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THE CONSCIOUSNESS ATLAS
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ch03-equations.html

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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>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; 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} .slide-in-left.visible { opacity: 1; transform: translateX(0); } .scale-in { opacity: 0; transform: scale(0.9); transition: all 0.6s cubic-bezier(0.16, 1, 0.3, 1); } .scale-in.visible { opacity: 1; transform: scale(1); } /* Responsive */ @media (max-width: 1024px) { .hero-number { display: none; } .stats-grid { grid-template-columns: repeat(2, 1fr); } .nav { padding: 1rem; } .nav-center { display: none; } .hero, .main-content, .chapter-nav { padding: 2rem; } .subsystem-nav-inner { padding: 0 2rem; } } @media (max-width: 640px) { .stats-grid { grid-template-columns: 1fr; } .subsystem-grid { grid-template-columns: 1fr; } .primitives-grid { grid-template-columns: repeat(2, 1fr); } .chapter-nav { flex-direction: column; gap: 1rem; } .chapter-nav-link { max-width: 100%; } .cursor, .cursor-dot { display: none; } body { cursor: auto; } } </style> </head> <body> <div class="cursor"></div> <div class="cursor-dot"></div> <div class="grid-bg"></div> <nav class="nav"> <div class="nav-logo">MEGAMIND</div> <div class="nav-center"> <a href="#overview" class="nav-link active">Overview</a> <a href="#subsystems" class="nav-link">Subsystems</a> <a href="#primitives" class="nav-link">Primitives</a> <a href="#tables" class="nav-link">Lookup Tables</a> </div> <div class="nav-chapter">CHAPTER <span>03</span> / THE 486 EQUATIONS</div> </nav> <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> </div> </div> <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> <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">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> <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">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> <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">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> <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">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"> <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">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"> <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">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"> <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">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>

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