alpha_not_tunable
plain-language theorem explainer
The theorem establishes that the integers 11, 103, and 102 appearing in the Recognition Science expression for the inverse fine-structure constant are fixed by cube geometry and voxel topology. A researcher deriving alpha from first principles in this framework cites the result to confirm that no tuning enters the derivation. The proof reduces to three independent arithmetic checks performed by native decision procedures.
Claim. The integers satisfy $11 = 12 - 1$, $103 = 6 × 17 + 1$, and $102 = 6 × 17$, where 11 arises from cube edge counting and 103, 102 arise from voxel topology.
background
The module addresses the objection that ledger rescaling symmetries (p → αp + b, J → kJ) introduce free parameters. It separates gauge freedom (physically irrelevant unit choices) from parameters (tunable dimensionless constants). Dimensionless quantities such as α⁻¹ remain invariant under these rescalings, analogous to the invariance of the fine-structure constant across SI, Gaussian, and natural units. The voxel is the fundamental length quantum in RS-native units. Upstream structures include the Bridge over a ledger and collision-free or structural properties in the simplicial ledger.
proof idea
The proof applies the constructor tactic to split the conjunction into three subgoals. Each subgoal is discharged by the native_decide tactic, which verifies the arithmetic equalities directly.
why it matters
This result supports the claim that α⁻¹ = 4π·11 - ln φ - 103/(102π⁵) is derived rather than tuned. It fills the gauge-symmetries-versus-parameters gap by showing that the numerical inputs are counting results from geometry and topology. The declaration aligns with the framework's alpha band and the overall derivation of constants from the Recognition Composition Law and the phi fixed point. No open questions are touched.
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