Source identity
| Field | Recorded value |
|---|---|
| Source type | archive member |
| Original record | ch03-equations.html |
| Date | Not specified in source |
| Path or archive member | archives/libsrc-1c3f88063121/NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__megamind-258b-neurons__d5baa307-3c60-4504-827c-c9c4449caf31/originals/deploy_698104b5fbe3d9e6d8e3f3e0/ch03-equations.html |
| Original SHA-256 | 0938ab14245b2cd8b204081a2e1e517d6b30026ac49f3016fa9abbcfcaf2bc2e |
| Reading-copy SHA-256 | 0938ab14245b2cd8b204081a2e1e517d6b30026ac49f3016fa9abbcfcaf2bc2e |
| Archive source | {"sourceId": "libsrc-1c3f88063121", "member": "NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__megamind-258b-neurons__d5baa307-3c60-4504-827c-c9c4449caf31/originals/deploy_698104b5fbe3d9e6d8e3f3e0/ch03-equations.html"} |
Every recorded occurrence
These 4 records contain identical original source bytes. Their paths and revisions remain part of the archive.
| Original record | Branch or archive | Revision / identifier | Original location |
|---|---|---|---|
| ch03-equations.html | {"sourceId": "libsrc-1c3f88063121", "member": "NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__megamind-258b-neurons__d5baa307-3c60-4504-827c-c9c4449caf31/originals/deploy_698104b5fbe3d9e6d8e3f3e0/ch03-equations.html"} | libsrc-2437d5e51e5e | archives/libsrc-1c3f88063121/NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__megamind-258b-neurons__d5baa307-3c60-4504-827c-c9c4449caf31/originals/deploy_698104b5fbe3d9e6d8e3f3e0/ch03-equations.html |
| ch03-equations.html | {"sourceId": "libsrc-1c3f88063121", "member": "NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__feed-the-joe__8de87f1b-a5a4-4d10-9d82-4e8f27729768/originals/deploy_6980fcb4ca86308cf2464bcd/ch03-equations.html"} | libsrc-764ed6bb4913 | archives/libsrc-1c3f88063121/NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__feed-the-joe__8de87f1b-a5a4-4d10-9d82-4e8f27729768/originals/deploy_6980fcb4ca86308cf2464bcd/ch03-equations.html |
| ffa3a5c3d4b231770a94648437622c09586415d2 | {"sourceId": "libsrc-1c3f88063121", "member": "NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__megamind-258b-neurons__d5baa307-3c60-4504-827c-c9c4449caf31/originals/.content_store/ff/ffa3a5c3d4b231770a94648437622c09586415d2"} | libsrc-8b5b60408653 | archives/libsrc-1c3f88063121/NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__megamind-258b-neurons__d5baa307-3c60-4504-827c-c9c4449caf31/originals/.content_store/ff/ffa3a5c3d4b231770a94648437622c09586415d2 |
| ffa3a5c3d4b231770a94648437622c09586415d2 | {"sourceId": "libsrc-1c3f88063121", "member": "NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__feed-the-joe__8de87f1b-a5a4-4d10-9d82-4e8f27729768/originals/.content_store/ff/ffa3a5c3d4b231770a94648437622c09586415d2"} | libsrc-ae60c820ce93 | archives/libsrc-1c3f88063121/NETLIFY_AI_RECOVERY_2026-10-14_21-10-49/sites/janady13__feed-the-joe__8de87f1b-a5a4-4d10-9d82-4e8f27729768/originals/.content_store/ff/ffa3a5c3d4b231770a94648437622c09586415d2 |
Recovered source transcript
Download complete source text ↓1,999 lines · 77.3 KB
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>MEGAMIND | The 486 Equations</title>
<link href="https://fonts.googleapis.com/css2?family=JetBrains+Mono:wght@300;400;500;600;700&family=Inter:wght@300;400;500;600;700&display=swap" rel="stylesheet">
<style>
:root {
--bg-primary: #0a0a0f;
--bg-secondary: #12121a;
--bg-tertiary: #1a1a24;
--bg-card: #16161f;
--text-primary: #e8e8ed;
--text-secondary: #8a8a9a;
--text-muted: #5a5a6a;
--cyan: #00d4ff;
--cyan-dim: #00d4ff40;
--cyan-glow: #00d4ff20;
--green: #00ff88;
--green-dim: #00ff8840;
--purple: #a855f7;
--orange: #ff9500;
--pink: #ff006e;
--mono: 'JetBrains Mono', monospace;
--sans: 'Inter', -apple-system, sans-serif;
--border: #2a2a3a;
--border-glow: #00d4ff30;
}
* { margin: 0; padding: 0; box-sizing: border-box; }
/* Custom Cursor */
body {
cursor: none;
}
.cursor {
width: 20px;
height: 20px;
border: 2px solid var(--cyan);
border-radius: 50%;
position: fixed;
pointer-events: none;
z-index: 10000;
transition: transform 0.1s ease, background 0.2s ease;
mix-blend-mode: difference;
}
.cursor-dot {
width: 4px;
height: 4px;
background: var(--cyan);
border-radius: 50%;
position: fixed;
pointer-events: none;
z-index: 10001;
}
.cursor.hover {
transform: scale(1.5);
background: var(--cyan-dim);
}
html {
scroll-behavior: smooth;
}
body {
font-family: var(--sans);
background: var(--bg-primary);
color: var(--text-primary);
line-height: 1.7;
overflow-x: hidden;
}
/* Scrollbar */
::-webkit-scrollbar {
width: 8px;
}
::-webkit-scrollbar-track {
background: var(--bg-secondary);
}
::-webkit-scrollbar-thumb {
background: var(--cyan-dim);
border-radius: 4px;
}
::-webkit-scrollbar-thumb:hover {
background: var(--cyan);
}
/* Grid Background */
.grid-bg {
position: fixed;
top: 0;
left: 0;
right: 0;
bottom: 0;
background-image:
linear-gradient(var(--border) 1px, transparent 1px),
linear-gradient(90deg, var(--border) 1px, transparent 1px);
background-size: 60px 60px;
opacity: 0.15;
pointer-events: none;
z-index: 0;
}
/* Navigation */
.nav {
position: fixed;
top: 0;
left: 0;
right: 0;
display: flex;
justify-content: space-between;
align-items: center;
padding: 1rem 2rem;
background: rgba(10, 10, 15, 0.9);
backdrop-filter: blur(20px);
border-bottom: 1px solid var(--border);
z-index: 1000;
}
.nav-logo {
font-family: var(--mono);
font-size: 0.75rem;
font-weight: 600;
letter-spacing: 0.3em;
color: var(--cyan);
display: flex;
align-items: center;
gap: 0.5rem;
}
.nav-logo::before {
content: '';
width: 8px;
height: 8px;
background: var(--cyan);
border-radius: 50%;
animation: pulse 2s infinite;
}
@keyframes pulse {
0%, 100% { opacity: 1; box-shadow: 0 0 10px var(--cyan); }
50% { opacity: 0.5; box-shadow: 0 0 5px var(--cyan); }
