;continue;}
	if(o.op==="show"&&S.layers[li].hidden){S.layers[li].hidden=false;continue;}
	if(o.op==="front"){S.layers[li].depth=nextDepth++;continue;}
	if(o.op==="back"){S.layers[li].depth=Math.min(...S.placed.map(x=>S.layers[x].depth))-1;continue;}
	const c=[S.mu[o.k][0],S.mu[o.k][1]];
	if(o.op==="move"){applyGesture(o.k,gestureTranslate(o.dx,o.dy));touched.add(o.k);}
	if(o.op==="moveto"){applyGesture(o.k,gestureTranslate(o.x-c[0],o.y-c[1]));touched.add(o.k);}
	if(o.op==="rotate"){applyGesture(o.k,gestureRotateAbout(c,o.deg*Math.PI/180));touched.add(o.k);}
	if(o.op==="scale"){applyGesture(o.k,gestureScaleAbout(c,o.ds));touched.add(o.k);}
	}
	for(const k of touched) resettle(k,S.mu[k]);
	rebuildGroupBuffers();occlusionRefresh(true);renderScene();refreshOwnership();
	drawOverlay();updatePanels();renderLayerList();
	promptLog.textContent="Clamped: "+ops.map(o=>`${o.op} ${S.layers[S.placed[o.k]].name}`).join(", ")+
	" — beliefs re-settled around the intervention.";
	}
	async function doPrompt(){
	if(S.phase!=="bound"){promptLog.textContent="Bind first — there is nothing to address in a soup.";return;}
	const text=document.getElementById("prompt").value.trim();
	if(!text)return;
	let ops=localParse(text);
	if(!ops.length){
	promptLog.textContent="Local grammar found nothing; asking Claude\u2026";
	try{ops=await claudeParse(text);}
	catch{promptLog.textContent="Claude unavailable outside claude.ai — try: move/rotate/scale/hide/front/back + a layer name.";return;}
	}
	execOps(ops);
	}
	document.getElementById("btn-prompt").addEventListener("click",doPrompt);
	document.getElementById("prompt").addEventListener("keydown",e=>{if(e.key==="Enter")doPrompt();});
	document.getElementById("auto-occ").addEventListener("change",()=>{
	if(S.phase==="bound"){occlusionRefresh(false);renderScene();}
	});

	/* ------------- edit & look wiring (Bet 9) ------------- */
	document.getElementById("btn-undo-erase").addEventListener("click",()=>undoErase());
	document.getElementById("btn-restore-erase").addEventListener("click",restoreAllErases);
	document.querySelectorAll('input[name=tool]').forEach(el=>el.addEventListener("change",()=>{
	stage.classList.toggle("erasing",toolMode()==="erase");
	if(toolMode()!=="erase") lastCursor=null;
	drawOverlay();
	}));
	document.querySelectorAll('input[name=brush]').forEach(el=>el.addEventListener("change",drawOverlay));
	document.getElementById("bg-color").addEventListener("input",e=>{
	const h=e.target.value;
	backdrop.rgb=[parseInt(h.slice(1,3),16),parseInt(h.slice(3,5),16),parseInt(h.slice(5,7),16)];
	backdrop.custom=true;renderScene();
	});
	document.getElementById("bg-file").addEventListener("change",e=>{
	const f=e.target.files[0];if(!f)return;
	const img=new Image();
	img.onload=()=>{
	const c=document.createElement("canvas");c.width=c.height=RES;
	const sc=Math.max(RES/img.width,RES/img.height); // cover-crop
	c.getContext("2d").drawImage(img,(RES-img.widthsc)/2,(RES-img.heightsc)/2,img.widthsc,img.heightsc);
	backdrop.img=c.getContext("2d").getImageData(0,0,RES,RES).data;
	backdrop.custom=true;renderScene();
	URL.revokeObjectURL(img.src);
	};
	img.src=URL.createObjectURL(f);
	});
	document.getElementById("btn-bg-clear").addEventListener("click",()=>{
	backdrop.img=null;document.getElementById("bg-file").value="";
	renderScene();
	});
	for(const [id,set] of [
	["g-coarse",v=>GAINS.band[0]=v],["g-mid",v=>GAINS.band[1]=v],
	["g-fine",v=>GAINS.band[2]=v],["g-op",v=>GAINS.opacity=v]]){
	const el=document.getElementById(id);
	el.addEventListener("input",()=>{
	const v=el.value/100; set(v);
	document.getElementById(id+"-v").textContent=v.toFixed(2);
	renderScene();
	});
	}

	/* ------------- boot ------------- */
	document.getElementById("btn-scramble").addEventListener("click",scramble);
	document.getElementById("btn-bind").addEventListener("click",()=>bind(true));
	addLayer("tractor",BUILTINS.tractor,false);
	addLayer("star",BUILTINS.star,false);
	addLayer("boat",BUILTINS.boat,false);
	S.layers[0].placed=true;S.layers[0].depth=nextDepth++;S.layers[0].pose=[0.3,-0.25,0.3,Math.log(0.55)];
	S.layers[1].placed=true;S.layers[1].depth=nextDepth++;S.layers[1].pose=[-0.4,0.35,-0.9,Math.log(0.5)];
	fitStage();
	rebuildScene();
	</script>
	</body>
	</html>