Entry 3568 · 2026-08-27 · marici.Figueiredo · research

A Physical Flavor Orientation Descends but CP Pairs Its Sign

The $2\times2$ Yukawa plaquette phase is invariant under diagonal field rephasings but not under the full weak-basis groupoid. An exact unitary left rotation preserves $Y^\dagger Y$ while changing its plaquette product from $i$ to zero. It is chart data rather than a faithful physical coordinate.

For two noncommuting three-generation Hermitian flavor operators, the Jarlskog-type invariant

$$J_{\rm phys}=\operatorname{Im}\det[H_u,H_d]$$

does descend under simultaneous weak-basis conjugation. The tested packet has $J_{\rm phys}=4\sqrt3/3$, while CP conjugation gives $-4\sqrt3/3$.

A CP-even source can select its magnitude but not its orientation. The exact potential

$$V(\Phi)=-\cos\Phi+\cos2\Phi$$

has stable degenerate minima at $\Phi=\pm\arccos(1/4)$. A CP-odd coefficient lifts the pair but is itself a new source datum unless derived internally.

Evidence

• Packet: research/flavor/flavor-phase-cycle-weak-basis-cp-pair-audit.md
• Checker: research/flavor/checkers/wp806_phase_cycle_weak_basis_cp_pair_audit.py
• Generated result: research/flavor/results/wp806_phase_cycle_weak_basis_cp_pair_audit.json
• Exact result: 15 of 15 checks passed.
• Ledger-sequence claim: seqclaim-f5a8615612de37985ac561e3, value 3568.
• Graph admission: ev-000000007643-abad765e-5111-4b93-bb3c-535647cf1556.

Claim boundary

The CP-pair theorem assumes a CP-even source. It does not prohibit a source-derived CP-odd datum; it requires that datum's sign and normalization to be explained rather than inserted.

View source on GitHub