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<!DOCTYPE html>
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<title>How Codecs Work — Silk Docs</title>
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.chapter-num{font-family:'Fragment Mono',monospace;font-size:0.7rem;letter-spacing:0.15em;color:var(--text-muted);margin-bottom:0.5rem;display:block;}
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  <span class="chapter-num">rmk-silk-002 · page 01</span>
  <h1>how codecs work today</h1>
  <p class="subtitle">every voice AI codec in production uses the same core approach. it works, but it has a fundamental flaw.</p>

  <!-- ============ SECTION 1: THE PROBLEM ============ -->
  <h2>the compression problem</h2>
  <p>raw audio is 24,000 numbers per second. an LLM processes maybe 100-200 <span class="term" data-term="tokens">tokens</span> per second. you can't feed 24,000 numbers/sec into an LLM directly.</p>
  <p>every codec compresses. the question: <strong>how do you compress without losing the important stuff?</strong></p>

  <!-- Animated: waveform → spectrogram -->
  <div class="interactive-block fade-in">
    <h3>step 1: waveform → spectrogram</h3>
    <p class="description">first, convert the raw <span class="term" data-term="waveform">waveform</span> into a <span class="term" data-term="spectrogram">spectrogram</span> — a "heat map" of which frequencies are active at each moment.</p>
    <div style="display:grid;grid-template-columns:1fr 40px 1fr;align-items:center;gap:0;">
      <div style="background:var(--code-bg);border-radius:var(--radius-md);overflow:hidden;">
        <canvas id="wave-raw" height="140" style="display:block;width:100%;"></canvas>
        <div style="padding:0.6rem;font-family:'Fragment Mono',monospace;font-size:0.8rem;color:rgba(255,255,255,0.5);text-align:center;">waveform (time domain)</div>
      </div>
      <div style="text-align:center;color:var(--accent);font-size:1.5rem;font-weight:600;">→</div>
      <div style="background:#0f0f1a;border-radius:var(--radius-md);overflow:hidden;">
        <canvas id="spec-demo" height="140" style="display:block;width:100%;"></canvas>
        <div style="padding:0.6rem;font-family:'Fragment Mono',monospace;font-size:0.8rem;color:rgba(255,255,255,0.5);text-align:center;">spectrogram (freq × time)</div>
      </div>
    </div>
  </div>

  <!-- ============ SECTION 2: ENCODER ============ -->
  <div class="interactive-block fade-in">
    <h3>step 2: neural network <span class="term" data-term="encoder">encoder</span></h3>
    <p class="description">a neural network processes the spectrogram and compresses each time slice into a small vector of numbers.</p>
    <div style="background:#1a1a2e;border-radius:var(--radius-lg);padding:2rem 1.5rem;">
      <svg id="encoder-nn-svg" viewBox="0 0 700 260" style="width:100%;height:auto;display:block;">
        <text x="60" y="18" text-anchor="middle" fill="rgba(85,85,85,0.7)" font-size="11" font-weight="600" font-family="Fragment Mono">input</text>
        <text x="640" y="18" text-anchor="middle" fill="rgba(45,138,78,0.6)" font-size="11" font-weight="600" font-family="Fragment Mono">output</text>
        <text x="350" y="252" text-anchor="middle" fill="rgba(255,255,255,0.3)" font-size="11" font-family="Fragment Mono">128 mel bands → neural network → 128 continuous numbers</text>
      </svg>
    </div>
  </div>

  <p>at this point, discrete and continuous codecs are identical. the encoder produces a <strong>continuous vector</strong> — floating point numbers like <code>[0.73, -1.2, 0.04, ...]</code>.</p>
  <p>what happens next is where everything diverges.</p>

  <div class="visual-break"></div>

  <!-- ============ SECTION 3: QUANTIZATION ============ -->
  <span class="chapter-num">the critical step</span>
  <h2 style="border:none;padding:0;margin-top:0;">step 3: quantization (the "snap")</h2>

  <!-- CODEBOOK EXPLAINER -->
  <div class="interactive-block fade-in" style="padding:2.5rem;">
    <h3 style="margin-bottom:0.5rem;">what is a codebook?</h3>
    <p class="description" style="font-size:0.95rem;max-width:640px;">a <span class="term" data-term="codebook">codebook</span> is a <strong>dictionary of reference sounds</strong>. during training, the network learns a fixed set of "representative" vectors — like a color palette. every new sound must be matched to the closest entry in this palette.</p>

