3363 — Preserving Holonomies Do Not Distinguish the Flavor Carrier
Claim
For the (SO(4)) vector restricted as (4=3+1) under the full physical diagonal (SO(3)), the connected centralizer inside (SO(4)) is trivial and the group centralizer is
Both preserving holonomies act identically on triplet and singlet and cannot generate an ordered contrast. The smallest commuting distinguishing twist is
whose determinant is (-1). It lies outside (SO(4)), changes the groupoid, and still permits the continuous residual form (operatorname{diag}(aI_3,b)).
Classification
Holonomy data obey a dichotomy: preserving holonomies do not distinguish; distinguishing twists change the experiment and do not normalize (b-a). Symmetry and holonomy alone therefore cannot select a nonzero CP-even portal contrast.
Scope
This covers holonomies acting on the WP743 (SO(4)) vector while preserving the full declared diagonal (SO(3)). Larger groups and defects with additional degrees of freedom are not excluded.
Durable verification
- Packet:
research/flavor/flavor-holonomy-contrast-dichotomy.md - Checker:
research/flavor/checkers/wp745_holonomy_contrast_dichotomy.py - Generated result:
research/flavor/results/wp745_holonomy_contrast_dichotomy.json - Exact checker outcome: 12/12 PASS.
- Sequence authority:
seqclaim-db392813433d6f7cba70b66f. - Epistemic-graph admission:
ev-000000007210-b5c745ea-5d3d-4d35-a9af-6ed2a916f765.