### Serve Project Locally with Python

Source: https://github.com/shikhargen/xplain/blob/main/README.md

Use this command to serve the static site locally using Python's built-in HTTP server. Access the site at http://localhost:8000.

```bash
python -m http.server 8000
```

--------------------------------

### Initialize and Draw Animated Retrieval Plot

Source: https://context7.com/shikhargen/xplain/llms.txt

Use `initPlot` to set up the visualization container with candidate and query dots. Use `drawRetrievalPlot` to update query positions and redraw lines connecting to nearest neighbors in real-time.

```javascript
function initPlot() {
  const candidates = [
    [14,28],[20,74],[28,24],[35,68],[39,52],[47,78],
    [61,36],[64,18],[73,62],[81,28],[84,74],[24,46],
    [18,55],[44,18],[68,80],[55,65],[32,42],[76,45],
    [57,24],[49,39],
  ]; // [x%, y%] in the plot coordinate space

  const queries = [
    { x:48, y:46, radius:10, speed:0.00068, phase:0   },
    { x:66, y:57, radius: 8, speed:0.00056, phase:2.2 },
    { x:42, y:30, radius: 7, speed:0.00062, phase:4.1 },
  ];

  const plot = document.getElementById('retrievalPlot');
  plot.innerHTML = `
    <svg class="plot-edges" viewBox="0 0 100 100"
         preserveAspectRatio="none" aria-hidden="true"></svg>
    ${candidates.map(() => '<span class="plot-dot candidate"></span>').join('')}
    ${queries   .map(() => '<span class="plot-dot query"></span>'    ).join('')}
  `;
  // … position candidate nodes via style.left / style.top …
}

function queryPosition(query, time) {
  const angle = time * query.speed + query.phase;
  return {
    x: query.x + Math.cos(angle) * query.radius + Math.sin(angle * 0.7) * 3,
    y: query.y + Math.sin(angle) * query.radius * 0.72 + Math.cos(angle * 0.8) * 2,
  };
}

function drawRetrievalPlot(time) {
  if (!retrievalPlot) return;
  const lines = [];

  retrievalPlot.queries.forEach((query, qi) => {
    const pos = queryPosition(query, time);
    const x = Math.max(8,  Math.min(92, pos.x));
    const y = Math.max(10, Math.min(90, pos.y));

    // Move the query dot element
    retrievalPlot.queryNodes[qi].style.left = `${x}%`;
    retrievalPlot.queryNodes[qi].style.top  = `${y}%`;

    // Connect to the 4 nearest candidates (approximate KNN)
    retrievalPlot.candidates
      .map(c => ({ c, dist: (c.x - x) ** 2 + (c.y - y) ** 2 }))
      .sort((a, b) => a.dist - b.dist)
      .slice(0, 4)
      .forEach(({ c }) => {
        lines.push(
          `<line x1="${x.toFixed(2)}" y1="${y.toFixed(2)}"
                 x2="${c.x}" y2="${c.y}" />`
        );
      });
  });

  retrievalPlot.edges.innerHTML = lines.join('');
  // SVG lines styled via .plot-edges line { stroke: rgba(244,184,96,0.32); }
}
```