    <div style="display:grid;grid-template-columns:1fr 1fr;gap:2rem;margin:2rem 0;">
      <!-- Left: the palette analogy -->
      <div style="background:var(--bg);border-radius:var(--radius-md);padding:1.75rem;">
        <div style="font-family:'Fragment Mono',monospace;font-size:0.8rem;font-weight:600;color:var(--text);margin-bottom:1rem;">the codebook (1,024 entries)</div>
        <div id="codebook-palette" style="display:grid;grid-template-columns:repeat(8,1fr);gap:6px;"></div>
        <div style="font-size:0.85rem;color:var(--text-muted);margin-top:1rem;line-height:1.6;">each colored block is one codebook entry — a vector that represents a specific type of sound. the network has <strong>only these to choose from.</strong></div>
      </div>
      <!-- Right: the snapping in action -->
      <div style="background:var(--code-bg);border-radius:var(--radius-md);padding:1.75rem;">
        <div style="font-family:'Fragment Mono',monospace;font-size:0.8rem;font-weight:600;color:rgba(255,255,255,0.7);margin-bottom:1rem;">what happens to a new sound</div>
        <div style="display:flex;flex-direction:column;gap:1.25rem;">
          <div style="display:flex;align-items:center;gap:1rem;">
            <div style="width:40px;height:40px;border-radius:50%;background:#555;flex-shrink:0;display:flex;align-items:center;justify-content:center;font-size:0.75rem;color:white;font-family:'Fragment Mono',monospace;">in</div>
            <div style="font-size:0.85rem;color:rgba(255,255,255,0.6);line-height:1.5;">the encoder outputs a <strong style="color:#555;">continuous vector</strong> — a precise point in space, like [0.73, -1.2, 0.04, ...]</div>
          </div>
          <div style="text-align:center;font-size:1.5rem;color:rgba(255,255,255,0.3);">↓ <span style="font-size:0.75rem;vertical-align:middle;">find nearest</span> ↓</div>
          <div style="display:flex;align-items:center;gap:1rem;">
            <div style="width:40px;height:40px;border-radius:8px;background:#d4cfc7;flex-shrink:0;display:flex;align-items:center;justify-content:center;font-size:0.65rem;color:#2c2a26;font-family:'Fragment Mono',monospace;font-weight:600;">#47</div>
            <div style="font-size:0.85rem;color:rgba(255,255,255,0.6);line-height:1.5;">snapped to <strong style="color:#d4cfc7;">codebook entry #47</strong> — the closest match. everything between the original point and this entry is <span style="color:#d32f2f;font-weight:600;">lost forever.</span></div>
          </div>
        </div>
        <div style="margin-top:1.25rem;padding:0.75rem 1rem;background:rgba(196,64,64,0.15);border-radius:var(--radius-sm);border-left:3px solid #d32f2f;">
          <div style="font-size:0.85rem;color:rgba(255,255,255,0.7);line-height:1.5;">this is like rounding <code style="color:#1a1a1a;">3.7429</code> to <code style="color:#d4cfc7;">4</code>. the decimals — the nuance, the subtlety — are gone.</div>
        </div>
      </div>
    </div>

    <!-- Animated codebook lookup -->
    <div style="margin-top:1.5rem;">
      <div style="font-family:'Fragment Mono',monospace;font-size:0.8rem;font-weight:600;color:var(--text);margin-bottom:0.75rem;">interactive: click any palette block to see how it maps</div>
      <div style="background:var(--bg);border-radius:var(--radius-md);padding:1.5rem;">
        <canvas id="codebook-visual" height="280" style="display:block;width:100%;cursor:pointer;"></canvas>
        <div id="codebook-info" style="text-align:center;margin-top:0.75rem;font-family:'Fragment Mono',monospace;font-size:0.85rem;color:var(--text-muted);min-height:1.5em;">hover over points to see the snap in action</div>
      </div>
    </div>
  </div>

  <p style="margin-top:1.5rem;">discrete codecs take that continuous vector and <strong>snap it to the nearest entry in a codebook</strong> — a lookup table of pre-learned vectors.</p>

  <div class="interactive-block fade-in">
    <h3>interactive: see quantization happen</h3>
    <p class="description">the orange dot is the encoder's continuous output. gray dots are codebook entries. drag the slider to change codebook size. watch how the orange dot gets "snapped" to the nearest gray dot.</p>
    <div style="display:flex;justify-content:space-between;align-items:center;margin-bottom:0.5rem;">
      <div style="font-family:'Fragment Mono',monospace;font-size:0.8rem;">codebook size: <strong id="cb-label" style="color:var(--accent);">8</strong></div>
      <div style="font-family:'Fragment Mono',monospace;font-size:0.8rem;color:var(--text-muted);">error: <span id="q-error" style="color:var(--error);font-weight:600;">—</span></div>
    </div>
    <div class="slider-control">
      <input type="range" id="cb-slider" min="2" max="64" value="8">
    </div>
    <div class="viz-area" id="quant-viz" style="height:400px;background:var(--bg);cursor:crosshair;">
      <svg id="quant-svg" viewBox="0 0 700 400" style="width:100%;height:100%;"></svg>
    </div>
    <div style="display:flex;justify-content:center;gap:2rem;margin-top:1rem;font-size:0.85rem;color:var(--text-light);">
      <span>🟠 original continuous vector</span>
      <span>⬜ codebook entry</span>
      <span style="color:var(--error);">--- quantization error</span>
    </div>
  </div>

  <!-- ============ SECTION 4: RESIDUAL CHAIN ============ -->
  <h2>step 4: the residual trick</h2>
  <p>one codebook isn't enough. the error from the first quantization step gets passed to a SECOND codebook. that error's error goes to a THIRD. this is <strong><span class="term" data-term="rvq">Residual Vector Quantization (RVQ)</span></strong>.</p>

