Epoch 14: Harmonic 600-cell (candidate, HOLD)

This archived page is the exact-byte provenance snapshot for the Epoch 14 pilot lab. It is not the live interactive experience -- that is served by the gallery single-page application at /ecosystems/mathematics_v14.html via the discovered epoch package epoch14-harmonic-600cell-r1. This static snapshot documents, in isolation, the mathematics the live lab renders.

Mapping

The 600-cell's 120 vertices have coordinates in ℤ[φ], the ring of integer combinations a + bφ where φ = (1 + √5) / 2 is the golden ratio. For the k vertices whose 4D-to-3D perspective projection lies nearest the camera at any instant, this lab computes a chosen coordinate function of each vertex and normalizes its exact algebraic value into [1, 2) by repeated doubling/halving by powers of two. The resulting ratio belongs to the finite family {1, φ, φ², 2, 1/φ, ...} (each value taken modulo the same normalization), and is sounded as a partial over a 110 Hz base using additive synthesis. Rotation drives glide (a vertex's ratio glides only when its occupied rank among the k nearest vertices changes between control ticks) and amplitude (nearer vertices sound louder, subject to a -12 dBFS ceiling).

Determinism

sonicTable(seed, rotationAngles, time) is a pure function, exported from gallery/src/sonic/sonic-table.mjs and mirrored bit-for-bit in gallery/scripts/sonic_render.py (numpy only). The same inputs always produce the same table and the same rendered PCM SHA-256, in both the browser's additive renderer and the offline Python twin.

Citations