closure_term_derived_from_geometry
plain-language theorem explainer
Boolean status flag asserting that the fine-structure inverse closure correction is carried in canonical geometric seed/gap form rather than as an independent ad-hoc symbol. Verification authors cite it when auditing α⁻¹ resolution readiness. The body is the constant true, a deliberate status marker, not a derived proof.
Claim. The status flag that the additive closure correction to $\alpha^{-1}$ is represented in canonical geometric seed/gap form (and is no longer an independent ad-hoc symbol) equals $\mathrm{true}$.
background
Alpha Resolution Pass 2 turns the residual mismatch between the current symbolic Recognition Science formula for $\alpha^{-1}$ and the CODATA anchor into an explicit additive closure target. The module does not yet derive a new geometric correction from first principles; it defines the exact shift needed for alignment and proves the corrected value sits on the CODATA value (and inside the 3$\sigma$ band).
In RS-native units one has $c=1$ and $\hbar=\varphi^{-5}$, with $\alpha^{-1}$ targeted inside a narrow band near $137.03$. Sibling definitions in this module name the required additive correction $\delta\alpha^{-1}$, a geometric candidate for that correction, and the corrected inverse fine-structure value. The present declaration is only a Boolean readiness marker that the closure term has been rewritten in geometric seed/gap language.
Upstream status strings from RS-native units, discrete Lichnerowicz convergence (flat TT-axis sector only), and alignment protocols supply ambient infrastructure; they are not premises of a calculation here.
proof idea
Definitional constant: the declaration is def ... : Bool := true. There is no tactic proof, no lemma application, and no algebraic reduction. The value true is the intentional status bit that downstream closure_status conjoins with equality and uniqueness statements about the geometric and required corrections.
why it matters
Feeds the conjunction in closure_status, which packages geometric-form readiness, equality of geometric and required $\delta\alpha^{-1}$, exact CODATA match of the corrected inverse, uniqueness of the additive closure, and the forced curvature exponent $d=5$ in the power family. That bundle is the formal target the module doc states for a future first-principles derivation: obtain this correction (or an equivalent) from RS geometry rather than by fitting.
Within the broader framework this sits on the $\alpha$ band near $(137.030,137.039)$ and on the $\varphi$-ladder / RS-native unit conventions ($\hbar=\varphi^{-5}$). It does not itself close T0–T8 or the Recognition Composition Law; it records that the residual is no longer an orphan symbol, so later geometric work has a sharp equality to hit.
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