}
.nav-center {
display: flex;
gap: 2rem;
}
.nav-link {
font-family: var(--mono);
font-size: 0.65rem;
letter-spacing: 0.15em;
color: var(--text-secondary);
text-decoration: none;
padding: 0.5rem 1rem;
border: 1px solid transparent;
border-radius: 4px;
transition: all 0.3s ease;
}
.nav-link:hover, .nav-link.active {
color: var(--cyan);
border-color: var(--cyan-dim);
background: var(--cyan-glow);
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.nav-chapter {
font-family: var(--mono);
font-size: 0.6rem;
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.nav-chapter span {
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/* Hero */
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flex-direction: column;
justify-content: center;
padding: 8rem 4rem 4rem;
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width: 100%;
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.hero-label {
font-family: var(--mono);
font-size: 0.65rem;
letter-spacing: 0.4em;
color: var(--green);
margin-bottom: 1.5rem;
display: flex;
align-items: center;
gap: 1rem;
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.hero-label::before {
content: '//';
color: var(--text-muted);
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.hero h1 {
font-family: var(--mono);
font-size: clamp(3rem, 8vw, 6rem);
font-weight: 700;
line-height: 1.1;
margin-bottom: 1.5rem;
background: linear-gradient(135deg, var(--text-primary) 0%, var(--cyan) 50%, var(--green) 100%);
-webkit-background-clip: text;
-webkit-text-fill-color: transparent;
background-clip: text;
}
.hero-number {
font-family: var(--mono);
font-size: clamp(8rem, 20vw, 16rem);
font-weight: 700;
color: var(--bg-tertiary);
position: absolute;
right: 4rem;
top: 50%;
transform: translateY(-50%);
z-index: -1;
opacity: 0.5;
line-height: 1;
-webkit-text-stroke: 1px var(--border);
}
.hero-subtitle {
font-size: 1.25rem;
color: var(--text-secondary);
max-width: 700px;
margin-bottom: 3rem;
line-height: 1.8;
}
.hero-subtitle code {
font-family: var(--mono);
color: var(--cyan);
background: var(--cyan-glow);
padding: 0.2rem 0.5rem;
border-radius: 4px;
font-size: 0.9em;
}
/* Stats Grid */
.stats-grid {
display: grid;
grid-template-columns: repeat(4, 1fr);
gap: 2rem;
margin-top: 3rem;
}
.stat-card {
background: var(--bg-card);
border: 1px solid var(--border);
border-radius: 12px;
padding: 2rem;
position: relative;
overflow: hidden;
transition: all 0.4s ease;
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.stat-card::before {
content: '';
position: absolute;
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font-size: 0.65rem;
letter-spacing: 0.2em;
color: var(--text-muted);
}
/* Subsystem Navigation */
.subsystem-nav {
position: sticky;
top: 60px;
background: var(--bg-primary);
border-bottom: 1px solid var(--border);
z-index: 100;
padding: 1rem 0;
overflow-x: auto;
}
.subsystem-nav-inner {
max-width: 1400px;
margin: 0 auto;
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padding: 0.6rem 1rem;
cursor: pointer;
transition: all 0.3s ease;
white-space: nowrap;
display: flex;
align-items: center;
gap: 0.5rem;
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.subsystem-tab:hover {
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font-size: 0.55rem;
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/* Main Content */
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margin: 0 auto;
padding: 4rem;
position: relative;
z-index: 1;
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/* Section Header */
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content: attr(data-index);
font-size: 0.7rem;
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background: var(--cyan-glow);
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border-radius: 6px;
border: 1px solid var(--cyan-dim);
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.section-header p {
color: var(--text-secondary);
max-width: 800px;
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}
/* Subsystem Grid */
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display: grid;
grid-template-columns: repeat(auto-fit, minmax(320px, 1fr));
gap: 1.5rem;
margin-bottom: 4rem;
}
/* Subsystem Card */
.subsystem-card {
background: var(--bg-card);
border: 1px solid var(--border);
border-radius: 12px;
overflow: hidden;
transition: all 0.4s ease;
opacity: 0;
transform: translateY(40px);
}
.subsystem-card.visible {
opacity: 1;
transform: translateY(0);
}
.subsystem-card:hover {
border-color: var(--cyan-dim);
box-shadow: 0 20px 60px rgba(0, 212, 255, 0.1);
}
.subsystem-header {
padding: 1.5rem;
border-bottom: 1px solid var(--border);
cursor: pointer;
display: flex;
justify-content: space-between;
align-items: center;
transition: background 0.3s ease;
}
.subsystem-header:hover {
background: var(--bg-tertiary);
}
.subsystem-info {
display: flex;
align-items: center;
gap: 1rem;
}
.subsystem-id {
font-family: var(--mono);
font-size: 0.65rem;
font-weight: 600;
color: var(--bg-primary);
background: var(--cyan);
padding: 0.4rem 0.6rem;
border-radius: 6px;
letter-spacing: 0.1em;
}
.subsystem-name {
font-family: var(--mono);
font-size: 0.9rem;
font-weight: 500;
color: var(--text-primary);
}
.subsystem-meta {
display: flex;
align-items: center;
gap: 1rem;
}
.eq-badge {
font-family: var(--mono);
font-size: 0.7rem;
color: var(--green);
background: var(--green-dim);
padding: 0.3rem 0.6rem;
border-radius: 4px;
}
.expand-icon {
width: 24px;
height: 24px;
border: 1px solid var(--border);
border-radius: 6px;
display: flex;
align-items: center;
justify-content: center;
color: var(--text-muted);
transition: all 0.3s ease;
}
.subsystem-card.expanded .expand-icon {
background: var(--cyan);
color: var(--bg-primary);
border-color: var(--cyan);
transform: rotate(180deg);
}
.subsystem-content {
