IndisputableMonolith.Constants.AlphaPrecision
The AlphaPrecision module certifies numerical bounds on the inverse fine-structure constant within Recognition Science. It defines alpha_seed together with curvature and gap corrections, then establishes the existence of AlphaPrecisionCert to place alpha inverse inside (137.030, 137.039). Researchers deriving masses or couplings from the phi-ladder would cite these lemmas for RS-native constant values. The module consists of sequential definitions and short positivity lemmas.
claimDefines $132 < alpha_seed < 176$ with $alpha_seed_eq$ and positivity, introduces positive curvature_correction and gap_correction, and certifies existence of AlphaPrecisionCert such that $alpha^{-1} in (137.030, 137.039)$.
background
Recognition Science derives all constants from the J-cost function and the phi-ladder in RS-native units where the base time quantum tau_0 equals 1 tick. The parent Constants module supplies this foundation together with the relations c=1, hbar=phi^{-5}, and G=phi^5/pi. The present module specializes to the fine-structure constant by introducing alpha_seed as the initial phi-ladder value and then adding explicit curvature and gap corrections.
proof idea
This is a definition module. It opens with the alpha_seed definition and its equality and bound lemmas, then defines curvature_correction and gap_correction with their positivity statements, and closes with the AlphaPrecisionCert construction and existence theorem.
why it matters in Recognition Science
The module supplies the certified alpha band required by the mass formula and the T8 step that forces D=3. It feeds downstream constant derivations that rely on the interval (137.030, 137.039) for alpha inverse. No open scaffolding remains inside the module.
scope and limits
- Does not derive alpha from the forcing chain T0-T8.
- Does not compute numerical values beyond the seed and two corrections.
- Does not address other constants such as G or hbar.