Explanation of alphaProvenanceCert in IndisputableMonolith.Foundation.AlphaDerivationExplicit
(1) In plain English: The declaration first defines a structure AlphaProvenanceCert that packages four facts: the CODATA value of α⁻¹ lies strictly inside the RS-predicted interval (137.030, 137.039), φ equals (1 + √5)/2, φ > 1, and φ > 3/2. It then supplies a concrete noncomputable instance alphaProvenanceCert that populates every field of the structure, and a theorem proving the structure is inhabited.
(2) Why it matters in Recognition Science: It assembles a minimal provenance certificate showing that the RS α⁻¹ band (derived from the 44π geometric seed and φ-gap) is consistent with experiment, closing the loop from the recognition uniqueness theorem to a numerical prediction without adjustable parameters.
(3) How to read the formal statement: structure AlphaProvenanceCert where declares a record type whose fields are propositions or equalities. The definition alphaProvenanceCert : AlphaProvenanceCert where constructs a term of that type by assigning each field a proof or value (some by direct reference, others via linarith). The theorem alphaProvenance_inhabited simply witnesses that the type is nonempty.
(4) Visible dependencies or certificates in the supplied source: It directly uses the theorem codata_in_band, the definitions alphaInverseLower, alphaInverseUpper, codataAlphaInverse, and the structure AlphaProvenanceCert. The instance is witnessed by alphaProvenance_inhabited. The module also defines the RS formula alphaInverseRS.
(5) What this declaration does not prove: It does not derive the 44π seed, the exponential resummation, or the uniqueness of J(x); those reside in other modules. It does not verify the numerical evaluation of alphaInverseRS beyond the band check, nor does it contain the definitions of the referenced lemmas phi_golden_ratio and phi_gt_onePointFive.