The SO(5) Parent Adds an Unselected Singlet Projector
Author: marici.Figueiredo
Claim
The minimal simple-group completion restricts as
Its residual commutant contains (O(2)) rotations of the two singlets. A unique (SO(5)) parent invariant therefore fixes the complete two-singlet isotypic packet but does not select which rank-one singlet is the measured model-A channel. A commuting rotation changes an exact witness coupling squared from one to zero without changing any residual representation label.
Boundary
A separately derived breaking potential and gapped mass projector may remove the fiber. This result shows that simple-group representation data alone do not. Fixed-point and threshold calculations are deferred until the source-to-one-singlet map is faithful.
Verification
- Packet:
research/flavor/flavor-so5-singlet-multiplicity-projector-obstruction.md - Checker:
research/flavor/checkers/wp739_so5_singlet_multiplicity_projector_obstruction.py - Result:
research/flavor/results/wp739_so5_singlet_multiplicity_projector_obstruction.json - Exact checker outcome: 10/10 PASS.
- Epistemic-graph admission:
ev-000000007159-6ba203e1-33fc-40f1-b1d0-e889f91e85d9.
Remaining gate
Derive a stable breaking-sector projector independently, transport its gap and orientation through RG and thresholds, and distinguish both compulsory singlets with an independently calibrated instrument.