ckmElementScoreCardCert_holds
The declaration certifies existence of a score card structure confirming that Recognition Science geometric predictions for the leading CKM magnitudes match PDG-style experimental values inside one-sigma error bands. Flavor physicists checking cube-geometry derivations against mixing data would cite the result when validating the Phase 2 P2-CKM predictions. The proof constructs the required record by direct substitution of the three matching theorems and three geometric derivation theorems.
claimThere exists a certificate structure $C$ such that $|V_{us}^{pred}-V_{us}^{exp}|<V_{us}^{err}$, $|V_{cb}^{pred}-V_{cb}^{exp}|<V_{cb}^{err}$, $|V_{ub}^{pred}-V_{ub}^{exp}|<V_{ub}^{err}$, together with the geometric identities $V_{us}^{pred}=$ torsion overlap minus Cabibbo radiative correction, $V_{cb}^{pred}=$ edge dual ratio, and $V_{ub}^{pred}=$ fine structure leakage.
background
The CKMElementScoreCard module assembles a certificate structure whose fields are three absolute-difference inequalities and three geometric equalities for the leading CKM elements. Module documentation states the Recognition Science predictions $V_{us}^{pred}=φ^{-3}-(3/2)α$, $V_{cb}^{pred}=1/24$, $V_{ub}^{pred}=α/2$ together with PDG-style experimental central values and 1-sigma bands; the falsifier is any future PDG update that pushes one of the three elements outside its certified inequality. Upstream theorems supply the concrete bounds (row_V_us, row_V_cb, row_V_ub) and the geometric derivations (row_vus_eq_geometry, row_vcb_eq_geometry, row_vub_eq_leakage).
proof idea
The proof is a term-mode record construction that populates the six fields of CKMElementScoreCardCert by direct reference to the six upstream row theorems: row_V_us supplies the V_us inequality, row_vus_eq_geometry supplies the corresponding geometric equality, and likewise for the cb and ub pairs.
why it matters in Recognition Science
The theorem discharges the PARTIAL_THEOREM status recorded in the module documentation for the sigma matches of the leading CKM magnitudes. It thereby certifies the cube-geometry predictions inside the Recognition Science Phase 2 P2-CKM row and supplies the concrete witness required by the certificate structure. No downstream consumers are recorded, leaving open the question of how the certified elements will be packaged into higher-level Wolfenstein or CKMExact statements.
scope and limits
- Does not derive the geometric predictions from the forcing chain or RCL.
- Does not address the full CKM matrix or CP-violating phase.
- Does not incorporate Wolfenstein parametrization or higher-order mixing.
- Does not guarantee invariance under future PDG central-value shifts.
- Does not certify the error bands themselves, only the inequalities given fixed bands.
formal statement (Lean)
54theorem ckmElementScoreCardCert_holds : Nonempty CKMElementScoreCardCert :=
proof body
Term-mode proof.
55 ⟨{ vus := row_V_us
56 vcb := row_V_cb
57 vub := row_V_ub
58 vus_geo := row_vus_eq_geometry
59 vcb_geo := row_vcb_eq_geometry
60 vub_geo := row_vub_eq_leakage }⟩
61
62end
63
64end IndisputableMonolith.Physics.CKMElementScoreCard