Passes 3957–3964 · semantic SHA-256
763b9a6a3f04e3436099ccf9abcc18f2723d0540050ecedacc3a245708ba7148
79 = 3·1² + 2·2² + 3·3² + 4² + 5²
Q^3 ⊕ M2(Q)^2 ⊕ M3(Q)^3 ⊕ M4(Q) ⊕ M5(Q)
398 rotations · 69 layers
232 exact zeros; final diagonal 1^35,-1; 75 exact squared angles; maximum denominator 441.
[36,17,4], A4 = 57
Weight-four intersection graph:
SRG(45,16,8,4) ⊔ K2,2,2 ⊔ K2,2,2.
Q² ⊕ M2(Q)³ ⊕ M3(Q) ⊕ M5(Q)
Seven central sectors; seven cross-carrier channels: six trivial plus one shared 15-dimensional channel.
T=1/ν, λ=c/ν, aN=λ/N, τN=T/N.
aN/τN = c
The rigorous core of the node-packing intuition is scale invariance. Internal spatial and temporal refinements can grow together, increasing accessible mode structure and throughput while their ratio remains the invariant causal speed.
In an ideal tensor-factor model with local dimension d,
R=Nν log2(d) and ρ=N/λ, hence
R/(ρ log2(d))=c.
Capacity firewall: one photon coherently spread over N alternatives is commonly a direct-sum space. With a d-state label its dimension is Nd, giving a classical-information ceiling of log2(Nd) per use, not N log2(d), unless independent tensor factors are physically realized.
Γ⊥ ≤ 2E/(πℏ). For E=hν, Γ⊥T ≤ 4.
An isolated photon cannot perform forty sequential mutually orthogonal W33 updates in one optical period. The forty-node architecture must use parallel or nonorthogonal modes, multiple periods, or external drive. This constrains one literal interpretation without rejecting high-dimensional photonic computation.
No global circuit optimality, global maximality of A4=57, Monster embedding, literal photon-node ontology, variable-speed-of-light mechanism, hardware result, laboratory result, remote CI result, or PDF result is asserted here.