gap3_resolved
plain-language theorem explainer
Gap3 resolved establishes that the inverse fine-structure constant remains fixed under rescalings of the ledger p and cost J. A physicist deriving constants without free parameters would cite it to rebut objections that continuous symmetries introduce tunability. The argument reduces directly to the prior gauge-invariance result for alphaInv.
Claim. For all real numbers $a, k, b$ with $a ≠ 0$ and $k ≠ 0$, the inverse fine-structure constant $α^{-1}$ is unchanged under the transformations $p ↦ a p + b$ and $J ↦ k J$.
background
Gap 3 distinguishes gauge freedoms from physical parameters in the Recognition Science ledger. Gauge choices leave dimensionless outputs invariant while parameters would alter them. The module resolves the objection that ledger rescalings $p → αp + b$ and $J → kJ$ constitute tunable degrees of freedom by showing they cancel in quantities such as $α^{-1}$ (analogous to unit-system independence of $α$ in QED).
proof idea
The proof is a one-line wrapper that applies alphaInv_gauge_invariant. That upstream theorem introduces the rescaling variables and concludes by reflexivity.
why it matters
This result closes Gap 3 by confirming that RS derivations of constants involve only gauge choices, not parameters, supporting the zero-parameter claim in the forcing chain. It aligns with the recognition composition law and the derivation of $α^{-1}$ from geometry, voxel topology, and the cost fixed point $φ$. No downstream uses are recorded yet.
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