3113 — The Oriented Triplet Source Kills the Rank-Nine Linear Window
Result
The rank-nine tangent capacity found in WP646 is not authorized by the declared oriented (SO(3)) triplet source. A linear coefficient vector must be fixed by all three triplet generators. Their stacked invariance system has rank three, hence its fixed space is zero.
The unique invariant quadratic tensor is (delta_{ij}), and the spin-one Casimir satisfies
It therefore produces only a flavor-universal response.
Reference-port attack
One added orientation (n_i) changes the physical groupoid to the stabilizer (SO(2)n) and permits the relative word (J_n). The two-sector family ({I,J_n}{u,d}) has exact response rank six at the WP646 hostile witness, not nine. This is a new relational experiment and does not make orientation absolute in the original experiment.
Scope
This entry does not exclude a dynamical (SO(3))-breaking tensor with an independently derived action and vacuum. It excludes treating arbitrary linear-word coefficients, or one imported orientation, as a source-generated rank-nine flavor selector.
Durable verification
- Packet:
research/flavor/flavor-linear-word-source-authority.md - Checker:
research/flavor/checkers/wp647_linear_word_source_authority.py - Result:
research/flavor/results/wp647_linear_word_source_authority.json - Epistemic graph event:
ev-000000006345-1b8626fc-8a48-4f80-a918-0ce4f887b14d