# Spin(2,3) Global Path Selection v31: Chirality Moves the Obstruction into Reality and Constraints

**Frozen:** 23 October 2026

The most economical escape from the indefinite real Lorentz Yang--Mills form
has been executed.  Lorentzian self-duality has eigenvalues \(\pm i\), so a
one-sided connection is complex and a real connection requires conjugate
chiral data.  Projection alone supplies no positive real kinetic norm.

| ID | Path | State | Result or blocker |
|---|---|---|---|
| SD | Exact self-dual decomposition | completed | chiral sectors and reality relation derived |
| PP | Projection gives positivity | rejected as selector | holomorphic bilinear is not a positive real norm |
| SS | SUSY supplies reality and pole | rejected as selector | compatibility is known; required dynamics is not |
| CG | Constrained chiral gravity | externally blocked | action, reality, constraints, spectrum and matching absent |
| NR | Nonlinear compact-subgroup realization | externally blocked | breaking sector, vacuum and spectrum absent |
| HD | Higher parent | externally blocked | normalized torsion reduction/dictionary absent |

The self-dual shortcut is terminal.  Chiral gravity remains open only as a
new constrained model, not as an operation on the failed vector multiplet.
The next finite escape to audit is nonlinear realization to a compact
subgroup; after that, every live route requires externally absent microscopic
action or vacuum data.

## Reproduction

~~~powershell
node verification/verify/verify_spin23_self_dual_connection_reality_audit.mjs
node verification/verify/verify_spin23_new_model_path_selection_v19.mjs
~~~