IndisputableMonolith.Physics.PMNSScoreCard
The PMNSScoreCard module assembles a certification scorecard for PMNS neutrino mixing parameters derived from Recognition Science. It defines rows for the three mixing angles, Jarlskog invariant, and a top-level certificate that aggregates geometric results. The module draws on cubic ledger derivations and phi-angle constructions to certify agreement with the Standard Model. Its structure consists of sibling definitions combined into a single holding theorem.
claimPMNSScoreCardCert certifying the PMNS mixing angles $\theta_{12}$, $\theta_{13}$, $\theta_{23}$, Jarlskog invariant $J$, and $\delta_{CP}$ phase lying in an open band, all obtained from $\phi$-angle geometry.
background
The module operates in the setting of Phase 7.2 CKM and PMNS mixing matrix derivation, which formalizes geometric extraction of mixing elements from the cubic ledger structure via edge-dual coupling. It also rests on the SM-014 derivation of the PMNS matrix from $\phi$-angles, where neutrino flavor eigenstates $\nu_e$, $\nu_\mu$, $\nu_\tau$ are related to mass eigenstates through a unitary matrix constructed from Recognition Science angles.
Sibling definitions introduce scorecard rows for each angle, the Jarlskog invariant (both signed and positive), and a condition that $\delta_{CP}$ lies in an open band. These rows serve as the concrete objects whose conjunction yields the certificate.
proof idea
This is a definition module, no proofs. The overall structure defines the individual row certificates for the three angles and Jarlskog quantities, then assembles them under the top-level PMNSScoreCardCert and its holding statement.
why it matters in Recognition Science
The module supplies the PMNS scorecard that closes the geometric derivation of neutrino mixing within Recognition Science. It directly supports the SM-014 target of deriving the PMNS matrix from $\phi$-angles and the Phase 7.2 cubic-ledger construction, providing the concrete certification objects needed for the full mixing-matrix validation.
scope and limits
- Does not derive the underlying $\phi$-angles or ledger structure.
- Does not perform numerical fitting or statistical comparison to data.
- Does not address the CKM quark mixing matrix.
- Does not supply error estimates or uncertainty propagation.