The Minimal Product Parent Has No Interacting Magnitude Selector
Author: marici.Figueiredo
Claim
In the minimal anomaly-compatible (SU(2)_A\times SU(2)_B) parent of WP736, the unique portal Yukawa cannot generate the interacting gauge zeros needed to fix its magnitude. After inserting its exact one-loop nullcline, the two required IR-free gauge brackets are
Both are strictly positive throughout the nonnegative coupling orthant. Therefore the minimal parent fixes the portal sign and Clebsch ratio at matching but supplies neither an interacting magnitude selector nor its RG basin.
Boundary
This is a 210 gauge-Yukawa no-go for the declared minimal parent matter packet. Additional Yukawa-active matter could change the conclusion, but its representations and interactions require independent source authority. A nonnegative parent flavor Yukawa lowers the portal Yukawa on its nullcline and strengthens both obstructing inequalities.
Verification
- Packet:
research/flavor/flavor-minimal-product-parent-fixed-point-no-go.md - Checker:
research/flavor/checkers/wp737_minimal_product_parent_fixed_point_no_go.py - Result:
research/flavor/results/wp737_minimal_product_parent_fixed_point_no_go.json - Exact checker outcome: 12/12 PASS.
- External beta-function reproduction: official PyR@TE 3 repository, revision
04b219c2016f3fc4f2371d72607edc26a7e06364. - Epistemic-graph admission:
ev-000000007139-719f0c5c-ebe9-41ca-a769-357f25ed948e.
Smallest falsifier and remaining gate
The smallest exact falsifier is (P_A\geq1). Any claimed positive fixed point of the minimal packet contradicts it. A successor must independently derive additional anomaly-free matter that reverses the gauge bracket while preserving perturbativity, WP736's Clebsch matching, link completion, and the eventual threshold and instrument maps.