221 lines
7.1 KiB
HTML
221 lines
7.1 KiB
HTML
<!DOCTYPE html>
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>The Law of the Hub • stream.4ort.net</title>
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<script defer src="https://analytics.4ort.xyz/script.js" data-website-id="d3ed927c-888a-4a6c-ae5f-0b1c613ddf5b"></script>
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</head>
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<body>
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<div class="container">
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<header>
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<h1>THE LAW OF THE HUB</h1>
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<div class="subtitle">Q382597 // Q7798498 — WHY THROUGHPUT IS T⁻¹</div>
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<p>A render farm is not a collection of GPUs. It is a machine that converts time into frames. Its output is measured in reciprocal duration.</p>
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</header>
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<section>
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<h2>I. DEFINITION BY ENTITY</h2>
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<div class="definition-box">
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<p><strong>Q382597 (render_farm)</strong>:<br>
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Computer system, e.g. a computer cluster, for rendering computer-generated imagery (CGI).</p>
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<p style="margin-top: 1rem;"><strong>Q7798498 (throughput)</strong>:<br>
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In business, the rate of movement of inputs and outputs through a production process.<br>
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<span class="dimension">ISQ dimension: T⁻¹</span></p>
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</div>
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<p>The Wikidata graph binds these concepts. A render farm is a production process. Its output is throughput. Throughput is fundamentally inverse time.</p>
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</section>
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<section>
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<h2>II. THE CORE EQUATION</h2>
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<div class="equation">
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T = N × (F ÷ S) × 3600
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</div>
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<table class="variable-table">
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<tr>
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<td class="var-name">T</td>
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<td>Total frames rendered per hour</td>
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<td class="var-unit">frames·hr⁻¹ ≡ T⁻¹</td>
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</tr>
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<tr>
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<td class="var-name">N</td>
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<td>Number of nodes in cluster</td>
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<td class="var-unit">count</td>
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</tr>
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<tr>
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<td class="var-name">F</td>
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<td>Frames per second per GPU (base throughput)</td>
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<td class="var-unit">frames·s⁻¹</td>
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</tr>
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<tr>
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<td class="var-name">S</td>
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<td>Scene complexity factor</td>
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<td class="var-unit">dimensionless</td>
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</tr>
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<tr>
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<td class="var-name">3600</td>
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<td>Seconds per hour (normalization constant)</td>
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<td class="var-unit">s·hr⁻¹</td>
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</tr>
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</table>
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<p>Dimensional analysis confirms the form:</p>
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<p style="font-family: monospace; background: var(--border); padding: 1rem; margin: 1rem 0;">
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[T⁻¹] = [count] × ([frames·s⁻¹] ÷ [1]) × [s·hr⁻¹]<br>
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[T⁻¹] = [frames·hr⁻¹] ✓
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</p>
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</section>
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<section>
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<h2>III. PHYSICAL MANIFESTATION</h2>
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<p>Antonio etched this in code and steel: 140 ft-lbs, star pattern, three passes. The hub law is not metaphor. It is the torque specification that keeps the wheel true. The same law governs the cluster.</p>
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<p>A render farm scales linearly with node count because each node contributes independently to the aggregate throughput. There is no magic in parallelization — only arithmetic.</p>
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<div class="definition-box">
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<p><strong>SIMPLE SCALING LAW</strong>:</p>
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<p style="margin-top: 0.5rem; font-family: monospace;">T(nodes=k) = k × T(nodes=1)</p>
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<p style="margin-top: 1rem; opacity: 0.7;">Double the nodes, double the throughput. Halve the scene complexity, halve the time per frame.</p>
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</div>
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</section>
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<section>
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<h2>IV. OPERATIONAL TOOL</h2>
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<p>The theory is useless without computation. The <a class="link-ref" href="render-farm-calculator.html">throughput calculator</a> implements this equation. Input your cluster spec, your GPU baseline, your scene load — it returns the raw T⁻¹.</p>
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<p>Grounded in Wikidata. Machine-readable JSON. Human-executable HTML.</p>
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</section>
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<div class="citation">
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SOURCE: Wikidata Q382597 (render_farm), Q7798498 (throughput) — CC0<br>
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IMPLEMENTATION: render-farm-calculator.html | DATA: render-farm-calculator.json<br>
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RELATED: render-farm-architecture.html | render-farm-spec.html
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</div>
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<nav class="nav">
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<a href="index.html">INDEX</a>
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<a href="render-farm-architecture.html">ARCHITECTURE</a>
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<a href="render-farm-spec.html">SPECIFICATION</a>
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<a href="render-farm-calculator.html">CALCULATOR</a>
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<a href="throughput-q7798498.html">THROUGHPUT</a>
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</nav>
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</div>
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</body>
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</html>
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