Spin(2,3) Global Path Selection v7: Parent-Covariance Closure
Frozen: 23 October 2026
Version 6 left open the logical possibility that a complete unbroken-parent action would forbid the nonminimal axial operator. The compensator closes that escape explicitly. With projected coframe (E^A), torsion (T^A) and axial current (J_5^A), the four-form
\[
\kappa(J_{5,A}E^A)\wedge(E_B\wedge T^B)
\]
is fully (Spin(2,3)) covariant and reduces to the axial torsion-current operator in physical gauge. Parity also permits it.
| ID | Path | State | Result or blocker |
|---|---|---|---|
| PL | Parent operator lift | completed | explicit invariant four-form |
| PG | Parent gauge protection | rejected | invariant reduces to (S\cdot J_5) |
| PP | Parity protection | rejected | pseudovector times pseudovector is even |
| NS | New selection law | externally blocked | no such law is declared |
| TM | Threshold prediction | externally blocked | full action and spectrum absent |
The reachable protection graph is exhausted. The minimal value remains a standard conditional benchmark. Reopening requires a genuinely new symmetry or dynamical selection law that forbids the displayed parent invariant while retaining the minimal matter action, followed by complete heavy-threshold and anomaly matching.
Reproduction
node verification/verify/verify_spin23_parent_axial_operator_lift.mjs
node verification/verify/verify_spin23_uv_torsion_flavor_path_selection_v7.mjs