  <div class="interactive-block fade-in">
    <h3>interactive: watch the residual chain</h3>
    <p class="description">click "run" to see how each codebook reduces the error from the previous one.</p>
    <div style="text-align:center;margin-bottom:1rem;">
      <button id="rvq-run" style="padding:0.5rem 1.5rem;background:var(--accent);color:#fff;border:none;border-radius:var(--radius-sm);font-family:'Fragment Mono',monospace;font-size:0.8rem;cursor:pointer;">▶ run RVQ chain</button>
    </div>
    <div class="residual-chain" id="rvq-chain">
      <div class="residual-step" id="rvq-0">
        <div class="step-n">original vector</div>
        <div class="step-val" style="color:var(--accent);">2.73</div>
        <div class="step-desc">encoder output</div>
      </div>
      <div class="residual-arrow">→</div>
      <div class="residual-step" id="rvq-1" style="opacity:0.3;">
        <div class="step-n">codebook 1</div>
        <div class="step-val">3.00</div>
        <div class="step-desc">nearest entry</div>
        <div style="font-family:'Fragment Mono',monospace;font-size:0.7rem;color:var(--error);margin-top:0.25rem;">error: 0.27</div>
      </div>
      <div class="residual-arrow">→</div>
      <div class="residual-step" id="rvq-2" style="opacity:0.3;">
        <div class="step-n">codebook 2</div>
        <div class="step-val">0.25</div>
        <div class="step-desc">fixes residual</div>
        <div style="font-family:'Fragment Mono',monospace;font-size:0.7rem;color:var(--error);margin-top:0.25rem;">error: 0.02</div>
      </div>
      <div class="residual-arrow">→</div>
      <div class="residual-step" id="rvq-3" style="opacity:0.3;">
        <div class="step-n">codebook 3</div>
        <div class="step-val">0.02</div>
        <div class="step-desc">fixes residual</div>
        <div style="font-family:'Fragment Mono',monospace;font-size:0.7rem;color:var(--success);margin-top:0.25rem;">error: ~0.00</div>
      </div>
    </div>
    <div style="text-align:center;margin-top:1rem;">
      <div style="font-family:'Fragment Mono',monospace;font-size:0.75rem;color:var(--text-muted);">total output = codebook 1 + codebook 2 + codebook 3 = <span id="rvq-total" style="color:var(--accent);font-weight:600;">—</span></div>
    </div>
  </div>

  <p>8 codebooks × 1024 entries each covers a lot more ground than one codebook alone. but there's a structural problem that no amount of extra codebooks can fix.</p>

  <div class="visual-break"></div>

  <!-- ============ SECTION 5: THE PROBLEM ============ -->
  <span class="chapter-num">the fundamental flaw</span>
  <h2 style="border:none;padding:0;margin-top:0;">the information destruction problem</h2>

  <p>codebook entries are <strong>learned from training data.</strong> a codebook trained on english learns entries for english sounds. it literally has no entries for sounds it hasn't heard.</p>

  <div class="interactive-block fade-in">
    <h3>interactive: codebook coverage</h3>
    <p class="description">green = sounds the codebook has entries for (training language). red = sounds from another language that get mapped to the WRONG entries. use the toggle to switch languages.</p>
    <div class="tab-group">
      <button class="tab-btn active" data-tab="en">english (trained)</button>
      <button class="tab-btn" data-tab="zh">mandarin (unseen)</button>
      <button class="tab-btn" data-tab="ar">arabic (unseen)</button>
    </div>
    <div style="background:var(--code-bg);border-radius:var(--radius-md);padding:1rem;">
      <canvas id="coverage-viz" height="200" style="display:block;width:100%;"></canvas>
    </div>
    <div id="coverage-desc" style="text-align:center;margin-top:0.75rem;font-size:0.85rem;color:var(--text-muted);"></div>
  </div>

  <div class="callout insight fade-in">
    <div class="callout-title">the color palette analogy</div>
    <p>a color palette designed by someone who only saw forests would be heavy on greens and missing reds. try to paint a sunset — everything comes out greenish. that's what an english-trained codebook does to mandarin tones. the tonal information (which changes the meaning of words) gets snapped to flat english intonation entries.</p>
  </div>

  <!-- ============ SECTION 6: THE LANDSCAPE ============ -->
  <h2>the codec landscape</h2>
  <div class="interactive-block fade-in">
    <h3>token burden per second of audio</h3>
    <p class="description">every discrete codec produces hundreds of tokens per second. the LLM has to generate ALL of them to produce speech.</p>
    <div id="token-chart" style="min-height:250px;"></div>
  </div>

