alpha_seed
plain-language theorem explainer
The geometric seed 4π × 11 supplies the baseline spherical closure cost over eleven-edge paths for the inverse fine-structure constant. Researchers deriving α_EM from ledger structure in Recognition Science cite this constant. It enters the exponential resummation for alphaInv by direct substitution with no further derivation.
Claim. Let $s := 4π × 11$. This quantity encodes the baseline spherical closure cost over eleven-edge interaction paths in the ledger.
background
In the Constants.Alpha module the fine-structure constant is obtained from an exponential resummation that begins with a geometric seed. The seed represents the spherical closure cost for 11-edge paths. The companion quantity f_gap is the gap weight drawn from the DFT-8 projection in GapWeight. The definition appears in the expression for the dimensionless inverse fine-structure constant obtained as the seed times exp(−f_gap / seed). Upstream results establish the canonical arithmetic object and forcing structures that justify the ledger interpretation.
proof idea
This is a direct definition. No lemmas are applied; the value is fixed by the ledger geometry as 4π times the number of passive edges.
why it matters
This seed feeds the canonical alphaInv definition and the derived alpha. It supplies the structural starting point for the fine-structure constant whose value lies in the interval (137.030, 137.039) predicted by the Recognition framework. The construction closes the loop from the eight-tick octave and D=3 to electromagnetic constants without adjustable parameters.
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