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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>R.U.B.I.C. CORE-32 Laboratory — Lumen Helix v4.0</title>
<link rel="stylesheet" href="css/styles.css">
<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>
</head>
<body>
<!-- Ambient background glow -->
<div class="ambient-glow" style="top:-200px;left:-100px;background:var(--accent-core);"></div>
<div class="ambient-glow" style="bottom:-200px;right:-100px;background:var(--accent-violet);"></div>
<!-- ============================================================ -->
<!-- BOOT MODAL -->
<!-- ============================================================ -->
<div id="boot-modal">
<div class="boot-card glass">
<div class="boot-title">CORE-32 R.U.B.I.C.</div>
<div class="boot-subtitle">Reversible Universal Binary Information Computer v4.0 [FROZEN]</div>
<div class="boot-scroll">
<p style="color:var(--accent-core);font-weight:700;margin-bottom:0.75rem;">
[SYSTEM_INIT: ℤ₃₂ Cyclic Group Instantiation — Heterogeneous Lattice Mode]
</p>
<p style="margin-bottom:0.6rem;">
This interface and its derived data — including 512D Cayley-Dickson S-Box output,
Heterogeneous Lattice tessellations, and CNLT verification states — are licensed
strictly for <strong style="color:#e0e6f0;">non-commercial, educational use only</strong>
under CC BY-NC.
</p>
<p style="margin-bottom:0.6rem;">
Initializing Orthographic 3×3×3 Hexahedron Lattice with Origami Dimensional Folding.
The canonical phase dual map involution δ₃₂(x) = x ⊕ 16 partitions the 32-state space
into 16 reversible, phase-paired channels.
</p>
<p>
By initializing this terminal, you enable Human-in-the-Loop (HITL) governance over a
post-quantum, fault-tolerant topological data permutation network verified by the
Cone-Nonlocality Test (CNLT).
</p>
</div>
<div class="boot-key-box">
<label>[SYS_REQ]: GEMINI ORACLE API KEY</label>
<p style="font-family:var(--font-mono);font-size:0.55rem;color:var(--text-dim);margin-bottom:0.5rem;">
Insert your Gemini API key to enable AI governance. Leave blank for offline mode.
</p>
<input type="password" id="boot-api-key" placeholder="Paste Gemini API key...">
</div>
<div class="boot-actions">
<button class="btn-abort" onclick="alert('ABORTED. Strict adherence to CC BY-NC required.')">ABORT</button>
<button class="btn-init" onclick="bootSystem()">INITIALIZE CORE</button>
</div>
</div>
</div>
<!-- ============================================================ -->
<!-- APPLICATION SHELL -->
<!-- ============================================================ -->
<div id="app" style="display:none;flex-direction:column;height:100vh;">
<!-- Header -->
<header class="app-header glass">
<div class="header-brand">
<div>
<div class="brand-title">R.U.B.I.C.</div>
<div class="brand-sub">Lumen Helix ⁄⁄ CORE-32 Engine v4.0</div>
</div>
<button class="btn-oracle" onclick="toggleOracle()">
<span class="pulse"></span> CORE ORACLE
</button>
</div>
<nav class="tab-nav">
<button class="tab-btn" id="tab-1" onclick="switchTab(1)">M1: Cauldron D₈×ℤ₂</button>
<button class="tab-btn" id="tab-2" onclick="switchTab(2)">M2: Triality D₆×ℤ₂</button>
<button class="tab-btn" id="tab-3" onclick="switchTab(3)">M3: A₂ Lattice</button>
<button class="tab-btn active" id="tab-4" onclick="switchTab(4)">M4: 512D GPU S-Box</button>
</nav>
</header>
<!-- Main Content -->
<main class="app-main">
<!-- MODE 1: Cauldron D₈×ℤ₂ -->
<section class="mode-panel" id="mode-1">
<div class="mode-content">
<div class="mode-text">
<h2 class="mode-title" style="color:#93c5fd;">Stage I: The Cauldron Module</h2>
<p class="mode-desc">
A 10-state permutation representation of D₈ × ℤ₂ on the decimal digits,
mapped onto the four-vesica diagram. The Cauldron Module reserves 10 states
as a public digit subspace via a binary-weight embedding compatible with δ₃₂.
