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feat(solver): optimise interval solver with pooling and safety guards
- implemented rigorous mobius derivative intensity metric - added baseline euclidean particle tracer for verification - optimised solver with deep object pooling to eliminate GC stutter - forced safety guards: 3000 max segments, 0.001 min width, 32ms budget - tuned beam count to 30 for performance stability
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Lines changed: 1326 additions & 542 deletions

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‎projects/arithmetica-lucis/prototype/mobius-caustic-solver/index.html‎

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<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<head>
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<meta charset="UTF-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1.0" />
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<title>Möbius Caustic Solver</title>
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<style>
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body { margin: 0; overflow: hidden; background: #111; color: #eee; font-family: sans-serif; display: flex; justify-content: center; align-items: center; height: 100vh; }
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canvas { background: #000; }
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#controls { position: absolute; top: 10px; left: 10px; padding: 10px; background: rgba(0,0,0,0.5); border-radius: 5px;}
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body {
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margin: 0;
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overflow: hidden;
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background: #111;
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color: #eee;
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font-family: sans-serif;
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display: flex;
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justify-content: center;
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align-items: center;
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height: 100vh;
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}
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canvas {
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background: #000;
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}
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#controls {
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position: absolute;
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top: 10px;
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left: 10px;
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padding: 10px;
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background: rgba(0, 0, 0, 0.5);
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border-radius: 5px;
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}
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</style>
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</head>
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<body>
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</head>
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<body>
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<canvas id="viewport" width="800" height="800"></canvas>
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<div id="controls">
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<p>Möbius Caustic Solver</p>
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<p>Status: Initializing...</p>
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<div
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id="dashboard"
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style="
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position: absolute;
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top: 10px;
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left: 10px;
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background: rgba(0, 0, 0, 0.85);
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color: #fff;
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padding: 15px;
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border-radius: 8px;
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font-family: 'Courier New', Courier, monospace;
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min-width: 300px;
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border: 1px solid #444;
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box-shadow: 0 4px 6px rgba(0, 0, 0, 0.3);
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"
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>
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<h2
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style="
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margin: 0 0 10px 0;
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font-size: 16px;
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border-bottom: 1px solid #666;
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padding-bottom: 5px;
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"
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>
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Möbius Caustic Solver
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</h2>
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<div
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style="
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margin-bottom: 8px;
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display: flex;
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justify-content: space-between;
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"
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>
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<span style="color: #aaa">Status:</span>
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<span id="ui-status" style="color: #0f0; font-weight: bold"
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>Initializing...</span
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>
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</div>
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<div
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style="
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margin-bottom: 8px;
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display: flex;
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justify-content: space-between;
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"
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>
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<span style="color: #aaa">Quality:</span>
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<span id="ui-quality">LOW</span>
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</div>
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<div style="margin-bottom: 8px">
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<div
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style="
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display: flex;
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justify-content: space-between;
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margin-bottom: 4px;
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"
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>
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<span style="color: #aaa">FPS:</span>
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<span id="ui-fps">--</span>
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</div>
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<div style="display: flex; justify-content: space-between">
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<span style="color: #aaa">Latency:</span>
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<span id="ui-latency">-- ms</span>
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</div>
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<!-- Performance Graph -->
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<canvas
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id="perf-graph"
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width="270"
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height="60"
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style="
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width: 100%;
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height: 60px;
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margin-top: 8px;
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background: #222;
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border: 1px solid #444;
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"
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></canvas>
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</div>
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<div
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id="ui-alert"
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style="
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margin-top: 10px;
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padding: 5px;
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border-radius: 4px;
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display: none;
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"
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></div>
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</div>
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<script type="module" src="src/main.js"></script>
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</body>
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</body>
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</html>

‎projects/arithmetica-lucis/prototype/mobius-caustic-solver/src/core/complex.js‎

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@@ -101,4 +101,8 @@ export class Complex {
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const dy = this.im - c.im;
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return dx * dx + dy * dy;
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}
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toString() {
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return `${this.re} + ${this.im}i`;
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}
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}

‎projects/arithmetica-lucis/prototype/mobius-caustic-solver/src/core/logger.js‎

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/**
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* Centralized Logging System for Arithmetica Lucis.
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* Provides unified console output and optional UI overlay integration.
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*/
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export class Logger {
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static DEBUG = 0;
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static INFO = 1;
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static WARN = 2;
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static ERROR = 3;
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static LEVEL = Logger.INFO; // Default Limit
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static uiTarget = null; // HTML Element to append logs to
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static setMethod(uiElement) {
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Logger.uiTarget = uiElement;
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}
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static format(level, message, source) {
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const timestamp = new Date().toISOString().split("T")[1].slice(0, -1);
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const prefix = source ? `[${timestamp}] [${source}]` : `[${timestamp}]`;
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return `${prefix} ${message}`;
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}
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static debug(message, source) {
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if (Logger.LEVEL > Logger.DEBUG) return;
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console.debug(Logger.format("DEBUG", message, source));
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}
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static info(message, source) {
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if (Logger.LEVEL > Logger.INFO) return;
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const formatted = Logger.format("INFO", message, source);
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console.info(formatted);
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Logger.sendToServer(formatted); // Persist INFO too
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}
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static warn(message, source) {
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if (Logger.LEVEL > Logger.WARN) return;
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const formatted = Logger.format("WARN", message, source);
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console.warn(formatted);
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Logger.logToUI(formatted, "orange");
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}
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static error(message, source) {
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const formatted = Logger.format("ERROR", message, source);
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console.error(formatted);
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Logger.logToUI(formatted, "red");
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}
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static logToUI(text, color) {
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// Send to Server (Fire and Forget)
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Logger.sendToServer(text);
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if (!Logger.uiTarget) return;
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// Simple append, could be fancier
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// We use innerHTML += but strictly safely for prototype
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const div = document.createElement("div");
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div.style.color = color;
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div.style.fontFamily = "monospace";
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div.style.fontSize = "12px";
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div.textContent = text;
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Logger.uiTarget.appendChild(div);
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// Auto-scroll
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Logger.uiTarget.scrollTop = Logger.uiTarget.scrollHeight;
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}
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static sendToServer(message) {
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// We use the relative path '/log' which works if served by our custom server.
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// We use skip waiting for response to avoid blocking UI.
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try {
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fetch("/log", {
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method: "POST",
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headers: { "Content-Type": "text/plain" },
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body: message,
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}).catch((e) => console.error("Failed to send log to server", e));
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} catch (e) {
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// Ignore network errors
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}
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}
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}