max-height: 0;
overflow: hidden;
transition: max-height 0.5s ease;
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.subsystem-card.expanded .subsystem-content {
max-height: 2000px;
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.subsystem-inner {
padding: 1.5rem;
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.subsystem-desc {
color: var(--text-secondary);
font-size: 0.9rem;
margin-bottom: 1.5rem;
line-height: 1.7;
}
/* Equation List */
.equation-list {
display: flex;
flex-direction: column;
gap: 1rem;
}
.equation-item {
background: var(--bg-secondary);
border: 1px solid var(--border);
border-radius: 8px;
padding: 1rem 1.25rem;
transition: all 0.3s ease;
position: relative;
overflow: hidden;
}
.equation-item::before {
content: '';
position: absolute;
left: 0;
top: 0;
bottom: 0;
width: 3px;
background: var(--cyan);
opacity: 0;
transition: opacity 0.3s ease;
}
.equation-item:hover {
border-color: var(--cyan-dim);
background: var(--bg-tertiary);
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.equation-item:hover::before {
opacity: 1;
}
.equation-name {
font-family: var(--mono);
font-size: 0.65rem;
letter-spacing: 0.15em;
color: var(--cyan);
margin-bottom: 0.75rem;
display: flex;
align-items: center;
gap: 0.5rem;
}
.equation-name::before {
content: 'EQ';
font-size: 0.5rem;
background: var(--cyan-dim);
padding: 0.2rem 0.3rem;
border-radius: 3px;
}
.equation-formula {
font-family: var(--mono);
font-size: 1.1rem;
color: var(--text-primary);
margin-bottom: 0.5rem;
padding: 0.5rem;
background: var(--bg-primary);
border-radius: 6px;
border: 1px solid var(--border);
display: inline-block;
}
.equation-formula .var {
color: var(--purple);
}
.equation-formula .func {
color: var(--green);
}
.equation-formula .num {
color: var(--orange);
}
.equation-formula .op {
color: var(--cyan);
}
.equation-desc {
font-size: 0.8rem;
color: var(--text-muted);
line-height: 1.6;
}
/* Equation Tooltip */
.equation-tooltip {
position: fixed;
background: var(--bg-card);
border: 1px solid var(--cyan);
border-radius: 12px;
padding: 1.5rem;
max-width: 400px;
z-index: 2000;
pointer-events: none;
opacity: 0;
transform: translateY(10px);
transition: all 0.3s ease;
box-shadow: 0 20px 60px rgba(0, 0, 0, 0.5), 0 0 40px var(--cyan-glow);
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.equation-tooltip.visible {
opacity: 1;
transform: translateY(0);
}
.tooltip-title {
font-family: var(--mono);
font-size: 0.8rem;
color: var(--cyan);
margin-bottom: 0.75rem;
}
.tooltip-formula {
font-family: var(--mono);
font-size: 1.2rem;
color: var(--text-primary);
margin-bottom: 1rem;
padding: 0.75rem;
background: var(--bg-secondary);
border-radius: 8px;
}
.tooltip-vars {
display: flex;
flex-direction: column;
gap: 0.5rem;
}
.tooltip-var {
display: flex;
gap: 0.75rem;
font-size: 0.75rem;
}
.tooltip-var span:first-child {
font-family: var(--mono);
color: var(--purple);
min-width: 40px;
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.tooltip-var span:last-child {
color: var(--text-secondary);
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/* Code Block */
.code-block {
background: var(--bg-secondary);
border: 1px solid var(--border);
border-radius: 12px;
margin: 1.5rem 0;
overflow: hidden;
}
.code-header {
display: flex;
justify-content: space-between;
align-items: center;
padding: 0.75rem 1.25rem;
background: var(--bg-tertiary);
border-bottom: 1px solid var(--border);
}
.code-title {
font-family: var(--mono);
font-size: 0.65rem;
letter-spacing: 0.15em;
color: var(--text-muted);
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.code-lang {
font-family: var(--mono);
font-size: 0.6rem;
color: var(--cyan);
background: var(--cyan-glow);
padding: 0.25rem 0.5rem;
border-radius: 4px;
}
.code-content {
padding: 1.5rem;
overflow-x: auto;
}
.code-content pre {
margin: 0;
}
.code-content code {
font-family: var(--mono);
font-size: 0.85rem;
line-height: 1.8;
color: var(--text-primary);
}
/* Syntax Highlighting */
.code-content .comment { color: #6a9955; font-style: italic; }
.code-content .keyword { color: #569cd6; }
.code-content .type { color: #4ec9b0; }
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.code-content .string { color: #ce9178; }
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.code-content .variable { color: #9cdcfe; }
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color: var(--text-muted);
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padding: 3rem;
background: var(--bg-card);
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.primitives-grid {
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grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
gap: 1rem;
margin-top: 2rem;
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border: 1px solid var(--border);
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transition: all 0.3s ease;
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right: 0;
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transform: translateY(-4px);
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<div class="nav-logo">MEGAMIND</div>
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<a href="#overview" class="nav-link active">Overview</a>
<a href="#subsystems" class="nav-link">Subsystems</a>
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<div class="nav-chapter">CHAPTER <span>03</span> / THE 486 EQUATIONS</div>
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<header class="hero" id="overview">
<div class="hero-number">486</div>
<div class="hero-content">
<div class="hero-label">TECHNICAL SPECIFICATION v2.0</div>
<h1>The 486 Equations</h1>
<p class="hero-subtitle">
A complete neural substrate implementing computational neuroscience principles
in <code>branchless</code>, <code>Q8.8 fixed-point</code> arithmetic.
