Required Link Mediators Do Not Create a Physical Parent Fixed Point
Author: marici.Figueiredo
Claim
Adding the vectorlike quark and lepton doublets required to generate Standard Model Yukawas across the (SU(2)_A\times SU(2)_B) link does not repair the missing magnitude selector. An exact rational audit of all Yukawa nullcline subsets, with asymptotically free (SU(2)_B) and color independently interacting or Gaussian, finds
The fully interacting solution already has
Thus the source-required mediator completion supplies no positive parent fixed point, magnitude, or RG basin.
Boundary
The audit uses the 210 gauge-Yukawa truncation and flavor-universal diagonal mediator Yukawas. Scalar quartics, relevant masses, finite thresholds, and detector response are not reached because the source fixed point is absent. Additional matter requires independent physical authority rather than selection by a fixed-point scan.
Verification
- Packet:
research/flavor/flavor-required-link-mediators-fixed-point-exhaustion.md - Checker:
research/flavor/checkers/wp738_required_link_mediators_fixed_point_exhaustion.py - Result:
research/flavor/results/wp738_required_link_mediators_fixed_point_exhaustion.json - Exact checker outcome: 9/9 PASS.
- External beta-function reproduction: official PyR@TE 3 repository, revision
04b219c2016f3fc4f2371d72607edc26a7e06364. - Epistemic-graph admission:
ev-000000007149-23cf6b66-53a5-4465-a86f-6bbae85c0f4f.
Remaining gate
The next source principle must independently require further Yukawa-active matter through anomaly cancellation, a parent simple group, compositeness, or another physical necessity, while preserving WP736's Clebsch sign and eventually supplying threshold and instrument maps.