‎projects/arithmetica-lucis/prototype/mobius-caustic-solver/src/core/mobius.js‎

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@@ -42,22 +42,22 @@ export class Mobius {
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// (a b) (A B) = (aA+bC aB+bD)
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// (c d) (C D) (cA+dC cB+dD)
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const a = Complex.add(
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temp1,
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new Complex(),
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Complex.mul(temp2, this.a, other.a),
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Complex.mul(temp3, this.b, other.c)
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);
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const b = Complex.add(
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temp1,
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new Complex(),
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Complex.mul(temp2, this.a, other.b),
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Complex.mul(temp3, this.b, other.d)
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);
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const c = Complex.add(
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temp1,
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new Complex(),
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Complex.mul(temp2, this.c, other.a),
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Complex.mul(temp3, this.d, other.c)
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);
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const d = Complex.add(
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temp1,
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new Complex(),
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Complex.mul(temp2, this.c, other.b),
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Complex.mul(temp3, this.d, other.d)
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);
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const theta = Math.atan2(det.im, det.re) / 2;
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const sqrtDet = temp4.set(r * Math.cos(theta), r * Math.sin(theta));
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if (r === 0) return this; // Should not happen for valid transforms
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if (r < 1e-9) {
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throw new Error("Mobius: Singular Matrix (Det=0). Cannot normalize.");
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}
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Complex.div(this.a, this.a, sqrtDet);
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Complex.div(this.b, this.b, sqrtDet);
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return this;
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}
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/**
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* Calculates the derivative f'(z) at a point z.
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* f'(z) = (ad - bc) / (cz + d)^2
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* Since normalized, ad-bc = 1.
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* f'(z) = 1 / (cz + d)^2
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*/
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derivative(z) {
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// 1 / (cz + d)^2
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// denom = cz + d
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const denom = Complex.add(temp3, Complex.mul(temp4, this.c, z), this.d);
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// denomSq = denom * denom
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const denomSq = Complex.mul(temp1, denom, denom);
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// result = 1 / denomSq
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// 1 is (1, 0)
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const one = new Complex(1, 0);
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const out = new Complex();
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Complex.div(out, one, denomSq);
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return out;
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}
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}

‎projects/arithmetica-lucis/prototype/mobius-caustic-solver/src/core/performance_monitor.js‎

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import { Logger } from "./logger.js";
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export class PerformanceMonitor {
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constructor(callbacks = {}) {
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this.callbacks = callbacks; // { onDegrade: (msg) => {}, ... }
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this.stats = {
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frameCount: 0,
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lastTime: performance.now(),
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frameTimes: [],
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consecutiveBadFrames: 0,
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degraded: false,
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budgetExceeded: false,
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};
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}
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// Called every frame
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update() {
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const now = performance.now();
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const dt = now - this.stats.lastTime;
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this.stats.lastTime = now;
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// --- INSTANT REACTIVITY ---
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// Rule: Degradation if > 33ms latency OR Budget Flag (> 12ms render time)
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if ((dt > 33 || this.stats.budgetExceeded) && !this.stats.degraded) {
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const msg = this.stats.budgetExceeded
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? "Frame Budget Exceeded > 12ms"
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: `High Latency (${Math.round(dt)}ms)`;
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Logger.error(`${msg}. Degrading Quality IMMEDIATELY.`, "Watchdog");
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this.stats.budgetExceeded = false;
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this.stats.degraded = true;
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if (this.callbacks.onDegrade) {
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this.callbacks.onDegrade(msg);
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}
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}
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// --- Graph Data ---
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this.stats.frameTimes.push(dt);
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if (this.stats.frameTimes.length > 270) this.stats.frameTimes.shift();
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if (this.callbacks.onGraphDraw) {
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this.callbacks.onGraphDraw(this.stats.frameTimes);
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}
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// --- Periodic Logging & UI (1Hz) ---
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if (this.stats.frameCount++ % 60 === 0) {
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const fps = Math.round(1000 / (dt || 1));
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const latency = Math.round(dt);
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if (this.callbacks.onStatsUpdate) {
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this.callbacks.onStatsUpdate(fps, latency);
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}
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}
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}
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markBudgetExceeded() {
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this.stats.budgetExceeded = true;
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}
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}

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