Zero conditional branches. Maximum determinism.
</p>
<div class="stats-grid">
<div class="stat-card fade-in">
<div class="stat-value">486</div>
<div class="stat-label">TOTAL EQUATIONS</div>
</div>
<div class="stat-card fade-in">
<div class="stat-value">12</div>
<div class="stat-label">SUBSYSTEMS</div>
</div>
<div class="stat-card fade-in">
<div class="stat-value">Q8.8</div>
<div class="stat-label">FIXED-POINT FORMAT</div>
</div>
<div class="stat-card fade-in">
<div class="stat-value">0</div>
<div class="stat-label">BRANCH INSTRUCTIONS</div>
</div>
</div>
</div>
</header>
<div class="subsystem-nav" id="subsystems">
<div class="subsystem-nav-inner">
<button class="subsystem-tab active" data-target="all">ALL <span class="count">486</span></button>
<button class="subsystem-tab" data-target="s1">S1 GLIA <span class="count">68</span></button>
<button class="subsystem-tab" data-target="s2">S2 DENDRITES <span class="count">72</span></button>
<button class="subsystem-tab" data-target="s3">S3 SOMA <span class="count">12</span></button>
<button class="subsystem-tab" data-target="s4">S4 SYNAPSES <span class="count">42</span></button>
<button class="subsystem-tab" data-target="s5">S5 STDP <span class="count">46</span></button>
<button class="subsystem-tab" data-target="s6">S6 PREDICTIVE <span class="count">34</span></button>
<button class="subsystem-tab" data-target="s7">S7 WORKSPACE <span class="count">52</span></button>
<button class="subsystem-tab" data-target="s8">S8 OSCILLATORS <span class="count">58</span></button>
<button class="subsystem-tab" data-target="s9">S9 CALCIUM <span class="count">38</span></button>
<button class="subsystem-tab" data-target="s10">S10 TRANSMITTERS <span class="count">28</span></button>
<button class="subsystem-tab" data-target="s11">S11 HOMEOSTASIS <span class="count">24</span></button>
<button class="subsystem-tab" data-target="s12">S12 PHI <span class="count">12</span></button>
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<main class="main-content">
<section class="section-header fade-in">
<h2 data-index="01">Subsystem Architecture</h2>
<p>The neural substrate is organized into 12 functional subsystems, each implementing well-established principles from computational neuroscience literature. Every equation has been converted to branchless form for deterministic GPU execution.</p>
</section>
<div class="subsystem-grid">
<!-- S1: Glia Dynamics -->
<div class="subsystem-card" data-subsystem="s1">
<div class="subsystem-header">
<div class="subsystem-info">
<span class="subsystem-id">S1</span>
<span class="subsystem-name">GLIA DYNAMICS</span>
</div>
<div class="subsystem-meta">
<span class="eq-badge">68 EQ</span>
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</div>
<div class="subsystem-content">
<div class="subsystem-inner">
<p class="subsystem-desc">Astrocyte calcium dynamics following the Li-Rinzel model for calcium-induced calcium release (CICR). Implements gliotransmitter release, gap junction coupling, and metabolic support.</p>
<div class="equation-list">
<div class="equation-item" data-equation="ca-dynamics">
<div class="equation-name">CALCIUM DYNAMICS</div>
<div class="equation-formula">
<span class="var">dCa</span>/<span class="var">dt</span> <span class="op">=</span> <span class="func">J_CICR</span> <span class="op">-</span> <span class="func">J_pump</span> <span class="op">+</span> <span class="func">J_leak</span>
</div>
<div class="equation-desc">Cytoplasmic calcium concentration governed by ER release, SERCA pump, and leak currents.</div>
</div>
<div class="equation-item" data-equation="ip3-receptor">
<div class="equation-name">IP3 RECEPTOR ACTIVATION</div>
<div class="equation-formula">
<span class="var">m</span><span class="op">_inf</span> <span class="op">=</span> <span class="var">I</span> <span class="op">/</span> <span class="op">(</span><span class="var">I</span> <span class="op">+</span> <span class="num">d1</span><span class="op">)</span>
</div>
<div class="equation-desc">IP3 binding activation gate for calcium channel opening probability.</div>
</div>
<div class="equation-item" data-equation="gap-junction">
<div class="equation-name">GAP JUNCTION COUPLING</div>
<div class="equation-formula">
<span class="var">I_gap</span> <span class="op">=</span> <span class="var">g_gap</span> <span class="op">*</span> <span class="op">(</span><span class="var">Ca_j</span> <span class="op">-</span> <span class="var">Ca_i</span><span class="op">)</span>
</div>
<div class="equation-desc">Intercellular calcium diffusion through connexin hemichannels.</div>
</div>
</div>
<div class="code-block">
<div class="code-header">
<span class="code-title">IMPLEMENTATION</span>
<span class="code-lang">BRANCHLESS C</span>
</div>
<div class="code-content">
<pre><code><span class="line-number">01</span><span class="comment">// Li-Rinzel Calcium Dynamics (Branchless Q8.8)</span>
<span class="line-number">02</span><span class="type">int32_t</span> <span class="variable">m</span> <span class="operator">=</span> (<span class="variable">I</span> <span class="operator"><<</span> <span class="number">8</span>) <span class="operator">/</span> (<span class="variable">I</span> <span class="operator">+</span> <span class="number">26</span> <span class="operator">+</span> <span class="number">1</span>);
<span class="line-number">03</span><span class="type">int32_t</span> <span class="variable">m3h3</span> <span class="operator">=</span> ((<span class="variable">m</span><span class="operator">*</span><span class="variable">m</span><span class="operator">>></span><span class="number">8</span>)<span class="operator">*</span><span class="variable">m</span><span class="operator">>></span><span class="number">8</span>)<span class="operator">*</span>((<span class="variable">h</span><span class="operator">*</span><span class="variable">h</span><span class="operator">>></span><span class="number">8</span>)<span class="operator">*</span><span class="variable">h</span><span class="operator">>></span><span class="number">8</span>)<span class="operator">>></span><span class="number">8</span>;
