Spin(2,3) Global Path Selection v9: Commuting-Grading Closure
Frozen: 23 October 2026
Schur's lemma closes the last conventional UV-grading class. A linear internal symmetry commuting with (Spin(2,3)) acts on the real multiplicity-one compensator only by a sign and on families by a unitary matrix. The compensator sign occurs twice in each factor of
\[
(J_{5,A}E^A)\wedge(E_B\wedge T^B),
\]
while family conjugation preserves the identity. The operator is therefore invariant for the entire class.
| ID | Path | State | Result or blocker |
|---|---|---|---|
| CL | Commuting linear grading | rejected | parent operator remains invariant |
| NC | Noncommuting enlargement | externally blocked | new algebra and action absent |
| SP | Charged extra spurion | externally blocked | field and vacuum absent |
| NT | Nonlinear/topological rule | externally blocked | rule and invariant absent |
| FP | Interacting fixed point | externally blocked | beta functional and trajectory absent |
Every surviving route now requires a new object-level model. There is no remaining transformation to test on the currently declared field content.
Reproduction
node verification/verify/verify_spin23_commuting_uv_grading_no_go.mjs
node verification/verify/verify_spin23_uv_torsion_flavor_path_selection_v9.mjs