  <table class="comparison-table fade-in">
    <thead>
      <tr><th>codec</th><th>frame rate</th><th>codebooks</th><th>tokens/sec</th><th>type</th></tr>
    </thead>
    <tbody>
      <tr><td><strong>DAC</strong></td><td>~86 Hz</td><td>9</td><td>774</td><td><span style="background:var(--error-light);color:var(--error);font-size:0.7rem;padding:2px 8px;border-radius:3px;font-family:'Fragment Mono',monospace;">DISCRETE</span></td></tr>
      <tr><td><strong>EnCodec</strong></td><td>75 Hz</td><td>8</td><td>600</td><td><span style="background:var(--error-light);color:var(--error);font-size:0.7rem;padding:2px 8px;border-radius:3px;font-family:'Fragment Mono',monospace;">DISCRETE</span></td></tr>
      <tr><td><strong>Mimi</strong></td><td>12.5 Hz</td><td>8</td><td>100</td><td><span style="background:var(--error-light);color:var(--error);font-size:0.7rem;padding:2px 8px;border-radius:3px;font-family:'Fragment Mono',monospace;">DISCRETE</span></td></tr>
      <tr><td><strong>SNAC</strong></td><td>multi-scale</td><td>4</td><td>82.5</td><td><span style="background:var(--error-light);color:var(--error);font-size:0.7rem;padding:2px 8px;border-radius:3px;font-family:'Fragment Mono',monospace;">DISCRETE</span></td></tr>
      <tr style="background:var(--accent-light);"><td><strong style="color:var(--accent);">Silk Codec</strong></td><td>2.5 Hz</td><td>19 FSQ groups</td><td style="font-weight:700;color:var(--accent);">47.5</td><td><span style="background:var(--success-light);color:var(--success);font-size:0.7rem;padding:2px 8px;border-radius:3px;font-family:'Fragment Mono',monospace;">FSQ</span></td></tr>
    </tbody>
  </table>

  <!-- Go Deeper -->
  <div class="depth-section fade-in">
    <button class="depth-toggle" data-target="depth-gradient"><span class="arrow">▸</span> go deeper: the gradient problem with quantization</button>
    <div class="depth-content" id="depth-gradient">
      <div class="depth-inner">
        <h4>you can't differentiate through a lookup table</h4>
        <p>the "snap to nearest entry" operation has zero gradient everywhere except at the boundary (where it's undefined). this means during training, the encoder never gets precise feedback about the quantization error. the standard workaround is the <strong>straight-through estimator</strong> — pretend quantization didn't happen during backpropagation.</p>
        <p>the Silk Codec uses <span class="term" data-term="fsq">FSQ (Finite Scalar Quantization)</span> instead of VQ. FSQ quantizes each dimension independently to 8 levels, and uses dimension-level straight-through estimation — much more precise than vector-level STE used in RVQ codecs.</p>
      </div>
    </div>
  </div>

  <div class="depth-section fade-in">
    <button class="depth-toggle" data-target="depth-bandwidth"><span class="arrow">▸</span> go deeper: the bandwidth vs quality tradeoff</button>
    <div class="depth-content" id="depth-bandwidth">
      <div class="depth-inner">
        <h4>more codebooks = better quality but more tokens</h4>
        <p>each additional codebook reduces reconstruction error. but each codebook also produces one token per frame. at 75 Hz with 8 codebooks, that's <strong>600 tokens/sec</strong> the downstream LLM must generate — 6x faster than GPT generates text.</p>
        <p>SNAC tried multi-scale codebooks. Mimi reduced frame rate to 12.5 Hz. but they're all still discrete, still destroying information at every quantization step.</p>
      </div>
    </div>
  </div>

  <!-- Nav -->
  <div style="display:flex;justify-content:space-between;margin-top:4rem;padding-top:1.5rem;border-top:1px solid var(--border-light);">
    <a href="index.html" style="color:var(--accent);text-decoration:none;font-size:0.9rem;">← how voice AI works</a>
    <a href="silk-codec.html" style="color:var(--accent);text-decoration:none;font-size:0.9rem;">LSL & the codec →</a>
  </div>

</div>
</main>

<script src="js/shared.js"></script>
<script>
// === WAVEFORM ===
(function(){
  const c=document.getElementById('wave-raw');if(!c)return;
  const ctx=c.getContext('2d');c.width=c.parentElement.offsetWidth*2;c.height=200;let t=0;
  function draw(){ctx.clearRect(0,0,c.width,c.height);ctx.strokeStyle='rgba(100,100,100,0.8)';ctx.lineWidth=1.5;ctx.beginPath();for(let x=0;x<c.width;x++){const y=c.height/2+Math.sin(x*0.02+t*0.04)*30+Math.sin(x*0.05+t*0.06)*15+Math.sin(x*0.008+t*0.02)*10;x===0?ctx.moveTo(x,y):ctx.lineTo(x,y);}ctx.stroke();t++;requestAnimationFrame(draw);}draw();
})();

// === SPECTROGRAM ===
(function(){
  const c=document.getElementById('spec-demo');if(!c)return;
  const ctx=c.getContext('2d');c.width=c.parentElement.offsetWidth*2;c.height=200;let t=0;
  const data=[];for(let i=0;i<100;i++){const col=[];for(let j=0;j<50;j++)col.push(Math.random());data.push(col);}
  function draw(){
    // Shift data
    data.shift();const col=[];for(let j=0;j<50;j++){col.push(0.3*Math.sin(j*0.1+t*0.05)+0.3+Math.random()*0.2+(j<15?0.3:0)*(0.5+0.5*Math.sin(t*0.03)));}data.push(col);
    ctx.clearRect(0,0,c.width,c.height);
    const cw=c.width/100,ch=c.height/50;
    data.forEach((col,x)=>{col.forEach((v,y)=>{const h=240-v*200;ctx.fillStyle=`hsl(${h},70%,${20+v*40}%)`;ctx.fillRect(x*cw,(49-y)*ch,cw+1,ch+1);});});
    t++;requestAnimationFrame(draw);
  }draw();
})();

