Passes 3989–3996: Physical W33 Photon Processor and Causal Memory

Two physical coupler routes

An ideal 40-mode equal-edge W33 Hamiltonian implements the exact global reflection at κz=π/2. A complementary sparse route uses the 40×40 point–line incidence matrix N, satisfying NNᵀ=4I+A_W33.

The incidence lift has 40 point modes, 40 line buses, 160 couplings, degree four, girth eight, and spectrum -4¹, -√6²⁴, 0³⁰, √6²⁴, 4¹. With bus detuning Δ, its point-sector effective Hamiltonian is -(g²/Δ)(A+4I)+O(g⁴/Δ³).

Dual-geometry echo

For D=A-(J-I-A), the exact sectors are -15¹,5²⁴,-7¹⁵. Two measured moments, ⟨D⟩ and ⟨D²⟩, recover all sector populations. Identical commuting errors in the graph and complement arms cancel exactly.

Maximum-code census

The fixed-parent compatibility graph contains exactly 945 maximum 57-cliques in three parent-group orbits:

945 = 540 + 270 + 135
stabilizers = 96, 192, 384

Two independent exact implementations agree. Maximum-code uniqueness is false in this fixed-parent problem.

Central fusion lattice

The seven simple central degrees 1,1,2,2,2,3,5 produce Bell(7)=877 central coarse-grainings. Quotienting the interchangeable equal-degree blocks leaves exactly 198 inequivalent types.

Wigner–Smith time as operational memory

For S(ω)=exp(iθ(ω)L_W33), the proper-delay operator is exactly Q=-iS†dS/dω=θ′L_W33. Its delay sectors are 0¹,(10θ′)²⁴,(16θ′)¹⁵, with mean 12θ′, variance 12(θ′)², and total trace 480θ′.

This turns “time as memory” into a measurable dwell/storage spectrum. It does not imply a changed vacuum causal-front speed.

Three chained photon constructions

• Dark memory and clock: the incidence lift has 30 exact zero modes, while V=exp(-iπL/4) obeys V²=U and V⁴=I.
• Self-similar history ledger: proper-delay shells are generated by (1+24z¹⁰+15z¹⁶)^m; mean delay is 12mθ′ and relative width is 1/√(12m).
• Information–delay invariant: address bits are m log₂40, so bits per mean proper delay equal log₂40/(12θ′), independent of tensor depth. Preserving a local internal causal cone under refinement requires aJ to remain fixed.

Evidence firewall

These are exact finite-geometry, spectral, code, and Hamiltonian identities plus declared physical models. They do not establish a fabricated processor, literal hidden photon nodes, changed vacuum light speed, measured Wigner–Smith delays, laboratory performance, or a Monster embedding.