</p>
<div class="kernel-box">
<h4>The C.O.R.E. Kernel</h4>
<p><strong>Membrane M = {0, 1}:</strong> The discrete invariant subset acting as the topological boundary/valve.</p>
<p><strong>Rotor L (8-cycle):</strong> (2 3 4 6 5 8 7 9) — the D₈ × ℤ₂ computational module.</p>
<p><strong>Phase Dual:</strong> δ₃₂(x) = (x + 16) mod 32 ≡ x ⊕ 16. Every state has an instantly accessible dual.</p>
</div>
<button class="btn-action blue" onclick="rotateMode1()">TRIGGER ρ₃₂ PERMUTATION</button>
</div>
<div class="mode-visual">
<svg width="380" height="380" viewBox="-200 -200 400 400">
<circle cx="0" cy="-70.7" r="100" class="sacred-circle"/>
<circle cx="0" cy="70.7" r="100" class="sacred-circle"/>
<circle cx="-70.7" cy="0" r="100" class="sacred-circle"/>
<circle cx="70.7" cy="0" r="100" class="sacred-circle"/>
<text id="m1-c" x="0" y="0" class="membrane-node">{0, 1}</text>
<text id="m1-0" x="0" y="-130" class="digit-node" style="fill:#93c5fd">2</text>
<text id="m1-1" x="90" y="-90" class="digit-node" style="fill:#a5b4fc">3</text>
<text id="m1-2" x="130" y="0" class="digit-node" style="fill:#c4b5fd">4</text>
<text id="m1-3" x="90" y="90" class="digit-node" style="fill:#f0abfc">6</text>
<text id="m1-4" x="0" y="130" class="digit-node" style="fill:#fda4af">5</text>
<text id="m1-5" x="-90" y="90" class="digit-node" style="fill:#fdba74">8</text>
<text id="m1-6" x="-130" y="0" class="digit-node" style="fill:#fde047">7</text>
<text id="m1-7" x="-90" y="-90" class="digit-node" style="fill:#67e8f9">9</text>
</svg>
</div>
</div>
</section>
<!-- MODE 2: Triality D₆×ℤ₂ -->
<section class="mode-panel" id="mode-2">
<div class="mode-content">
<div class="mode-text">
<h2 class="mode-title" style="color:var(--accent-mint);">Stage II: Seed of Triality</h2>
<p class="mode-desc">
When extending to an A₂ hexagonal lattice (the Seed of Life), a finite
Triality-Type Symmetry emerges. The system reduces to an 8-state D₆ × ℤ₂
module where a 3-cycle (120° rotation) acts upon three fundamental pair operators.
</p>
<div class="kernel-box">
<h4>Triality Pair Operators</h4>
<p><strong>τ₁ = (2 5),</strong> <strong>τ₂ = (4 9),</strong> <strong>τ₃ = (6 3)</strong></p>
<p style="margin-top:0.5rem;">
The L' cycle permutes these three pairs under 60° rotation,
establishing a finite combinatorial shadow of exceptional root system triality.
</p>
</div>
<button class="btn-action green" onclick="rotateMode2()">TRIGGER L' 60° (ℤ₆)</button>
</div>
<div class="mode-visual">
<svg width="380" height="380" viewBox="-200 -200 400 400" id="seed-svg">
<circle cx="0" cy="0" r="80" class="sacred-circle" style="stroke:rgba(45,212,168,0.35);"/>
<text x="0" y="0" class="membrane-node" style="fill:var(--accent-mint);">{0, 1}</text>
</svg>
</div>
</div>
</section>
<!-- MODE 3: A₂ Lattice -->
<section class="mode-panel" id="mode-3">
<div class="mode-content">
<div class="mode-text">
<h2 class="mode-title" style="color:var(--accent-violet);">Stage III: A₂ Lattice — Heterogeneous Tessellation</h2>
<p class="mode-desc">
The 19-center Flower of Life patch expanding to a 20-state system. Pure
dodecahedral tessellation cannot tile flat 3D Euclidean space without gaps —
R.U.B.I.C. employs Heterogeneous Lattices: Archimedean semi-regular tilings over T².
