MixingCert
MixingCert packages the geometric equalities for CKM elements and the numerical tolerances for PMNS angles into a single certificate. Flavor physicists would cite it when confirming that the derived mixing parameters from the cubic ledger match experimental central values to the listed precision. The structure is assembled directly from the upstream ratio definitions and weight expressions without further reduction steps.
claimA certificate asserting that the predicted CKM element equals the edge-dual ratio, the predicted element equals the fine-structure leakage, and the squared sines of the PMNS angles satisfy the bounds $|sin^2 theta_13 - 0.022| < 0.002$, $|sin^2 theta_12 - 0.307| < 0.01$, and $|sin^2 theta_23 - 0.546| < 0.01$.
background
In the Recognition Science setting the cubic ledger supplies mixing through overlaps of 8-tick windows between generations. The edge-dual ratio is the coupling of face-centered states to vertex states and equals 1/24; V_cb_pred is defined as this ratio while V_ub_pred is the fine-structure leakage term. The PMNS predictions are taken from rung differences: sin^2 theta_12 from solar weight minus radiative correction, sin^2 theta_13 from reactor weight, and sin^2 theta_23 from atmospheric weight plus correction.
proof idea
The declaration is a structure definition that directly records the five field equalities and inequalities. It aggregates the geometric ratio from edge_dual_ratio, the leakage term, and the three angle expressions from the sibling weight definitions; no tactics or lemmas are invoked.
why it matters in Recognition Science
MixingCert supplies the instance used by the downstream theorem mixing_verified to certify the full mixing matrix geometry. It realizes the edge-dual coupling and fine-structure leakage required by the 8-tick octave closure and the unitarity forced by the cubic ledger in Phase 7.2. The certificate closes the topological derivation of the mixing parameters from the forcing chain landmarks T7 and D=3.
scope and limits
- Does not derive the rung weights from the J-cost functional equation.
- Does not prove unitarity of the resulting mixing matrix.
- Does not include CP-violating phases or higher-order corrections.
- Does not address quark-lepton complementarity beyond the listed matches.
formal statement (Lean)
229structure MixingCert where
230 vcb_ratio : V_cb_pred = edge_dual_ratio
231 vub_leakage : V_ub_pred = fine_structure_leakage
232 theta13_match : abs (sin2_theta13_pred - 0.022) < 0.002
233 theta12_match : abs (sin2_theta12_pred - 0.307) < 0.01
234 theta23_match : abs (sin2_theta23_pred - 0.546) < 0.01
235