3246 — Forbidding the Correlation Quartic Unrigidifies the Frame
Independent (SO(3)_n\times SO(3)_m) rotations forbid ((n\mathbin\cdot m)^2), but they also remove the angular term that rigidifies the WP649/WP661 ordered frame. The norm-only potential has four Hessian zero modes at an orthogonal pair, while the admitted diagonal rotation orbit has dimension three. One physical relative angle remains flat.
Restoring the correlation quartic lifts that mode, but also restores the infrared-repulsive direction that invalidated the WP704 selector. Moreover, coupling both triplets to one quark or messenger flavor space breaks the independent rotations to the diagonal and permits the quartic again.
The obvious symmetry repair therefore exchanges selector protection for loss of presentation rigidification. A different source grading is required.
Durable verification
- Packet: research/flavor/flavor-c-forbidding-symmetry-tradeoff.md
- Checker: research/flavor/checkers/wp706_c_forbidding_symmetry_tradeoff.py
- Result: research/flavor/results/wp706_c_forbidding_symmetry_tradeoff.json
- Sequence claim:
seqclaim-61934c5f251ba3ab121ecba7 - Epistemic graph event:
ev-000000006812-d89280c3-cce5-4954-bc33-9d527c4bc476