// === ENCODER NN (SVG-based) ===
(function(){
  const svg=document.getElementById('encoder-nn-svg');if(!svg)return;
  const layers=[8,10,8,5,3];
  const layerX=[60,210,360,510,640];
  function getY(l,i){const n=layers[l];const h=n*26;const start=(240-h)/2+20;return start+i*26;}
  let html='';
  for(let l=0;l<layers.length-1;l++){
    for(let i=0;i<layers[l];i++){
      for(let j=0;j<layers[l+1];j++){
        html+=`<line x1="${layerX[l]}" y1="${getY(l,i)}" x2="${layerX[l+1]}" y2="${getY(l+1,j)}" stroke="rgba(100,100,100,0.15)" stroke-width="0.5"/>`;
      }
    }
  }
  for(let l=0;l<layers.length;l++){
    const isLast=l===layers.length-1;const isFirst=l===0;
    for(let i=0;i<layers[l];i++){
      html+=`<circle cx="${layerX[l]}" cy="${getY(l,i)}" r="9" fill="${isFirst?'rgba(255,255,255,0.15)':isLast?'rgba(45,138,78,0.3)':'rgba(100,100,100,0.2)'}" stroke="${isLast?'rgba(45,138,78,0.5)':'rgba(100,100,100,0.4)'}" stroke-width="1.5"/>`;
    }
  }
  for(let p=0;p<8;p++){
    html+=`<circle class="enc-particle" cx="0" cy="0" r="3.5" fill="#555" opacity="0.7" style="display:none;"/>`;
  }
  svg.innerHTML+=html;
  const particles=svg.querySelectorAll('.enc-particle');
  let t=0;
  function animate(){
    particles.forEach((p,idx)=>{
      const layer=Math.floor((t*0.008+idx*0.28)%(layers.length-1));
      const prog=((t*0.008+idx*0.28)%(layers.length-1))-layer;
      const s=idx%layers[layer],d=idx%layers[layer+1];
      p.setAttribute('cx',layerX[layer]+(layerX[layer+1]-layerX[layer])*prog);
      p.setAttribute('cy',getY(layer,s)+(getY(layer+1,d)-getY(layer,s))*prog);
      p.style.display='';
    });
    t++;requestAnimationFrame(animate);
  }
  const obs=new IntersectionObserver(e=>{if(e[0].isIntersecting){animate();obs.unobserve(svg);}},{threshold:0.3});
  obs.observe(svg);
})();

// === QUANTIZATION VIZ ===
(function(){
  const svg=document.getElementById('quant-svg');
  const slider=document.getElementById('cb-slider');
  const label=document.getElementById('cb-label');
  const errLabel=document.getElementById('q-error');
  // Random points
  const pts=[];for(let i=0;i<25;i++)pts.push({x:40+Math.sin(i*2.5)*280+Math.random()*100,y:30+Math.cos(i*1.7)*120+Math.random()*50+20});
  function genCB(n){const e=[];const c=Math.ceil(Math.sqrt(n));const r=Math.ceil(n/c);let idx=0;for(let ri=0;ri<r&&idx<n;ri++)for(let ci=0;ci<c&&idx<n;ci++){e.push({x:60+ci/(c-1||1)*580,y:40+ri/(r-1||1)*230});idx++;}return e;}
  function nearest(p,cb){let md=Infinity,b=cb[0];cb.forEach(e=>{const d=Math.hypot(p.x-e.x,p.y-e.y);if(d<md){md=d;b=e;}});return{e:b,d:md};}
  function render(){
    const n=parseInt(slider.value);label.textContent=n;const cb=genCB(n);let html='';let totalErr=0;
    cb.forEach(e=>{html+=`<rect x="${e.x-5}" y="${e.y-5}" width="10" height="10" rx="2" fill="#d4cfc7" opacity="0.5"/>`;});
    pts.forEach(p=>{const{e,d}=nearest(p,cb);totalErr+=d;html+=`<line x1="${p.x}" y1="${p.y}" x2="${e.x}" y2="${e.y}" stroke="#d32f2f" stroke-width="1" stroke-dasharray="3,3" opacity="0.5"/>`;});
    pts.forEach(p=>{html+=`<circle cx="${p.x}" cy="${p.y}" r="5" fill="#555"/>`;});
    svg.innerHTML=html;
    errLabel.textContent=(totalErr/pts.length).toFixed(1)+' units';
  }
  slider.addEventListener('input',render);render();
})();

