IndisputableMonolith.Constants.AlphaNumericsScaffold
Numeric scaffold checking that the Recognition Science inverse-fine-structure construction lands near 137.036. Anyone citing the RS alpha band (137.030, 137.039) uses this as the floating-point certificate. The module wires Alpha constants to gap-weight numerics and runs range and approximation checks.
claimThe RS-native inverse fine-structure value $\alpha^{-1}$ satisfies $\alpha^{-1} \approx 137.036$ and lies in the predicted band $(137.030, 137.039)$, via the gap-weight numeric certificate.
background
Recognition Science fixes dimensionless constants from the forcing chain and the Recognition Composition Law. In RS-native units one has $c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$, and the inverse fine-structure constant is forced into a narrow window around $137.036$.
The parent Alpha module supplies the exact RS construction of $\alpha^{-1}$. GapWeightNumericsScaffold supplies the floating-point match certificate for the gap-weight piece of that construction ("Gap Weight Numeric Match Certificate"). This module only assembles those pieces into explicit numeric checks.
Sibling declarations include a predicted-range check for $\alpha^{-1}$ and an approximation lemma for the gap weight.
proof idea
Definition-and-check module, not a deep proof development. It imports the exact Alpha construction and the gap-weight numeric scaffold, then exposes two sibling checks: one that the constructed $\alpha^{-1}$ sits in the RS band, and one that the gap weight matches its floating-point target. No new analytic argument; the work is wiring and numeric verification.
why it matters in Recognition Science
Closes the numeric side of the RS alpha claim: the construction is not only formal but evaluates to the observed $137.036$ window cited in the framework primer. Downstream consumers of Constants.Alpha can point here for the floating-point certificate rather than re-deriving decimal bounds. No used_by edges are recorded yet; the module is a leaf scaffold under the Constants domain. It supports the broader claim that $\alpha^{-1}\in(137.030,137.039)$ without touching the forcing chain steps T5–T8 themselves.
scope and limits
- Does not prove the exact closed form of $\alpha^{-1}$, only numeric agreement.
- Does not derive the alpha band from the forcing chain; assumes Alpha and gap-weight scaffolds.
- Does not bound floating-point error beyond the stated approximation checks.
- Does not feed recorded downstream theorems yet (used_by is empty).