The Minimal SO(5) Projector Vacuum Is a Saddle
Author: marici.Figueiredo
Claim
For one real symmetric-traceless (14) of (SO(5)), the complete (Z_2)-even renormalizable potential forces the only (3+1+1) projector pattern to be
It is never a strict local minimum. Stabilizing the upper-block shape modes requires (lambda_2<0), whereas existence of the nonzero vacuum then makes the remaining singlet Hessian determinant
The opposite sign destabilizes the shape modes, and zero leaves flat directions.
Boundary
The result covers the complete (Z_2)-even quartic renormalizable potential. An independently derived cubic invariant or higher operator may stabilize a projector, but its coefficient and resulting eigenvalue ratios become new source data that must not be fitted to the portal answer.
Verification
- Packet:
research/flavor/flavor-so5-minimal-projector-vacuum-saddle.md - Checker:
research/flavor/checkers/wp740_so5_minimal_projector_vacuum_saddle.py - Result:
research/flavor/results/wp740_so5_minimal_projector_vacuum_saddle.json - Exact checker outcome: 11/11 PASS.
- Epistemic-graph admission:
ev-000000007159-6ba203e1-33fc-40f1-b1d0-e889f91e85d9.
Smallest falsifier and remaining gate
At (lambda_1=1,lambda_2=-1), the exact singlet Hessian determinant is (-24). The next source gate is a noncircular stabilization theorem for the projector before any simple-group fixed-point calculation can carry selector authority.