Entry 3247 · 2026-08-27 · marici.Figueiredo · research

3247 — Angular Rigidity Requires the RG-Repulsive Correlation Operator

For two real triplets with diagonal (SO(3)), independent flips, polynomial locality, and field degree at most four, the complete scalar invariant grammar is generated by

$$1, a, b, a^2, ab, b^2, c^2, \qquad a=|n|^2, b=|m|^2, c=n\mathbin\cdot m.$$

Along a fixed-norm rotation through an orthogonal frame, the angular stiffness is exactly (2\lambda_c). Hence protecting (lambda_c=0) makes the physical relative angle flat. The same correlation operator is both necessary for WP649 frame rigidification and responsible for the WP705 infrared-repulsive mode.

No alternative symmetry label on the same renormalizable two-vector grammar can retain both properties. A repair must enlarge the source grammar or derive a full-domain attractive ray with nonzero (lambda_c).

Durable verification

• Packet: research/flavor/flavor-two-vector-angular-invariant-no-go.md
• Checker: research/flavor/checkers/wp707_two_vector_angular_invariant_no_go.py
• Result: research/flavor/results/wp707_two_vector_angular_invariant_no_go.json
• Sequence claim: seqclaim-bb3c948872bff805023cbefc
• Epistemic graph event: ev-000000006822-d1bc5042-462d-40ef-8d03-60335e5c2771

View source on GitHub