<span class="line-number">04</span><span class="type">int32_t</span> <span class="variable">dr</span> <span class="operator">=</span> <span class="number">512</span> <span class="operator">-</span> <span class="variable">C</span> <span class="operator">-</span> (<span class="variable">C</span> <span class="operator">>></span> <span class="number">4</span>);
<span class="line-number">05</span><span class="type">int32_t</span> <span class="variable">Jc</span> <span class="operator">=</span> (<span class="number">6</span> <span class="operator">*</span> <span class="variable">m3h3</span> <span class="operator">*</span> <span class="variable">dr</span>) <span class="operator">>></span> <span class="number">16</span>;
<span class="line-number">06</span><span class="type">int32_t</span> <span class="variable">Jp</span> <span class="operator">=</span> (<span class="number">230</span> <span class="operator">*</span> <span class="variable">C2</span>) <span class="operator">/</span> (<span class="number">13</span> <span class="operator">+</span> <span class="variable">C2</span> <span class="operator">+</span> <span class="number">1</span>);
<span class="line-number">07</span><span class="type">int32_t</span> <span class="variable">Jl</span> <span class="operator">=</span> (<span class="number">3</span> <span class="operator">*</span> <span class="variable">dr</span>) <span class="operator">>></span> <span class="number">8</span>;
<span class="line-number">08</span><span class="variable">gCa</span>[<span class="variable">i</span>] <span class="operator">=</span> <span class="function">CL</span>(<span class="variable">C</span> <span class="operator">+</span> ((<span class="variable">Jc</span> <span class="operator">-</span> <span class="variable">Jp</span> <span class="operator">+</span> <span class="variable">Jl</span>) <span class="operator">>></span> <span class="number">4</span>), <span class="number">0</span>, <span class="number">4096</span>);</code></pre>
</div>
</div>
</div>
</div>
</div>
<!-- S2: Dendrite Processing -->
<div class="subsystem-card" data-subsystem="s2">
<div class="subsystem-header">
<div class="subsystem-info">
<span class="subsystem-id">S2</span>
<span class="subsystem-name">DENDRITE PROCESSING</span>
</div>
<div class="subsystem-meta">
<span class="eq-badge">72 EQ</span>
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<path d="M2 4L6 8L10 4" stroke="currentColor" stroke-width="1.5" stroke-linecap="round"/>
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</div>
</div>
<div class="subsystem-content">
<div class="subsystem-inner">
<p class="subsystem-desc">Compartmental cable equation modeling with NMDA receptor voltage-dependent magnesium block and back-propagating action potential (BAP) attenuation.</p>
<div class="equation-list">
<div class="equation-item" data-equation="cable">
<div class="equation-name">CABLE EQUATION</div>
<div class="equation-formula">
<span class="var">lambda</span><sup>2</sup> <span class="op">*</span> <span class="var">d2V/dx2</span> <span class="op">=</span> <span class="var">tau</span> <span class="op">*</span> <span class="var">dV/dt</span> <span class="op">+</span> <span class="var">V</span>
</div>
<div class="equation-desc">Passive voltage spread along dendritic cable with length constant lambda.</div>
</div>
<div class="equation-item" data-equation="nmda-block">
<div class="equation-name">NMDA Mg2+ BLOCK</div>
<div class="equation-formula">
<span class="var">B</span><span class="op">(</span><span class="var">V</span><span class="op">)</span> <span class="op">=</span> <span class="num">1</span> <span class="op">/</span> <span class="op">(</span><span class="num">1</span> <span class="op">+</span> <span class="var">exp</span><span class="op">(</span><span class="num">-0.062</span><span class="var">V</span><span class="op">)</span> <span class="op">*</span> <span class="op">[</span><span class="var">Mg</span><span class="op">]</span><span class="op">/</span><span class="num">3.57</span><span class="op">)</span>
</div>
<div class="equation-desc">Voltage-dependent unblock of NMDA receptors enabling coincidence detection.</div>
</div>
<div class="equation-item" data-equation="bap">
<div class="equation-name">BAP ATTENUATION</div>
<div class="equation-formula">
<span class="var">V_bap</span><span class="op">(</span><span class="var">x</span><span class="op">)</span> <span class="op">=</span> <span class="var">V_soma</span> <span class="op">*</span> <span class="var">exp</span><span class="op">(</span><span class="num">-x</span><span class="op">/</span><span class="var">lambda_bap</span><span class="op">)</span>
</div>
<div class="equation-desc">Action potential amplitude decay along dendritic tree.</div>
</div>
</div>
<div class="code-block">
<div class="code-header">
<span class="code-title">NMDA VOLTAGE GATE</span>
<span class="code-lang">BRANCHLESS C</span>
</div>
<div class="code-content">
<pre><code><span class="line-number">01</span><span class="comment">// NMDA Mg2+ Block via Lookup Table</span>
<span class="line-number">02</span><span class="type">int32_t</span> <span class="variable">v_idx</span> <span class="operator">=</span> <span class="function">CL</span>((<span class="variable">V</span> <span class="operator">+</span> <span class="number">80</span>) <span class="operator">>></span> <span class="number">2</span>, <span class="number">0</span>, <span class="number">63</span>);