// === RVQ CHAIN (dynamic) ===
(function(){
  const btn=document.getElementById('rvq-run');
  const steps=['rvq-1','rvq-2','rvq-3'];
  const totalEl=document.getElementById('rvq-total');
  const origEl=document.getElementById('rvq-0');
  btn.addEventListener('click',()=>{
    // Generate fresh random values each run
    const original=+(2+Math.random()*3).toFixed(2);
    origEl.querySelector('.step-val').textContent=original;
    steps.forEach(s=>{const el=document.getElementById(s);el.style.opacity='0.3';el.style.transition='none';});
    totalEl.textContent='—';
    let remaining=original;
    const vals=[];
    // Pre-compute codebook matches
    for(let i=0;i<3;i++){
      const snap=+remaining.toFixed(i===0?0:1); // round to nearest int, then tenth, etc.
      const nearest=i===0?Math.round(remaining):+(Math.round(remaining*10)/10).toFixed(1);
      const error=+(remaining-nearest).toFixed(4);
      vals.push({nearest,error:Math.abs(error)});
      remaining=error;
    }
    steps.forEach((s,i)=>{
      setTimeout(()=>{
        const el=document.getElementById(s);
        el.style.transition='opacity 0.4s';
        el.style.opacity='1';
        el.querySelector('.step-val').textContent=vals[i].nearest;
        const errEl=el.querySelector('[style*="color:var(--error)"], [style*="color:var(--success)"]');
        if(errEl){
          const err=vals[i].error;
          errEl.textContent='error: '+(err<0.005?'~0.00':err.toFixed(2));
          errEl.style.color=err<0.01?'var(--success)':'var(--error)';
        }
        if(i===steps.length-1){
          const sum=vals.map(v=>v.nearest).reduce((a,b)=>a+b,0);
          totalEl.textContent=vals.map(v=>v.nearest).join(' + ')+' = '+sum.toFixed(2)+' ≈ '+original;
        }
      },(i+1)*800);
    });
  });
})();

// === COVERAGE VIZ (improved) ===
(function(){
  const c=document.getElementById('coverage-viz');if(!c)return;
  const ctx=c.getContext('2d');c.width=c.parentElement.offsetWidth*2;c.height=500;
  const W=c.width,H=c.height;
  const desc=document.getElementById('coverage-desc');
  const tabs=document.querySelectorAll('.tab-btn');
  let lang='en';
  let animT=0;

  // English codebook entries with labels
  const enLabels=['ah','ee','oo','eh','ih','s','t','k','p','f','sh','th','ch','v','z','m','n','ng','l','r','w','b','d','g','uh','ey','ow','aw','oy','er'];
  const enSounds=[];for(let i=0;i<30;i++){
    const angle=i/30*Math.PI*2;const rad=W*0.2+Math.random()*W*0.15;
    enSounds.push({x:W*0.5+Math.cos(angle)*rad+(Math.random()-0.5)*W*0.1,y:H*0.5+Math.sin(angle)*rad*(H/W)+(Math.random()-0.5)*H*0.1,label:enLabels[i]});
  }

  function draw(){
    ctx.clearRect(0,0,W,H);

    // Soft Voronoi-like backgrounds for codebook regions
    enSounds.forEach(s=>{
      const grd=ctx.createRadialGradient(s.x,s.y,0,s.x,s.y,W*0.06);
      grd.addColorStop(0,'rgba(212,207,199,0.08)');grd.addColorStop(1,'transparent');
      ctx.fillStyle=grd;ctx.fillRect(0,0,W,H);
    });

    // Draw codebook entries (larger, with labels)
    enSounds.forEach(s=>{
      ctx.beginPath();ctx.arc(s.x,s.y,14,0,Math.PI*2);
      ctx.fillStyle='rgba(212,207,199,0.2)';ctx.fill();
      ctx.strokeStyle='rgba(212,207,199,0.45)';ctx.lineWidth=1.5;ctx.stroke();
      ctx.fillStyle='rgba(212,207,199,0.55)';ctx.font='bold 11px Fragment Mono';ctx.textAlign='center';
      ctx.fillText(s.label,s.x,s.y+4);
    });

    // Language-specific sounds
    let sounds=[];let closeCount=0,farCount=0;
    if(lang==='en'){
      for(let i=0;i<20;i++)sounds.push({x:enSounds[i%enSounds.length].x+(Math.random()-0.5)*25,y:enSounds[i%enSounds.length].y+(Math.random()-0.5)*25,label:enLabels[i]});
    }else if(lang==='zh'){
      const zhClose=['a','e','i','o','u','s','t','k','p','m','n','l','f','w'];
      const zhFar=['mā↑','má↗','mǎ↘↗','mà↘','zh','ch','x','j','q','ü'];
      for(let i=0;i<14;i++)sounds.push({x:enSounds[i%enSounds.length].x+(Math.random()-0.5)*25,y:enSounds[i%enSounds.length].y+(Math.random()-0.5)*25,label:zhClose[i]});
      for(let i=0;i<10;i++){
        const angle=Math.random()*Math.PI*2;const r=W*0.38+Math.random()*W*0.05;
        sounds.push({x:W*0.5+Math.cos(angle)*r,y:H*0.5+Math.sin(angle)*r*(H/W),label:zhFar[i],far:true});
      }
    }else{
      const arClose=['a','i','u','s','t','k','m','n','l','b'];
      const arFar=['ʕ ain','ħ ha','ʔ','q qaf','ḍ dad','ṣ sad','ṭ ta','ẓ za','ð dhal','ġ ghain','ḫ kha','θ tha','ʃ shin','dʒ jim','r raa'];
      for(let i=0;i<10;i++)sounds.push({x:enSounds[i%enSounds.length].x+(Math.random()-0.5)*25,y:enSounds[i%enSounds.length].y+(Math.random()-0.5)*25,label:arClose[i]});
      for(let i=0;i<15;i++){
        const angle=Math.random()*Math.PI*2;const r=W*0.35+Math.random()*W*0.08;
        sounds.push({x:W*0.5+Math.cos(angle)*r,y:H*0.5+Math.sin(angle)*r*(H/W),label:arFar[i],far:true});
      }
    }

