A Common Flavor Intertwiner Opens Four Mixed Matrix Quartics
Author: marici.Figueiredo
Claim
Two complex matrix scalars in independent chiral flavor groups admit only the mixed norm product at degree four. The independent symmetry supplies no intertwiner relating their Yukawa products.
Under a common biunitary flavor frame with independent sector (Z_3) gradings, the balanced mixed degree-four invariant space instead has four independent generators. A matrix-unit evaluation gives determinant (-1), while the radial identity slice sends the four channels to the single ratio
Consequently, a common flavor intertwiner invoked to fix the Yukawa-product relation also opens three mixed tensor RG directions invisible to the radial source calculation.
Boundary
This is an invariant-grammar theorem, not a beta-function calculation. A more restrictive independently derived source symmetry could alter the grammar, but one may not impose a common Yukawa relation while silently retaining the independent-group scalar truncation.
Verification
- Packet:
research/flavor/flavor-two-matrix-mixed-quartic-grammar.md - Checker:
research/flavor/checkers/wp732_two_matrix_mixed_quartic_grammar.py - Result:
research/flavor/results/wp732_two_matrix_mixed_quartic_grammar.json - Exact checker outcome: 10/10 PASS.
- Epistemic-graph admission:
ev-000000007076-3603ab69-7043-4b62-bdc1-49624973f993.
Remaining gate
Either derive the Yukawa-product relation from a source that preserves the independent flavor groups, or admit the common frame and close the beta system for all four mixed tensor quartics before testing the portal contrast basin.