seed_channel_count
plain-language theorem explainer
The α seed channel count is eleven: passive field edges on the three-cube after dropping the single active edge. Anyone auditing the U(1) normalization quarantine cites this as the ledger stiffness in the seed 4π·11. The proof is a one-line term alias of the native decision that passive edges at D=3 equal eleven.
Claim. For spatial dimension $D=3$, the number of passive field edges on the cube equals $11$. That is, total cube edges minus one active edge per tick satisfies $E-1=11$.
background
The Alpha Genesis U(1) module asks whether the geometric seed $4\pi\cdot 11$ promotes from a channel-budget identification to a theorem about gauge-invariant Maxwell normalization on the cube $Q_3$. The module's answer is negative and sharp: eleven is a ledger recognition-channel count, not the gauge-invariant photon degree-of-freedom count.
Passive field edges are total hypercube edges minus the single active edge per tick (the edges that "dress" the interaction). Spatial dimension is fixed at $D=3$ by the linking/forcing requirement. The three-cube has $V=8$ vertices and $E=12$ edges, so removing one active edge leaves eleven passive edges.
Upstream, the AlphaDerivation layer already records that passive edges at $D=3$ equal eleven by closed arithmetic. This declaration simply names that count as the α seed channel count, stressing that only the active edge is removed, not the $V-1=7$ gauge redundancies.
proof idea
One-line term proof. The claim is identified with the upstream theorem that passive field edges at dimension three equal eleven, itself discharged by native_decide on the finite arithmetic of the three-cube edge count. No extra rewriting or case analysis is introduced here.
why it matters
This is the ledger half of the combinatorial core of the U(1) normalization quarantine. Downstream, it is rewritten into the inequality that the seed channel count is not the cube cycle rank (eleven versus five), and it is packaged into the verdict record as the field seed_uses_ledger_count.
In framework terms the declaration blocks promoting $4\pi\cdot 11$ to a U(1) coupling-normalization theorem on $Q_3$. A genuine gauge-invariant Maxwell seed would count independent plaquette strengths, i.e. the cycle rank $b_1=E-V+1=5$ (equivalently six faces minus one Bianchi relation, or twelve links minus seven gauge fixings). That alternative seed is $4\pi\cdot 5=20\pi\approx 62.8$, excluded from the RS $\alpha^{-1}$ band near 137. The number eleven remains a cross-consistent ledger quantity (also in $\Omega_\Lambda=11/16$ and related constructions), but it is not photon stiffness.
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