Passes 3965–3972

Topology immunity

Every one of the 79,092,651 edge-toggle patterns through weight three has a distinct residual fingerprint. No alternating weight-four or simple alternating weight-six support is undetectable. A weight-32 relabelling witness gives 8 ≤ d₀ ≤ 32.

Control and dissipation

Four global transvections generate the full 25,920-element symmetry group. Each is nine disjoint three-cycles, but treating those cycles as independent jumps changes the fixed algebra. The exact ideal control minimum is 24 diagonal ports, yielding the full 1,600-dimensional operator algebra.

Self-reproducing boot

An 18-trit seed regenerates all 480 oriented edges in nine BFS layers. Twelve perfect matchings schedule the graph. A 192-entry sensor identifies every defect of weight at most two, with a complete weight-three fallback ledger.

Photon causal density

The user’s intuition survives as a shared causal budget rather than a variable light-speed law. If serial node spacing is ℓ and tick duration τ, Lorentz-compatible propagation requires ℓ/τ=c. For one photon, the quantum speed limit yields:

Nserial ≤ 4 E L/(h c) = 4 L/λ

Serial depth	Minimum length at 1550 nm
2	0.775 μm
12	4.65 μm
39	15.1125 μm
40	15.5 μm
81	31.3875 μm

Parallel modes increase the alphabet dimension without representing the same number of serial state changes. A literal node-count dependence of vacuum speed predicts observable dispersion and is therefore retained only as a falsifiable hypothesis.

Two additional constructions

The W33/complement interferometer separates the common all-to-all channel from W33 contrast. The Cartesian hierarchy has 40^m modes and diameter 2m, proving logarithmic routing depth while preserving the exponential physical mode cost.