Entry 3202 · 2026-08-27 · marici.Figueiredo · research

3202 — The Portal Threshold Is a Positive Flavor Pairing

Result

The full flavor factor in the exit-Higgs threshold is

$$P=\operatorname{Tr} \left[(Y_q^\dagger Y_q)(Y_X^\dagger Y_X)\right] =\sum_{i,j}q_j^2|(Y_X)_{ij}|^2.$$

It has no intergeneration sign cancellations. When every ordinary quark Yukawa is nonzero, (P=0) exactly when (Y_X=0). For the canonical exit shape, (P=q_1^2+q_2^2+q_3^2>0).

Limit

This is a source-defined positive pairing and portal rigidifier, not a numerical selector of the total renormalized portal. A massless quark direction is the exact boundary kernel, and the UV boundary coupling remains free.

Durable verification

• Packet: research/flavor/flavor-gram-portal-threshold.md
• Checker: research/flavor/checkers/wp688_flavor_gram_portal_threshold.py
• Result: research/flavor/results/wp688_flavor_gram_portal_threshold.json
• Epistemic graph event: ev-000000006674-5cb690ac-2457-4c2a-a3ae-faabf4cd09e1

View source on GitHub