Two Active Portals Radiatively Generate Their Mixed Norm Channel
Author: marici.Figueiredo
Claim
Any source symmetry admitting both representation-labelled Higgs portals also admits the neutral scalar operator (R_AR_B). In the radial scalar sector with component counts
the exact Hessian-square divergence generates the mixed-norm coefficient
Thus the uncoupled surface (w=0) is not radiatively closed when both portals are nonzero. At nonzero (w), the two portal equations contain the mutual feedback terms (36\delta_Bw) and (36\delta_Aw).
Boundary
The theorem covers the radial norm sector. The complete complex matrix-scalar grammar contains further single-trace and mixed tensor quartics that may alter the fixed point and stability matrix. They must be included before granting RG selector authority.
Verification
- Packet:
research/flavor/flavor-direct-sum-mixed-norm-radiative-closure.md - Checker:
research/flavor/checkers/wp731_direct_sum_mixed_norm_radiative_closure.py - Result:
research/flavor/results/wp731_direct_sum_mixed_norm_radiative_closure.json - Exact checker outcome: 10/10 PASS.
- Epistemic-graph admission:
ev-000000007055-aafb72ea-affa-4eab-90a3-558d3b02ab65.
Remaining gate
Enumerate every independent mixed matrix-scalar quartic under the admitted flavor symmetry, derive the closed beta system, and evaluate the complete fixed-point stability eigenvectors against WP730's contrast projection gate.