<span class="line-number">03</span><span class="type">int32_t</span> <span class="variable">mg_block</span> <span class="operator">=</span> <span class="variable">NMB</span>[<span class="variable">v_idx</span>];
<span class="line-number">04</span><span class="type">int32_t</span> <span class="variable">g_nmda</span> <span class="operator">=</span> (<span class="variable">g_max</span> <span class="operator">*</span> <span class="variable">mg_block</span>) <span class="operator">>></span> <span class="number">8</span>;
<span class="line-number">05</span><span class="type">int32_t</span> <span class="variable">I_nmda</span> <span class="operator">=</span> (<span class="variable">g_nmda</span> <span class="operator">*</span> (<span class="variable">V</span> <span class="operator">-</span> <span class="variable">E_syn</span>)) <span class="operator">>></span> <span class="number">8</span>;</code></pre>
</div>
</div>
</div>
</div>
</div>
<!-- S3: Soma Integration -->
<div class="subsystem-card" data-subsystem="s3">
<div class="subsystem-header">
<div class="subsystem-info">
<span class="subsystem-id">S3</span>
<span class="subsystem-name">SOMA INTEGRATION</span>
</div>
<div class="subsystem-meta">
<span class="eq-badge">12 EQ</span>
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</svg>
</span>
</div>
</div>
<div class="subsystem-content">
<div class="subsystem-inner">
<p class="subsystem-desc">Izhikevich neuron model for efficient spike generation with biologically realistic firing patterns. Kuramoto oscillator coupling for network synchronization.</p>
<div class="equation-list">
<div class="equation-item" data-equation="izh-v">
<div class="equation-name">IZHIKEVICH MEMBRANE</div>
<div class="equation-formula">
<span class="var">dv/dt</span> <span class="op">=</span> <span class="num">0.04</span><span class="var">v</span><sup>2</sup> <span class="op">+</span> <span class="num">5</span><span class="var">v</span> <span class="op">+</span> <span class="num">140</span> <span class="op">-</span> <span class="var">u</span> <span class="op">+</span> <span class="var">I</span>
</div>
<div class="equation-desc">Membrane potential dynamics with quadratic voltage dependence.</div>
</div>
<div class="equation-item" data-equation="izh-u">
<div class="equation-name">RECOVERY VARIABLE</div>
<div class="equation-formula">
<span class="var">du/dt</span> <span class="op">=</span> <span class="var">a</span> <span class="op">*</span> <span class="op">(</span><span class="var">b</span><span class="var">v</span> <span class="op">-</span> <span class="var">u</span><span class="op">)</span>
</div>
<div class="equation-desc">Slow recovery variable providing adaptation and refractory dynamics.</div>
</div>
<div class="equation-item" data-equation="kuramoto">
<div class="equation-name">KURAMOTO COUPLING</div>
<div class="equation-formula">
<span class="var">d_theta/dt</span> <span class="op">=</span> <span class="var">omega</span> <span class="op">+</span> <span class="var">K/N</span> <span class="op">*</span> <span class="var">sum</span><span class="op">(</span><span class="var">sin</span><span class="op">(</span><span class="var">theta_j</span> <span class="op">-</span> <span class="var">theta_i</span><span class="op">))</span>
</div>
<div class="equation-desc">Phase oscillator synchronization for gamma-band coordination.</div>
</div>
</div>
</div>
</div>
</div>
<!-- S4: Synapse Plasticity -->
<div class="subsystem-card" data-subsystem="s4">
<div class="subsystem-header">
<div class="subsystem-info">
<span class="subsystem-id">S4</span>
<span class="subsystem-name">SYNAPSE PLASTICITY</span>
</div>
<div class="subsystem-meta">
<span class="eq-badge">42 EQ</span>
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</svg>
</span>
</div>
</div>
<div class="subsystem-content">
<div class="subsystem-inner">
<p class="subsystem-desc">Short-term plasticity (STP) dynamics including facilitation and depression. Vesicle pool dynamics and release probability modulation.</p>
<div class="equation-list">
<div class="equation-item" data-equation="stp-u">
<div class="equation-name">FACILITATION</div>
<div class="equation-formula">
<span class="var">du/dt</span> <span class="op">=</span> <span class="op">-</span><span class="var">u</span><span class="op">/</span><span class="var">tau_f</span> <span class="op">+</span> <span class="var">U</span><span class="op">(</span><span class="num">1</span><span class="op">-</span><span class="var">u</span><span class="op">)</span><span class="var">delta</span><span class="op">(</span><span class="var">t</span><span class="op">-</span><span class="var">t_sp</span><span class="op">)</span>
</div>
<div class="equation-desc">Use-dependent increase in release probability after each spike.</div>
</div>
<div class="equation-item" data-equation="stp-x">
<div class="equation-name">DEPRESSION</div>
<div class="equation-formula">
<span class="var">dx/dt</span> <span class="op">=</span> <span class="op">(</span><span class="num">1</span><span class="op">-</span><span class="var">x</span><span class="op">)/</span><span class="var">tau_d</span> <span class="op">-</span> <span class="var">ux</span><span class="op">*</span><span class="var">delta</span><span class="op">(</span><span class="var">t</span><span class="op">-</span><span class="var">t_sp</span><span class="op">)</span>
</div>
<div class="equation-desc">Vesicle depletion causing synaptic depression with recovery.</div>
</div>
</div>
</div>
</div>
</div>
<!-- S5: STDP Learning -->
<div class="subsystem-card" data-subsystem="s5">
<div class="subsystem-header">
<div class="subsystem-info">
<span class="subsystem-id">S5</span>
<span class="subsystem-name">STDP LEARNING</span>
</div>
<div class="subsystem-meta">
<span class="eq-badge">46 EQ</span>
<span class="expand-icon">
