geometric_seed_factor
plain-language theorem explainer
The geometric seed factor counts the passive edges in the three-dimensional cube that dress the recognition interaction after subtracting the single active edge traversed per tick. Researchers deriving the fine-structure constant from Recognition Science geometry cite this as the source of the factor 11 inside the geometric seed 4π·11. It is obtained by a direct definition that subtracts one from the total edge count of the D=3 cube.
Claim. Let $D=3$ be the spatial dimension forced by the recognition framework. The geometric seed factor is the number of passive field edges, defined as the total number of cube edges minus the single active edge per tick, which equals 11.
background
In the alpha derivation module the fundamental unit cell is the three-dimensional cube with 8 vertices, 12 edges and 6 faces. During one atomic tick a recognition event traverses one edge, leaving the remaining edges to dress the vacuum geometry coupling. The upstream definition states: Passive (field) edges: total edges minus active edge. These are the edges that dress the interaction. The key number: for D=3, passive edges = 11.
proof idea
This is a one-line definition that applies the passive field edges function to the forced dimension D=3.
why it matters
This definition supplies the factor 11 that enters the geometric seed equal to solid angle times 11, which seeds the alpha derivation and appears in the lepton generation step and gauge coupling formulas. It is invoked by the theorem that assembles all magic numbers from D=3 cube geometry and by the verification that the alpha seed equals the geometric seed. It realizes the active-versus-passive distinction forced by single-edge traversal per tick in the cubic ledger and the T8 requirement that D=3.
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