alphaInv_derived
plain-language theorem explainer
This definition assembles the inverse fine-structure constant from the geometric seed of the cubic ledger minus the gap weight and curvature corrections. Researchers deriving constants from discrete geometry cite it to obtain the predicted α⁻¹ near 137 from first principles. The construction is a direct one-line composition of three upstream terms with no further reduction.
Claim. $α^{-1} = 4π·11 - f_{gap} + 103/(102 π^5)$, where $f_{gap}$ is the logarithmic gap correction from the eight-tick structure and the curvature term encodes the 103/102 seam topology of the cubic voxel.
background
Recognition Science builds constants from the cubic ledger on Z³ in D=3. The geometric seed equals 4π·11, with 4π the total curvature of the cube boundary via Gauss-Bonnet and 11 the count of passive edges after one active transition per tick. The curvature term equals -103/(102 π^5), obtained from the five-dimensional integration measure over space, time, and dual balance. The gap weight f_gap supplies the first-order logarithmic correction from the phi-ladder projection. The module states that the Meta-Principle forces a discrete ledger whose unit cell is the cube Q₃, with active edges per tick equal to one and passive field edges equal to eleven.
proof idea
This is a one-line definition that subtracts the sum of the gap weight and curvature term from the geometric seed. It composes the upstream definitions of geometric_seed as solid_angle_Q3 times the passive-edge factor and curvature_term as the negative fraction over π^5.
why it matters
The definition supplies the explicit expression for α⁻¹ that the downstream theorem alphaInv_derived_eq_formula shows equals the target formula 4π·11 minus the gap and curvature corrections. It completes the first-principles derivation of the fine-structure constant from the D=3 cube geometry and the eight-tick octave. The result advances the chain from the Recognition Composition Law through the forcing steps T5-T8 to observable constants.
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