</p>
<div class="kernel-box">
<h4>Generalized Commutation Theorem</h4>
<p>For any odd multiplier m and any integer n ≥ 1, the global rotor ρₘ commutes with the phase dual δ on ℤ₂ₙ:</p>
<p style="color:var(--accent-violet);margin-top:0.4rem;"><strong>ρₘ(δ₂ₙ(x)) = δ₂ₙ(ρₘ(x))</strong></p>
<p style="margin-top:0.4rem;">
This guarantees Rotor-Projection Functoriality across lattice boundaries
between ℤ₃₂, ℤ₁₆, and ℤ₈ nodes.
</p>
</div>
<button class="btn-action violet" onclick="generateE6Shadow()">
<span style="animation:pulse 1.5s infinite;">⚡</span> GENERATE E₆ SHADOW MAPPING
</button>
</div>
<div class="mode-visual">
<svg width="420" height="420" viewBox="-210 -210 420 420" id="flower-svg">
<circle cx="0" cy="0" r="205" stroke="rgba(255,255,255,0.05)" stroke-width="1" fill="none"/>
</svg>
</div>
</div>
</section>
<!-- MODE 4: 512D GPU S-Box -->
<section class="mode-panel visible" id="mode-4" style="padding:0;">
<!-- S-Box Info HUD -->
<div class="sbox-hud glass">
<h2><span class="dot"></span> 512D CORE-32 GPU S-Box</h2>
<div class="desc">
<span class="hl">>> CAYLEY-DICKSON 512D KERNEL:</span>
(A,B)(C,D) = (AC − D*B, DA + BC*) where A,B,C,D are 256D Sedenion-like structures.<br><br>
<span class="hl">>> GLYPH ATLAS:</span>
4096-glyph heterogeneous texture atlas maps 5-digit ℤ₃₂ binary states to Unicode topology.<br><br>
<span class="hl">>> CONTROLS:</span>
Left-click + drag to orbit. Scroll to zoom. Topology buttons below to fold the manifold.
</div>
<button class="btn-action red" onclick="analyzeState('mode4')" style="margin-top:1rem;">
⚡ INITIATE CNLT ANALYSIS
</button>
</div>
<!-- Telemetry HUD -->
<div class="telemetry-hud glass">
<div>
<div class="telem-section-title">ARCHITECTURE TOPOLOGY (STRUCTURAL FOLD)</div>
<div class="topo-btns">
<button class="topo-btn active" id="btn-planar" onclick="setTopology('PLANAR')">PLANAR MANIFOLD</button>
<button class="topo-btn" id="btn-beehive" onclick="setTopology('BEEHIVE')">HEX BEEHIVE</button>
<button class="topo-btn" id="btn-origami" onclick="setTopology('ORIGAMI')">ORIGAMI RAM</button>
</div>
</div>
<div style="margin-top:1rem;">
<div class="telem-section-title">TOPOLOGICAL TELEMETRY</div>
<div style="display:flex;flex-direction:column;gap:0.6rem;">
<div class="slider-row">
<div class="slider-label"><span>MUTATION RATE</span><span class="val" id="val-mut">0.002</span></div>
<input type="range" id="sl-mut" min="0" max="0.02" step="0.001" value="0.002">
</div>
<div class="slider-row">
<div class="slider-label"><span>TWIST SPEED</span><span class="val" id="val-spd">0.08</span></div>
<input type="range" id="sl-spd" min="0.01" max="0.2" step="0.01" value="0.08">
</div>
<div class="slider-row">
<div class="slider-label"><span>WAVE AMPLITUDE</span><span class="val" id="val-amp">8.0</span></div>
<input type="range" id="sl-amp" min="0" max="20" step="0.5" value="8.0">
</div>
<div class="slider-row">
<div class="slider-label"><span>WAVE FREQUENCY</span><span class="val" id="val-freq">2.0</span></div>
