The 3-D coherency channel — 3-PSK on cube-root-of-unity phases, orthogonal FDM,
activity-driven frequency deviation with return-to-baseline, GPU FFT decode, quaternion-delta
fusion + bit-packing, and attractor compression of the state-space trajectory. Same systems as
the original design, but every claim is now measured against theory, live in this page and
in the Python reference coherency_channel.py.
| Subsystem | Claim | Measured | Theory / target | |
|---|---|---|---|---|
| measuring… | ||||
All numbers above are computed in this page (Monte-Carlo,
exact algebra, and rate–distortion) and match coherency_channel.py. The 3-PSK
constellation is literally the cube roots of unity — 1+ω+ω²=0, the same identity
that zeroes the Trefoil_Streams emergent phase. The decoder is an exact certifier (Helix B);
the FFT bank that flags active bins is the heuristic oracle (Helix A).
Three semantic sub-states per carrier sit at {0°, 120°, 240°}.
Frequency deviates on activity, then drifts back to baseline — an Ornstein–Uhlenbeck / AR(1)
process whose settling time and noise floor are exactly characterizable.
Monte-Carlo decode (add complex Gaussian noise → atan2(Q,I) → nearest
symbol), measured against the nearest-neighbour MPSK law
SEP ≈ 2·Q(√(2·Es/N0)·sin(π/3)). Markers = measured; line = theory.
Carrier peaks align with the others' nulls. At integer-bin spacing the carriers are exactly orthogonal (measured crosstalk ~1e-16); half-bin spacing leaks.
A low-frequency semantic triplet provides context for a high-frequency quaternion
stream. The fused packet is 1 flag + 5 state-index + 16 Δq bits. The 16-bit delta is
a rotation-vector (log-map) quantization — the right tool for near-identity deltas — giving ~8×
compression vs float32 quaternions at sub-degree closed-loop error (the Engram_Codec offload).
Run-length-encode the piecewise-constant semantic states; delta-encode the smooth quaternion frames; store only on change. Measured end-to-end compression vs raw per-frame.
The semantic triplet (s₁,s₂,s₃) traces a path through a 27-state space. A learned,
stable pattern (attractor) has low transition entropy, so the path compresses far below
log₂(27) ≈ 4.75 bits/step — the same lesson as the Polycentria router/oracle:
structure is compressibility. The simulation shows three forward/reverse sequences feeding a
central coherency node.
Reference: coherency_channel.py
(pure stdlib; exact ℚ[√3] / ℚ[√5] checks, MPSK theory, OU/AR(1), rate–distortion) and its
captured output coherency_channel_output.txt. Part of Experimental Systems →
see ../POLYCENTRIA.md.