--------------------------------

### Seed and Draw Seven-Stage Pipeline Animation

Source: https://context7.com/shikhargen/xplain/llms.txt

Initializes particles for the pipeline animation and draws the animated pipeline with stage nodes, connectors, and moving particles. Particles are filtered out at stage 3 with a higher probability. Use this for visualizing a multi-stage process.

```javascript
function seedPipeline() {
  resizeCanvas(pipelineCanvas, pipelineCtx);
  pipelineParticles = Array.from({ length: 36 }, (_, i) => ({
    lane:   i % 7,
    offset: Math.random(),       // progress 0→1 along current lane
    drift:  Math.random() * 0.8, // vertical sine wobble seed
    size:   3 + Math.random() * 5,
    keep:   Math.random() > 0.26, // ~74 % survive the filter stage
    score:  0.4 + Math.random() * 0.55,
    color:  ['#4db7d9', '#f4b860', '#5bd69a', '#6574ff'][i % 4],
  }));
}

// Stage labels rendered inside the canvas nodes
const STAGE_LABELS = ['History', 'Sources', 'Hydrate', 'Filter', 'Predict', 'Rank', 'Feed'];

function drawPipeline(time) {
  const { width: w, height: h } = pipelineCanvas.getBoundingClientRect();
  pipelineCtx.clearRect(0, 0, w, h);

  // Zigzag node positions (alternating top / bottom row)
  const nodes = Array.from({ length: 7 }, (_, i) => ({
    x: w * (0.11 + i * 0.13),
    y: i % 2 === 0 ? h * 0.16 : h * 0.82,
  }));

  // Bezier connectors
  for (let i = 0; i < nodes.length - 1; i++) {
    pipelineCtx.beginPath();
    pipelineCtx.strokeStyle = 'rgba(255,255,255,0.18)';
    pipelineCtx.lineWidth   = 2;
    pipelineCtx.moveTo(nodes[i].x, nodes[i].y);
    pipelineCtx.bezierCurveTo(
      nodes[i].x   + w * 0.08, nodes[i].y,
      nodes[i+1].x - w * 0.08, nodes[i+1].y,
      nodes[i+1].x,            nodes[i+1].y
    );
    pipelineCtx.stroke();
  }

  // Stage node boxes
  nodes.forEach((node, i) => {
    const active = i === activeStage;
    pipelineCtx.fillStyle   = active ? 'rgba(91,214,154,0.22)' : 'rgba(255,255,255,0.08)';
    pipelineCtx.strokeStyle = active ? '#5bd69a'              : 'rgba(255,255,255,0.18)';
    pipelineCtx.lineWidth   = active ? 2 : 1;
    pipelineCtx.beginPath();
    pipelineCtx.roundRect(node.x - 44, node.y - 26, 88, 52, 8);
    pipelineCtx.fill();
    pipelineCtx.stroke();
    pipelineCtx.fillStyle = active ? '#f5f1e8' : '#a8b0b8';
    pipelineCtx.font      = '700 11px Inter, system-ui, sans-serif';
    pipelineCtx.textAlign = 'center';
    pipelineCtx.fillText(STAGE_LABELS[i], node.x, node.y + 4);
  });

  // Animate particles along lanes
  pipelineParticles.forEach((p) => {
    p.offset += 0.0025 + p.score * 0.002; // advance; faster for higher-scored posts
    if (p.offset > 1) {
      p.offset = 0;
      p.lane   = (p.lane + 1) % 6;
      p.keep   = Math.random() > (p.lane === 3 ? 0.42 : 0.16); // ~42% filtered at stage 3
    }
    const a    = nodes[Math.min(p.lane, nodes.length - 2)];
    const b    = nodes[Math.min(p.lane + 1, nodes.length - 1)];
    const ease = p.offset ** 2 * (3 - 2 * p.offset); // smoothstep
    const x    = a.x + (b.x - a.x) * ease;
    const y    = a.y + (b.y - a.y) * ease + Math.sin(time / 450 + p.drift) * 8;
    const fade = p.keep ? 0.85 : Math.max(0.18, 1 - p.offset * 1.4);

    pipelineCtx.beginPath();
    pipelineCtx.globalAlpha = fade;
    pipelineCtx.fillStyle   = p.keep ? p.color : '#ff5a61'; // red = filtered out
    pipelineCtx.arc(x, y, p.size, 0, Math.PI * 2);
    pipelineCtx.fill();
    pipelineCtx.globalAlpha = 1;
  });
}
```

--------------------------------

### Compute Weighted Ranking Score with `scoreState()`

Source: https://context7.com/shikhargen/xplain/llms.txt

Implements the production ranking formula, calculating a weighted score based on predicted action probabilities, negative feedback risk, diversity, and out-of-network factors. Returns a breakdown of intermediate values.

```javascript
const state = {
  favorite: 42,   // predicted like probability (0–100)
  reply:    18,   // predicted reply probability
  repost:   24,   // predicted repost probability
  dwell:    55,   // predicted dwell probability
  follow:   11,   // predicted follow-author probability
  negative:  8,   // predicted negative feedback risk
  repeat:    1,   // same-author repeat count in current feed response
  oon:      82,   // out-of-network context factor (50–120)
};

const weights = {
  favorite:  1.0,
  reply:     0.5,
  repost:    0.3,
  dwell:     0.2,
  follow:    0.35,
  negative: -1.1,  // negative weight; magnitude subtracted from score
};

function scoreState() {
  // Normalize all probabilities to [0, 1]
  const normalized = Object.fromEntries(
    Object.entries(state).map(([key, value]) => [key, value / 100])
  );

  // Positive contribution: sum(w_i * p_i)
  const positive = 
    normalized.favorite * weights.favorite +
    normalized.reply    * weights.reply    +
    normalized.repost   * weights.repost   +
    normalized.dwell    * weights.dwell    +
    normalized.follow   * weights.follow;

  // Negative contribution: risk score
  const negative = normalized.negative * Math.abs(weights.negative);

  const raw = positive - negative;

  // Diversity decay for same-author repeat appearances
  const decay = 0.72;
  const floor = 0.36;
  const diversity = (1 - floor) * decay ** state.repeat + floor;

  // Out-of-network penalty/bonus factor
  const oonFactor = state.oon / 100;

  // Final score: raw * diversity * oonFactor (clamped to 0)
  const final = Math.max(0, raw * diversity * oonFactor);

  return { positive, negative, raw, diversity, oonFactor, final };
}

// Example output for default slider values:
// {
//   positive:   0.6830,   // weighted sum of positive signals
//   negative:   0.0880,   // negative feedback penalty
//   raw:        0.5950,   // positive − negative
//   diversity:  0.6808,   // decay^1 * (1−0.36) + 0.36
//   oonFactor:  0.8200,   // oon / 100
//   final:      0.3321    // displayed as "0.332"
// }
console.log(scoreState());

