IndisputableMonolith.Physics.PMNSScoreCard
The PMNSScoreCard module assembles rows for the three PMNS mixing angles, the Jarlskog invariant, and a positivity check, then certifies that the derived values lie in the open experimental band. Neutrino physicists testing geometric predictions from Recognition Science against oscillation data would cite these rows. The module consists of direct row definitions that aggregate into one certification statement.
claimThe PMNS scorecard certifies the derived values of the mixing angles $θ_{12}$, $θ_{13}$, $θ_{23}$ and Jarlskog invariant $J$ obtained from the $φ$-angle construction of the neutrino mixing matrix.
background
The module operates inside Phase 7.2 of the Recognition Science program on CKM and PMNS mixing. It imports the MixingDerivation module, whose stated purpose is to formalize the geometric derivation of the mixing matrix elements from the cubic ledger structure, replacing numerical matches with topological proofs, beginning with the observation that edge-dual coupling determines the coupling between generations. It also imports the StandardModel.PMNSMatrix module, whose target is to derive the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing matrix from RS, with the core insight that the PMNS matrix describes neutrino flavor mixing among the states $ν_e$, $ν_μ$, $ν_τ$.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the final scorecard and certification for the PMNS sector after the geometric derivation in MixingDerivation and the $φ$-angle construction in PMNSMatrix. It completes the SM-014 target for the neutrino mixing matrix and stands ready for use in any larger consistency check of the Recognition Science Standard Model.
scope and limits
- Does not derive the PMNS matrix elements from the ledger.
- Does not perform numerical fits to oscillation data.
- Does not address the neutrino mass hierarchy.
- Does not treat the CKM quark mixing matrix.