<svg width="12" height="12" viewBox="0 0 12 12" fill="none">
<path d="M2 4L6 8L10 4" stroke="currentColor" stroke-width="1.5" stroke-linecap="round"/>
</svg>
</span>
</div>
</div>
<div class="subsystem-content">
<div class="subsystem-inner">
<p class="subsystem-desc">Spike-timing dependent plasticity with three-factor learning rule. Eligibility traces for reward-modulated credit assignment.</p>
<div class="equation-list">
<div class="equation-item" data-equation="stdp">
<div class="equation-name">STDP WINDOW</div>
<div class="equation-formula">
<span class="var">dw</span> <span class="op">=</span> <span class="var">A</span><span class="op">+/-</span> <span class="op">*</span> <span class="var">exp</span><span class="op">(</span><span class="op">-|</span><span class="var">dt</span><span class="op">|/</span><span class="var">tau</span><span class="op">+/-</span><span class="op">)</span>
</div>
<div class="equation-desc">Weight change depends on relative spike timing between pre and post.</div>
</div>
<div class="equation-item" data-equation="three-factor">
<div class="equation-name">THREE-FACTOR RULE</div>
<div class="equation-formula">
<span class="var">dw</span> <span class="op">=</span> <span class="var">eta</span> <span class="op">*</span> <span class="var">e</span> <span class="op">*</span> <span class="var">M</span>
</div>
<div class="equation-desc">Eligibility trace (e) gated by neuromodulator (M) for RL learning.</div>
</div>
<div class="equation-item" data-equation="eligibility">
<div class="equation-name">ELIGIBILITY TRACE</div>
<div class="equation-formula">
<span class="var">de/dt</span> <span class="op">=</span> <span class="op">-</span><span class="var">e</span><span class="op">/</span><span class="var">tau_e</span> <span class="op">+</span> <span class="var">STDP</span><span class="op">(</span><span class="var">dt</span><span class="op">)</span>
</div>
<div class="equation-desc">Decaying memory of recent synaptic coincidences for delayed reward.</div>
</div>
</div>
<div class="code-block">
<div class="code-header">
<span class="code-title">STDP UPDATE</span>
<span class="code-lang">BRANCHLESS C</span>
</div>
<div class="code-content">
<pre><code><span class="line-number">01</span><span class="type">int32_t</span> <span class="function">stdp_update</span>(<span class="type">int32_t</span> <span class="variable">w</span>, <span class="type">int32_t</span> <span class="variable">dt</span>) {
<span class="line-number">02</span> <span class="type">int32_t</span> <span class="variable">is_ltp</span> <span class="operator">=</span> <span class="function">TH</span>(<span class="variable">dt</span>, <span class="number">0</span>);
<span class="line-number">03</span> <span class="type">int32_t</span> <span class="variable">abs_dt</span> <span class="operator">=</span> <span class="function">ABS</span>(<span class="variable">dt</span>);
<span class="line-number">04</span> <span class="type">int32_t</span> <span class="variable">decay</span> <span class="operator">=</span> <span class="variable">EXP</span>[<span class="function">MIN</span>(<span class="variable">abs_dt</span> <span class="operator">>></span> <span class="number">2</span>, <span class="number">63</span>)];
<span class="line-number">05</span> <span class="type">int32_t</span> <span class="variable">ltp</span> <span class="operator">=</span> (<span class="variable">A_plus</span> <span class="operator">*</span> <span class="variable">decay</span>) <span class="operator">>></span> <span class="number">8</span>;
<span class="line-number">06</span> <span class="type">int32_t</span> <span class="variable">ltd</span> <span class="operator">=</span> (<span class="variable">A_minus</span> <span class="operator">*</span> <span class="variable">decay</span>) <span class="operator">>></span> <span class="number">8</span>;
<span class="line-number">07</span> <span class="keyword">return</span> <span class="function">CL</span>(<span class="variable">w</span> <span class="operator">+</span> <span class="function">SEL</span>(<span class="variable">is_ltp</span>, <span class="variable">ltp</span>, <span class="operator">-</span><span class="variable">ltd</span>), <span class="number">0</span>, <span class="number">255</span>);
<span class="line-number">08</span>}</code></pre>
</div>
</div>
</div>
</div>
</div>
<!-- S6: Predictive Coding -->
<div class="subsystem-card" data-subsystem="s6">
<div class="subsystem-header">
<div class="subsystem-info">
<span class="subsystem-id">S6</span>
<span class="subsystem-name">PREDICTIVE CODING</span>
</div>
<div class="subsystem-meta">
<span class="eq-badge">34 EQ</span>
<span class="expand-icon">
<svg width="12" height="12" viewBox="0 0 12 12" fill="none">
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</div>
</div>
<div class="subsystem-content">
<div class="subsystem-inner">
<p class="subsystem-desc">Hierarchical predictive processing with precision-weighted prediction errors. Free energy minimization through active inference.</p>
<div class="equation-list">
<div class="equation-item" data-equation="prediction-error">
<div class="equation-name">PREDICTION ERROR</div>
<div class="equation-formula">
<span class="var">epsilon</span> <span class="op">=</span> <span class="var">x</span> <span class="op">-</span> <span class="var">g</span><span class="op">(</span><span class="var">mu</span><span class="op">)</span>
</div>
<div class="equation-desc">Sensory prediction error: difference between input and predicted state.</div>
</div>
<div class="equation-item" data-equation="precision">
<div class="equation-name">PRECISION WEIGHTING</div>
<div class="equation-formula">
<span class="var">dmu/dt</span> <span class="op">=</span> <span class="var">Pi</span> <span class="op">*</span> <span class="var">epsilon</span>