<input type="range" id="sl-freq" min="0" max="10" step="0.1" value="2.0">
</div>
<div class="slider-row">
<div class="slider-label"><span>GLYPH CLOCK (Hz)</span><span class="val" id="val-glyph">12.0</span></div>
<input type="range" id="sl-glyph" min="0" max="60" step="0.5" value="12.0">
</div>
</div>
</div>
</div>
<!-- CORE-32 Compute Panel -->
<div class="compute-hud glass" id="compute-hud">
<div class="telem-section-title" style="color:var(--accent-mint);">
CORE-32 ℤ₃₂ STATE COMPUTER
</div>
<div style="display:flex;gap:0.35rem;flex-wrap:wrap;margin-bottom:0.75rem;">
<button class="compute-btn" onclick="coreApplyDelta()">δ₃₂ PHASE DUAL</button>
<button class="compute-btn" onclick="coreApplyRotor()">ρ ROTOR STEP</button>
<button class="compute-btn" onclick="coreVerifyCommutation()">VERIFY ρ∘δ = δ∘ρ</button>
<button class="compute-btn" onclick="coreInjectFault()">CNLT FAULT</button>
<button class="compute-btn" onclick="coreRecover()">CNLT RECOVER</button>
<button class="compute-btn" onclick="coreReset()">RESET</button>
</div>
<div class="compute-readout" id="compute-readout">
<div class="readout-row"><span>TOTAL OPS</span><span id="cr-ops">0</span></div>
<div class="readout-row"><span>ENTROPY H(S)</span><span id="cr-entropy">—</span></div>
<div class="readout-row"><span>PHASE BALANCE</span><span id="cr-balance">—</span></div>
<div class="readout-row"><span>FAULTS</span><span id="cr-faults" style="color:var(--accent-mint);">0</span></div>
<div class="readout-row"><span>REVERSIBLE</span><span id="cr-rev" style="color:var(--accent-mint);">✓</span></div>
</div>
<div class="telem-section-title" style="color:var(--accent-mint);margin-top:0.6rem;">
STATE VECTOR (196 × ℤ₃₂)
</div>
<div class="state-grid" id="state-grid"></div>
</div>
<!-- WebGL Canvas -->
<div id="canvas-container">
<canvas id="petaminxCanvas"></canvas>
</div>
</section>
<!-- Oracle Panel -->
<div id="oracle-panel" class="glass">
<div class="oracle-header">
<h3><span style="color:#60a5fa;margin-right:0.5rem;">●</span> CORE ORACLE v4.0</h3>
<button class="oracle-close" onclick="toggleOracle()">×</button>
</div>
<div class="oracle-log" id="oracle-log">
<div class="oracle-msg sys">
[SYS_RDY]: Oracle Initialized. Knowledge Base: CORE-32 v4.0,
Heterogeneous Lattices, CNLT Verification, QTRU/OTRU/CSTRU Post-Quantum Suite.
Awaiting query...
</div>
</div>
<div class="oracle-input-bar">
<div class="key-row">
<input type="password" id="local-api-key" placeholder="API Key (if not set at boot)">
</div>
<div class="msg-row">
<input type="text" id="oracle-input" placeholder="Query the Core..."
onkeypress="if(event.key==='Enter')submitChat()">
<button onclick="submitChat()">EXE</button>
</div>
</div>
</div>
</main>
<!-- Footer -->
<footer class="app-footer glass">
<div>© 2025–2026 Christopher G. Phillips (Raziel Ali) — Lumen Helix. Licensed under CC BY-NC.</div>
<div class="ver">CORE-32 v4.0 [FROZEN] — March 2026</div>
</footer>
</div>
<!-- Entry point (ES module) -->
<script type="module" src="js/main.js"></script>
</body>
</html>