```

--------------------------------

### Background Particle Network Animation (JavaScript)

Source: https://context7.com/shikhargen/xplain/llms.txt

Initializes and draws a network of floating particles on a canvas. Particles move, wrap around edges, and connect with lines to nearby particles, with line opacity decreasing with distance.

```javascript
function seedHero() {
  resizeCanvas(heroCanvas, heroCtx);
  const { width, height } = heroCanvas.getBoundingClientRect();

  heroParticles = Array.from({ length: 72 }, (_, i) => ({
    x:   Math.random() * width,
    y:   Math.random() * height,
    r:   1.4 + Math.random() * 3.8,          // radius 1.4–5.2 px
    vx: -0.18 + Math.random() * 0.36,         // horizontal velocity
    vy: -0.12 + Math.random() * 0.24,         // vertical velocity
    hue: i % 4,                               // index into palette
  }));
}

function drawHero() {
  const palette = ['#4db7d9', '#f4b860', '#5bd69a', '#ff5a61'];
  const { width: w, height: h } = heroCanvas.getBoundingClientRect();
  heroCtx.clearRect(0, 0, w, h);

  heroParticles.forEach((p, idx) => {
    // Advance position and wrap at edges
    p.x += p.vx;
    p.y += p.vy;
    if (p.x < -20) p.x = w + 20;
    if (p.x > w + 20) p.x = -20;
    if (p.y < -20) p.y = h + 20;
    if (p.y > h + 20) p.y = -20;

    // Draw particle dot
    heroCtx.beginPath();
    heroCtx.fillStyle   = palette[p.hue];
    heroCtx.globalAlpha = 0.45;
    heroCtx.arc(p.x, p.y, p.r, 0, Math.PI * 2);
    heroCtx.fill();

    // Draw connection lines to nearby particles
    for (let j = idx + 1; j < heroParticles.length; j++) {
      const q    = heroParticles[j];
      const dist = Math.hypot(p.x - q.x, p.y - q.y);
      if (dist < 120) {
        heroCtx.beginPath();
        heroCtx.strokeStyle  = palette[p.hue];
        heroCtx.globalAlpha  = (1 - dist / 120) * 0.12; // fade with distance
        heroCtx.lineWidth    = 1;
        heroCtx.moveTo(p.x, p.y);
        heroCtx.lineTo(q.x, q.y);
        heroCtx.stroke();
      }
    }
  });
  heroCtx.globalAlpha = 1; // reset alpha
}
```

--------------------------------

### scoreState()

Source: https://context7.com/shikhargen/xplain/llms.txt

Computes the weighted ranking score from the current slider state, implementing the full production ranking formula. It returns a breakdown object with intermediate values.

```APIDOC
## scoreState()

### Description
Computes the weighted ranking score from the current slider state, implementing the full production ranking formula. It returns a breakdown object with intermediate values.

### Parameters
This function does not take any explicit parameters. It uses an internal `state` object representing user interactions.

### State Object (Internal)
- **favorite** (number) - Predicted like probability (0–100)
- **reply** (number) - Predicted reply probability (0–100)
- **repost** (number) - Predicted repost probability (0–100)
- **dwell** (number) - Predicted dwell probability (0–100)
- **follow** (number) - Predicted follow-author probability (0–100)
- **negative** (number) - Predicted negative feedback risk (0–100)
- **repeat** (number) - Same-author repeat count in current feed response
- **oon** (number) - Out-of-network context factor (50–120)

### Weights Object (Internal)
- **favorite** (number) - Weight for favorite probability
- **reply** (number) - Weight for reply probability
- **repost** (number) - Weight for repost probability
- **dwell** (number) - Weight for dwell probability
- **follow** (number) - Weight for follow-author probability
- **negative** (number) - Negative weight for feedback risk (magnitude subtracted from score)

### Return Value
An object containing the breakdown of the calculated score:
- **positive** (number) - Weighted sum of positive signals.
- **negative** (number) - Negative feedback penalty.
- **raw** (number) - The score before diversity and out-of-network adjustments (positive - negative).
- **diversity** (number) - The diversity decay factor applied based on repeat count.
- **oonFactor** (number) - The out-of-network context factor, normalized.
- **final** (number) - The final calculated score, clamped to a minimum of 0.

### Example Usage
```javascript
// Internal state mirrors the eight slider inputs
const state = {
  favorite: 42,
  reply:    18,
  repost:   24,
  dwell:    55,
  follow:   11,
  negative:  8,
  repeat:    1,
  oon:      82,
};

