THE LAW OF THE HUB

Q382597 // Q7798498 — WHY THROUGHPUT IS T⁻¹

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.

I. DEFINITION BY ENTITY

Q382597 (render_farm):
Computer system, e.g. a computer cluster, for rendering computer-generated imagery (CGI).

Q7798498 (throughput):
In business, the rate of movement of inputs and outputs through a production process.
ISQ dimension: T⁻¹

The Wikidata graph binds these concepts. A render farm is a production process. Its output is throughput. Throughput is fundamentally inverse time.

II. THE CORE EQUATION

T = N × (F ÷ S) × 3600
T Total frames rendered per hour frames·hr⁻¹ ≡ T⁻¹
N Number of nodes in cluster count
F Frames per second per GPU (base throughput) frames·s⁻¹
S Scene complexity factor dimensionless
3600 Seconds per hour (normalization constant) s·hr⁻¹

Dimensional analysis confirms the form:

[T⁻¹] = [count] × ([frames·s⁻¹] ÷ [1]) × [s·hr⁻¹]
[T⁻¹] = [frames·hr⁻¹] ✓

III. PHYSICAL MANIFESTATION

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.

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.

SIMPLE SCALING LAW:

T(nodes=k) = k × T(nodes=1)

Double the nodes, double the throughput. Halve the scene complexity, halve the time per frame.

IV. OPERATIONAL TOOL

The theory is useless without computation. The throughput calculator implements this equation. Input your cluster spec, your GPU baseline, your scene load — it returns the raw T⁻¹.

Grounded in Wikidata. Machine-readable JSON. Human-executable HTML.

SOURCE: Wikidata Q382597 (render_farm), Q7798498 (throughput) — CC0
IMPLEMENTATION: render-farm-calculator.html | DATA: render-farm-calculator.json
RELATED: render-farm-architecture.html | render-farm-spec.html