    // Draw sounds with snap lines
    sounds.forEach(s=>{
      let minD=Infinity,best=enSounds[0];
      enSounds.forEach(e=>{const d=Math.hypot(s.x-e.x,s.y-e.y);if(d<minD){minD=d;best=e;}});
      const isClose=minD<60;
      if(isClose)closeCount++;else farCount++;

      if(!isClose){
        // Pulsing glow for far sounds
        const pulse=0.4+0.3*Math.sin(animT*0.05+s.x*0.01);
        const glow=ctx.createRadialGradient(s.x,s.y,0,s.x,s.y,20);
        glow.addColorStop(0,'rgba(196,64,64,'+pulse+')');glow.addColorStop(1,'transparent');
        ctx.fillStyle=glow;ctx.fillRect(s.x-20,s.y-20,40,40);
        // Error line
        ctx.strokeStyle='rgba(196,64,64,0.35)';ctx.lineWidth=1.5;ctx.setLineDash([4,4]);
        ctx.beginPath();ctx.moveTo(s.x,s.y);ctx.lineTo(best.x,best.y);ctx.stroke();ctx.setLineDash([]);
      }

      ctx.beginPath();ctx.arc(s.x,s.y,isClose?8:9,0,Math.PI*2);
      ctx.fillStyle=isClose?'rgba(45,138,78,0.85)':'rgba(196,64,64,0.85)';ctx.fill();
      // Labels for sounds
      if(s.label){
        ctx.fillStyle=isClose?'rgba(45,138,78,0.7)':'rgba(196,64,64,0.7)';
        ctx.font='bold 10px Fragment Mono';ctx.textAlign='left';
        ctx.fillText(s.label,s.x+13,s.y+4);
      }
    });

    // Coverage percentage bar
    const total=closeCount+farCount;
    if(total>0){
      const pct=Math.round(closeCount/total*100);
      const barY=H-40,barX=W*0.15,barW=W*0.7,barH=14;
      ctx.fillStyle='rgba(196,64,64,0.2)';
      ctx.fillRect(barX,barY,barW,barH);
      ctx.fillStyle='rgba(45,138,78,0.6)';
      ctx.fillRect(barX,barY,barW*(pct/100),barH);
      ctx.fillStyle='rgba(255,255,255,0.6)';ctx.font='bold 12px Fragment Mono';ctx.textAlign='center';
      ctx.fillText(pct+'% covered',barX+barW/2,barY+11);
    }

    // Legend
    ctx.font='bold 12px Fragment Mono';ctx.textAlign='left';
    ctx.fillStyle='rgba(212,207,199,0.45)';ctx.fillText('○ codebook entries (english)',20,22);
    ctx.fillStyle='rgba(45,138,78,0.7)';ctx.fillText('● close match',20,40);
    ctx.fillStyle='rgba(196,64,64,0.7)';ctx.fillText('● far (info lost)',W*0.35,40);

    // Description
    if(lang==='en')desc.textContent='english: '+closeCount+'/'+total+' sounds land near codebook entries. low error, great reconstruction.';
    else if(lang==='zh')desc.textContent='mandarin: '+closeCount+' shared sounds are fine, but '+farCount+' tones and phonemes land far from any entry. tonal information destroyed.';
    else desc.textContent='arabic: only '+closeCount+' sounds match. '+farCount+' pharyngeals, emphatics, and unique consonants have no nearby entry.';

    animT++;requestAnimationFrame(draw);
  }

  tabs.forEach(btn=>{btn.addEventListener('click',()=>{tabs.forEach(b=>b.classList.remove('active'));btn.classList.add('active');lang=btn.dataset.tab;});});
  draw();
})();

// === CODEBOOK PALETTE ===
(function(){
  const palette=document.getElementById('codebook-palette');if(!palette)return;
  const hues=[0,25,45,120,180,210,260,300,15,35,55,90,150,195,240,280];
  for(let i=0;i<32;i++){
    const h=hues[i%hues.length]+(i>15?15:0);
    const s=50+Math.random()*30;
    const l=35+Math.random()*25;
    const el=document.createElement('div');
    el.style.cssText=`aspect-ratio:1;border-radius:6px;background:hsl(${h},${s}%,${l}%);transition:all 0.2s;cursor:pointer;border:2px solid transparent;`;
    el.title=`entry #${i+1}`;
    el.addEventListener('mouseenter',()=>{el.style.transform='scale(1.2)';el.style.borderColor='#555';el.style.zIndex='2';});
    el.addEventListener('mouseleave',()=>{el.style.transform='';el.style.borderColor='transparent';el.style.zIndex='';});
    palette.appendChild(el);
  }
})();