const weights = {
  favorite:  1.0,
  reply:     0.5,
  repost:    0.3,
  dwell:     0.2,
  follow:    0.35,
  negative: -1.1,
};

function scoreState() {
  // Normalize all probabilities to [0, 1]
  const normalized = Object.fromEntries(
    Object.entries(state).map(([key, value]) => [key, value / 100])
  );

  // Positive contribution: sum(w_i * p_i)
  const positive = 
    normalized.favorite * weights.favorite +
    normalized.reply    * weights.reply    +
    normalized.repost   * weights.repost   +
    normalized.dwell    * weights.dwell    +
    normalized.follow   * weights.follow;

  // Negative contribution: risk score
  const negative = normalized.negative * Math.abs(weights.negative);

  const raw = positive - negative;

  // Diversity decay for same-author repeat appearances
  const decay = 0.72;
  const floor = 0.36;
  const diversity = (1 - floor) * decay ** state.repeat + floor;

  // Out-of-network penalty/bonus factor
  const oonFactor = state.oon / 100;

  // Final score: raw * diversity * oonFactor (clamped to 0)
  const final = Math.max(0, raw * diversity * oonFactor);

  return { positive, negative, raw, diversity, oonFactor, final };
}

// Example output for default slider values:
// {
//   positive:   0.6830,
//   negative:   0.0880,
//   raw:        0.5950,
//   diversity:  0.6808,
//   oonFactor:  0.8200,
//   final:      0.3321
// }
console.log(scoreState());
```
```

--------------------------------

### Set Active Pipeline Stage and CSS Classes

Source: https://context7.com/shikhargen/xplain/llms.txt

Updates the active stage index and toggles the 'active' CSS class on corresponding HTML elements for stage nodes and list items. This ensures visual consistency across the pipeline visualization and its textual description. Use this to synchronize UI elements with the current pipeline stage.

```javascript
let activeStage    = 0;
let stageStartedAt = performance.now();

function setActiveStage(next) {
  activeStage = next;
  // CSS class on the HTML stage-node strip
  document.querySelectorAll('.stage-node').forEach((node, i) =>
    node.classList.toggle('active', i === activeStage)
  );
  // CSS class on the numbered prose steps list
  document.querySelectorAll('#steps li').forEach((step, i)
    step.classList.toggle('active', i === activeStage)
  );
}

// Auto-advance every 2100 ms inside the rAF loop
function tick(time) {
  drawHero();
  if (time - stageStartedAt > 2100) {
    setActiveStage((activeStage + 1) % 7);
    stageStartedAt = time;
  }
  drawPipeline(time);
  drawRetrievalPlot(time);
  requestAnimationFrame(tick);
}

// Replay button resets to stage 0
document.getElementById('replayPipeline').addEventListener('click', () => {
  setActiveStage(0);
  stageStartedAt = performance.now();
  seedPipeline();
});
```

