corrected_at_zero
plain-language theorem explainer
Vanishing second-order spectral load recovers the forward genesis value of the inverse fine-structure constant. Anyone working the Alpha Genesis residual target or the unique closing-load problem cites this as the base case of the load-form correction. The proof is a two-line unfold-and-rewrite: both sides reduce to the same channel-budget times continuous weight of the bare spectral load.
Claim. The load-form correction of the inverse fine-structure constant at zero second-order load equals the forward genesis value: if $\mathrm{corrected}(\delta_2) := B\,w(\ell+\delta_2)$ and $\alpha^{-1}_{\mathrm{gen}} := B\,w(\ell)$, then $\mathrm{corrected}(0)=\alpha^{-1}_{\mathrm{gen}}$.
background
This lives in the Alpha Genesis M4 residual-target quarantine. M1–M3 derive $\alpha^{-1}$ blind to CODATA; only this module states the comparison and the open second-order target. Nothing upstream depends on the measured value.
The forward genesis object is $\alpha^{-1}{\mathrm{gen}} = B,w(\ell)$: channel budget times the T9-forced continuous weight at the spectral load, with no legacy pipeline or measurement in the definition. The load-form correction is the same expression with an extra second-order load in the exponent argument: $\mathrm{corrected}(\delta_2) = B,w(\ell+\delta_2)$. M1 forces any second-order term to enter multiplicatively as spectral load, never as an additive display patch (the legacy $\delta\kappa$ form is retired).
The module’s larger goal is uniqueness of the closing load $\delta_2$ that aligns the dressed value with CODATA, and localization of the open seam-geometry derivation of that single number.
proof idea
Term-mode, two steps. Unfold both correctedAlphaInv and alphaInvGenesis so the goal is equality of $B,w(\ell+0)$ and $B,w(\ell)$. Rewrite with add_zero on the spectral-load argument; the continuous weights match and the products agree. No interval arithmetic or CODATA facts are used.
why it matters
Base case of the residual-target pipeline: it pins that the load-form family is a genuine deformation of the genesis value, not a redefinition. Downstream siblings (corrected_at_closingLoad, corrected_eq_codata_iff, existsUnique_closingLoad, seam_closes_iff) build the unique $\delta_2$ that hits CODATA and the open seam-closure criterion on top of this identity.
In the framework, this sits under the Alpha band target ($\alpha^{-1}$ inside $(137.030,137.039)$) and the forced continuous weight from MeasureForcing (T9-adjacent). The anti-epicycle rule still applies: admission of any candidate $\delta_2$ requires a blind seam-geometry derivation, not numerical proximity. Used_by is currently empty; the declaration is infrastructure for the closing-load uniqueness and the OPEN seam target stated in the module doc.
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