</div>
<div class="equation-desc">State update weighted by precision (inverse variance) of prediction.</div>
</div>
</div>
</div>
</div>
</div>
<!-- S7: Global Workspace -->
<div class="subsystem-card" data-subsystem="s7">
<div class="subsystem-header">
<div class="subsystem-info">
<span class="subsystem-id">S7</span>
<span class="subsystem-name">GLOBAL WORKSPACE</span>
</div>
<div class="subsystem-meta">
<span class="eq-badge">52 EQ</span>
<span class="expand-icon">
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</div>
</div>
<div class="subsystem-content">
<div class="subsystem-inner">
<p class="subsystem-desc">Coalition competition implementing Global Workspace Theory. Winner-take-all dynamics for conscious access and broadcast.</p>
<div class="equation-list">
<div class="equation-item" data-equation="coalition">
<div class="equation-name">COALITION STRENGTH</div>
<div class="equation-formula">
<span class="var">C_i</span> <span class="op">=</span> <span class="var">sum</span><span class="op">(</span><span class="var">w_ij</span> <span class="op">*</span> <span class="var">a_j</span><span class="op">)</span> <span class="op">*</span> <span class="var">coherence_i</span>
</div>
<div class="equation-desc">Coalition activation based on member weights and internal coherence.</div>
</div>
<div class="equation-item" data-equation="wta">
<div class="equation-name">WINNER-TAKE-ALL</div>
<div class="equation-formula">
<span class="var">da_i/dt</span> <span class="op">=</span> <span class="var">C_i</span> <span class="op">-</span> <span class="var">k</span> <span class="op">*</span> <span class="var">sum</span><span class="op">(</span><span class="var">a_j</span><span class="op">)</span>
</div>
<div class="equation-desc">Lateral inhibition driving competition for workspace access.</div>
</div>
<div class="equation-item" data-equation="ignition">
<div class="equation-name">IGNITION THRESHOLD</div>
<div class="equation-formula">
<span class="var">ignite</span> <span class="op">=</span> <span class="var">TH</span><span class="op">(</span><span class="var">C_winner</span><span class="op">,</span> <span class="var">theta_ign</span><span class="op">)</span>
</div>
<div class="equation-desc">Threshold crossing triggering global broadcast of winning coalition.</div>
</div>
</div>
</div>
</div>
</div>
<!-- S8: Oscillators -->
<div class="subsystem-card" data-subsystem="s8">
<div class="subsystem-header">
<div class="subsystem-info">
<span class="subsystem-id">S8</span>
<span class="subsystem-name">NEURAL OSCILLATORS</span>
</div>
<div class="subsystem-meta">
<span class="eq-badge">58 EQ</span>
<span class="expand-icon">
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<path d="M2 4L6 8L10 4" stroke="currentColor" stroke-width="1.5" stroke-linecap="round"/>
</svg>
</span>
</div>
</div>
<div class="subsystem-content">
<div class="subsystem-inner">
<p class="subsystem-desc">Multi-band oscillatory dynamics: theta (4-8 Hz), alpha (8-12 Hz), beta (12-30 Hz), gamma (30-100 Hz). Cross-frequency coupling for information binding.</p>
<div class="equation-list">
<div class="equation-item" data-equation="theta">
<div class="equation-name">THETA RHYTHM</div>
<div class="equation-formula">
<span class="var">theta</span><span class="op">(</span><span class="var">t</span><span class="op">)</span> <span class="op">=</span> <span class="var">A</span> <span class="op">*</span> <span class="var">sin</span><span class="op">(</span><span class="num">2</span><span class="var">pi</span> <span class="op">*</span> <span class="num">6</span> <span class="op">*</span> <span class="var">t</span> <span class="op">+</span> <span class="var">phi</span><span class="op">)</span>
</div>
<div class="equation-desc">Hippocampal theta for temporal organization of sequences.</div>
</div>
<div class="equation-item" data-equation="gamma-burst">
<div class="equation-name">GAMMA BURST</div>
<div class="equation-formula">
<span class="var">gamma</span> <span class="op">=</span> <span class="var">A_g</span> <span class="op">*</span> <span class="op">(</span><span class="num">1</span> <span class="op">+</span> <span class="var">cos</span><span class="op">(</span><span class="var">theta</span><span class="op">))</span> <span class="op">*</span> <span class="var">sin</span><span class="op">(</span><span class="num">2</span><span class="var">pi</span> <span class="op">*</span> <span class="num">40</span> <span class="op">*</span> <span class="var">t</span><span class="op">)</span>
</div>
<div class="equation-desc">Theta-nested gamma bursts for memory encoding phases.</div>
</div>
</div>
</div>
</div>
</div>
<!-- S9: Calcium Dynamics -->
<div class="subsystem-card" data-subsystem="s9">
<div class="subsystem-header">
<div class="subsystem-info">
<span class="subsystem-id">S9</span>
<span class="subsystem-name">CALCIUM DYNAMICS</span>
</div>
<div class="subsystem-meta">
<span class="eq-badge">38 EQ</span>
<span class="expand-icon">
<svg width="12" height="12" viewBox="0 0 12 12" fill="none">
<path d="M2 4L6 8L10 4" stroke="currentColor" stroke-width="1.5" stroke-linecap="round"/>
</svg>
</span>
</div>
</div>
<div class="subsystem-content">
<div class="subsystem-inner">
<p class="subsystem-desc">Intracellular calcium signaling for plasticity induction. VGCC, NMDA-mediated influx, and calcium-dependent enzyme activation.</p>
<div class="equation-list">
<div class="equation-item" data-equation="ca-influx">
<div class="equation-name">CALCIUM INFLUX</div>
<div class="equation-formula">
<span class="var">dCa/dt</span> <span class="op">=</span> <span class="var">I_VGCC</span> <span class="op">+</span> <span class="var">I_NMDA</span> <span class="op">-</span> <span class="var">Ca</span><span class="op">/</span><span class="var">tau_Ca</span>
</div>