IndisputableMonolith.Verification.AlphaCorrectionAnalysis
Verification module that isolates the exact additive correction needed for the RS inverse fine-structure value to match the CODATA anchor. Auditors of the alpha gap cite it for positivity, the numerical window from current interval bounds, and four closed-form candidates. The argument is definitional packaging plus bound arithmetic, not a first-principles derivation of alpha.
claimLet $\alpha^{-1}_{\mathrm{RS}}$ be the Recognition-Science inverse fine-structure constant (from the cubic-ledger seed and $\varphi$-dressing) and $\alpha^{-1}_{\mathrm{CODATA}}$ the external anchor. The module defines the required correction $\delta := \alpha^{-1}_{\mathrm{CODATA}} - \alpha^{-1}_{\mathrm{RS}}$, records that $\delta > 0$ under present bounds, extracts a numerical window for $\delta$, and lists candidate closed forms for $\delta$.
background
Recognition Science forces $O(4\pi)$ recognition-scale content and $\varphi$-dressing of the electromagnetic coupling, but the exact infrared value $\alpha^{-1}(0)$ remains an open boundary condition. The cubic-ledger seed $4\pi\cdot 11$ assembles combinatorially; identifying that seed with the measured inverse coupling fails the audit, so comparison to experiment is quarantined.
Constants.ExternalAnchors is the single home for CODATA and other empirical calibration data. Numerics.Interval.AlphaBounds supplies rigorous interval bounds on $\alpha^{-1}$ from the symbolic derivation. This module sits downstream of both: it treats the residual between the RS construction and the CODATA anchor as an explicit correction object rather than absorbing it into the core cost calculus.
Sibling objects include the required correction, positivity lemmas, a correction window from current bounds, four candidate expressions, and a bundled CorrectionAnalysis record.
proof idea
Definition-and-analysis module, not a single theorem. It introduces required_correction as the CODATA-minus-RS residual, then proves positivity from the standing interval bounds (correction_positive, correction_positive_of_alphaInv_lt, correction_window_from_current_bounds). Four named candidates are recorded with value or bound lemmas. A structure CorrectionAnalysis and an analysis instance package the window and candidates for downstream audit. No new derivation of $\alpha$ is attempted; the work is residual bookkeeping against imported anchors and bounds.
why it matters in Recognition Science
Closes a verification gap: the framework primer places $\alpha^{-1}$ in a narrow band near $137.03$–$137.04$, while AlphaDerivation leaves exact $\alpha^{-1}(0)$ OPEN. By naming the residual, proving it is positive under current bounds, and listing candidate closed forms, the module makes the infrared mismatch inspectable rather than hidden in numerics.
No downstream consumers are wired yet (used_by is empty); the module is a leaf in the verification layer. It supports honest status reporting against ExternalAnchors and AlphaBounds without claiming to discharge the open boundary condition in AlphaDerivation or AlphaGenesis.
scope and limits
- Does not derive $\alpha^{-1}(0)$ from the Recognition Composition Law or forcing chain.
- Does not close the OPEN infrared boundary condition stated in AlphaDerivation.
- Does not replace or modify quarantined CODATA anchors.
- Does not assert any candidate correction is forced by T0–T8.
- Does not feed a proved parent theorem yet (no used_by edges).