aeon-hexon-braid — noise → absolute resolution

A signal generator that models how information flows: it starts at maximum entropy (broadband noise) and evolves, along the hexon braid, through a fractional (Hurst/Wiener) regime that contracts the spectrum to a single coherent mode — absolute resolution (gnosis geodesicLength:0).

This is the computational/spectral realization of two existing Lean modules in open-source/gnosis-math/Gnosis/:

SpectralNoiseEquilibrium.lean — signedAlpha: white 0, pink 1, brown 2, blue −1, violet −2 (PSD ∝ 1/f^α); skyrmsBaseDim := 6; soundPlaneDim lift = 6 + lift (the tower). The magnitude-2 colors brown/violet don't fit the dim-6 base plane (brown_not_base_plane, violet_not_base_plane) — they ride a tower lift.
HexonBraid.lean — Hexon = Triton × 2: 6 phases = (past/present/future) × (lifted/contracted), cycling via hexonSucc with proven period 6.

The mapping (both modules, fused): triton phase = spectral magnitude (past 2, present 1, future 0), lifted/contracted = slope sign (+/−). So the hexonSucc 6-cycle is the color journey

brown(+2) → violet(−2) → pink(+1) → blue(−1) → white(0) → grey(0) → brown …
 magnitude   2      2       1       1      0      0

— a weave that spirals inward in spectral magnitude toward the flat future. The braid is the resolution arc: one full hexon period takes max-entropy noise to a single resolved carrier.

Verified (`node hexon-braid.mjs`, real FFT)

Each color's measured spectral exponent matches signedAlpha (brown 2.07, pink 1.05, white 0.07, blue −0.95, violet −1.96).
Resolution (1 − normalized spectral entropy) climbs from 0.069 (primordial white) to ≥ 0.99 (absolute resolution) in one hexon period, climbing to tower lift 1 (soundPlaneDim 7) en route.

Run

/opt/homebrew/bin/node open-source/gnosis/aeon-hexon-braid/hexon-braid.mjs

(Use real node — the sovereign node shim routes .mjs through monster, which rejects the float literals.)

Transmit the braid over the SDR bench (Pluto TX → RTL RX) and verify the per-color spectral slope survives the air — the colors as a real RF journey.
A Lean bridge module tying SpectralNoiseEquilibrium + HexonBraid to the geodesicLength:0 resolution target (the braid-as-resolution theorem).

forkjoin-ai/gnosis