--------------------------------

### Update Score Readout and Visualizations (JavaScript)

Source: https://context7.com/shikhargen/xplain/llms.txt

Updates the DOM with score data, including a large numeric display, progress bars, and hero panel metrics. Initializes the score display on page load and listens for input events to update the score live.

```javascript
function makeBar(label, value, negative = false) {
  const pct = Math.max(0, Math.min(100, value * 100));
  return `
    <div class="bar-row">
      <span>${label}</span>
      <span class="bar-track">
        <span class="bar-fill ${negative ? 'negative' : ''}"
              style="width:${pct}%"></span>
      </span>
      <strong>${value.toFixed(2)}</strong>
    </div>
  `;
}

function updateScore() {
  const s = scoreState();

  // Large score display
  document.getElementById('scoreValue').textContent = s.final.toFixed(3);

  // Five decomposition bars
  document.getElementById('scoreBars').innerHTML = [
    makeBar('Positive',   s.positive),
    makeBar('Negative',   s.negative,        true),  // red bar
    makeBar('Raw',        Math.max(0, s.raw)),
    makeBar('Diversity',  s.diversity),
    makeBar('OON factor', s.oonFactor),
  ].join('');

  // Hero panel live metrics
  document.getElementById('heroRetrieval').textContent =
    (0.64 + state.dwell / 500).toFixed(2);   // proxy for retrieval score
  document.getElementById('heroPositive').textContent =
    s.positive.toFixed(2);
  document.getElementById('heroRisk').textContent =
    s.negative.toFixed(2);
  document.getElementById('heroFinal').textContent =
    s.final.toFixed(2);
}

// Wire up all range inputs to live-update the score
document.getElementById('scoreControls').addEventListener('input', (event) => {
  const input = event.target;
  if (!(input instanceof HTMLInputElement)) return;
  state[input.dataset.key] = Number(input.value); // e.g. data-key="favorite"
  updateScore();
});

updateScore(); // initialize on page load
```

--------------------------------

### Ranking Equation Formula

Source: https://github.com/shikhargen/xplain/blob/main/index.html

The core ranking equation combines weighted probabilities of user actions with risk and context factors. This formula is central to determining a post's visibility.

```plaintext
score = sum(w_i * p_i) - risk + context
```

--------------------------------

### Retrieval Model Similarity Calculation

Source: https://github.com/shikhargen/xplain/blob/main/index.html

The retrieval model uses vector similarity to find candidate posts relevant to a user's history and topic context. This is a key step in identifying potential content.

```plaintext
top_k = argmax(user_vector dot post_author_vector)
```

--------------------------------

### Diversity Multiplier Calculation

Source: https://github.com/shikhargen/xplain/blob/main/index.html

This formula determines the multiplier applied to posts from the same author to ensure feed diversity. It attenuates repeated content based on its position.

```plaintext
multiplier = (1 - floor) * decay^position + floor
```

--------------------------------

### Raw and Final Ranking Equation

Source: https://github.com/shikhargen/xplain/blob/main/index.html

This shows the raw score calculation and how it's adjusted by diversity and out-of-network factors to produce the final ranking. It highlights the impact of external content.

```plaintext
S_raw = sum(w_i p_i)
S_final = diversity(S_raw) * oon_factor
```

--------------------------------

### HiDPI-Aware Canvas Resize

Source: https://context7.com/shikhargen/xplain/llms.txt

Ensures canvas drawing coordinates remain consistent across high-resolution displays by scaling the canvas dimensions and resetting the context transform. This function should be called whenever the canvas resizes.

```javascript
function resizeCanvas(canvas, ctx) {
  const dpr  = Math.min(window.devicePixelRatio || 1, 2);
  const rect = canvas.getBoundingClientRect();
  canvas.width  = Math.max(1, Math.floor(rect.width  * dpr));
  canvas.height = Math.max(1, Math.floor(rect.height * dpr));
  ctx.setTransform(dpr, 0, 0, dpr, 0, 0); // scale drawing commands to CSS px
}

// Re-seed on viewport resize to redistribute particles
window.addEventListener('resize', () => {
  seedHero();
  seedPipeline();
});
```

--------------------------------

### CanvasRenderingContext2D.prototype.roundRect Polyfill

Source: https://context7.com/shikhargen/xplain/llms.txt

Provides a `roundRect` method for the 2D canvas context, enabling the drawing of rounded rectangles in browsers that do not natively support this feature. This is useful for creating visually distinct node boxes.

```javascript
CanvasRenderingContext2D.prototype.roundRect ||= function roundRect(
  x, y, width, height, radius
) {
  const r = Math.min(radius, width / 2, height / 2);
  this.moveTo(x + r, y);
  this.arcTo(x + width, y,      x + width, y + height, r);
  this.arcTo(x + width, y + height, x,     y + height, r);
  this.arcTo(x,         y + height, x,     y,           r);
  this.arcTo(x,         y,          x + r, y,           r);
  this.closePath();
};

// Usage (pipeline stage nodes):
pipelineCtx.beginPath();
pipelineCtx.roundRect(node.x - 44, node.y - 26, 88, 52, 8);
pipelineCtx.fill();
pipelineCtx.stroke();
```

--------------------------------

### Scoring Formula for Actions

Source: https://github.com/shikhargen/xplain/blob/main/index.html

This formula calculates the weighted score based on predicted probabilities of various user actions. Both positive and negative actions contribute to the final score.

```plaintext
sum(action_probability * action_weight)
```

=== COMPLETE CONTENT === This response contains all available snippets from this library. No additional content exists. Do not make further requests.