// === CODEBOOK VISUAL (2D snap) ===
(function(){
  const c=document.getElementById('codebook-visual');if(!c)return;
  const ctx=c.getContext('2d');c.width=c.parentElement.offsetWidth*2;c.height=560;
  const W=c.width,H=c.height;const info=document.getElementById('codebook-info');
  // Codebook entries — fixed positions
  const entries=[];
  for(let i=0;i<24;i++){
    entries.push({x:W*0.08+Math.random()*W*0.84,y:H*0.08+Math.random()*H*0.84,
      label:['ah','ee','oo','s','t','k','sh','f','th','p','m','n','eh','ih','uh','v','z','ch','ng','l','r','w','j','b'][i],
      hue:[0,20,40,200,210,220,190,215,205,225,170,175,10,15,5,230,235,195,180,165,160,150,155,240][i]});
  }
  // Free-floating input points
  const inputs=[];
  for(let i=0;i<12;i++){
    inputs.push({x:W*0.1+Math.random()*W*0.8,y:H*0.1+Math.random()*H*0.8});
  }
  let hovered=-1;
  function nearest(p){let md=Infinity,bi=0;entries.forEach((e,i)=>{const d=Math.hypot(p.x-e.x,p.y-e.y);if(d<md){md=d;bi=i;}});return{idx:bi,dist:md};}

  function draw(){
    ctx.clearRect(0,0,W,H);
    // Draw grid background with Voronoi-like regions
    entries.forEach(e=>{
      const grd=ctx.createRadialGradient(e.x,e.y,0,e.x,e.y,W*0.12);
      grd.addColorStop(0,`hsla(${e.hue},50%,50%,0.08)`);grd.addColorStop(1,'transparent');
      ctx.fillStyle=grd;ctx.fillRect(0,0,W,H);
    });
    // Draw snap lines for all inputs
    inputs.forEach((p,i)=>{
      const{idx,dist}=nearest(p);const e=entries[idx];
      ctx.setLineDash([4,4]);ctx.strokeStyle=i===hovered?'rgba(196,64,64,0.7)':'rgba(196,64,64,0.2)';
      ctx.lineWidth=i===hovered?2:1;ctx.beginPath();ctx.moveTo(p.x,p.y);ctx.lineTo(e.x,e.y);ctx.stroke();ctx.setLineDash([]);
    });
    // Draw codebook entries
    entries.forEach((e,i)=>{
      ctx.beginPath();ctx.arc(e.x,e.y,14,0,Math.PI*2);
      ctx.fillStyle=`hsla(${e.hue},50%,50%,0.3)`;ctx.fill();
      ctx.strokeStyle=`hsla(${e.hue},50%,50%,0.6)`;ctx.lineWidth=2;ctx.stroke();
      ctx.fillStyle='rgba(0,0,0,0.7)';ctx.font='bold 13px Fragment Mono';ctx.textAlign='center';
      ctx.fillText(e.label,e.x,e.y+5);
    });
    // Draw input points
    inputs.forEach((p,i)=>{
      const r=i===hovered?10:8;
      ctx.beginPath();ctx.arc(p.x,p.y,r,0,Math.PI*2);
      ctx.fillStyle=i===hovered?'#555':'rgba(100,100,100,0.8)';ctx.fill();
      if(i===hovered){ctx.strokeStyle='#fff';ctx.lineWidth=2;ctx.stroke();}
    });
  }
  draw();

  c.addEventListener('mousemove',function(ev){
    const rect=c.getBoundingClientRect();
    const mx=(ev.clientX-rect.left)/rect.width*W;
    const my=(ev.clientY-rect.top)/rect.height*H;
    hovered=-1;
    inputs.forEach((p,i)=>{if(Math.hypot(p.x-mx,p.y-my)<25)hovered=i;});
    if(hovered>=0){
      const{idx,dist}=nearest(inputs[hovered]);
      info.innerHTML=`sound snapped to <strong>"${entries[idx].label}"</strong> — distance: <span style="color:#d32f2f;">${(dist/W*100).toFixed(1)}%</span> of the space lost`;
    }else{info.textContent='hover over orange dots to see the snap in action';}
    draw();
  });
  c.addEventListener('mouseleave',()=>{hovered=-1;info.textContent='hover over orange dots to see the snap in action';draw();});
})();

// === TOKEN CHART ===
createBarChart('token-chart',[
  {label:'DAC (9×86Hz)',value:774},
  {label:'EnCodec (8×75Hz)',value:600},
  {label:'Silk (19×2.5Hz)',value:47.5},
  {label:'Mimi (8×12.5Hz)',value:100},
  {label:'SNAC (multi)',value:82.5},
],{highlight:'DAC (9×86Hz)',yLabel:'tokens per second',height:320});
</script>
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