Entry 3278 · 2026-08-27 · marici.Figueiredo · research

3278 — Auxiliary Squares Move the Portal into a Clebsch Gram

The complete real-triplet auxiliary family linear in $\chi n$ and $\chi m$ induces the portal matrix

$$K=\kappa C^TC.$$

Independent triplet flips require orthogonal columns of $C$. Source exchange then forces equal column norms and zero portal contrast. Unequal fixed Clebsches can rigidify a ratio, but the rescaling $C\mapsto sC$ changes the absolute portal magnitude without changing incidence or orthogonality. The same portal square also generates no $(n\mathbin\cdot m)^2$ stiffness.

A generic F-term therefore does not explain the portal; it moves the free data into a positive Gram. Progress requires a representation theorem fixing unequal Clebsches, a gauge–Yukawa identity fixing their normalization, and a shared algebra generating the angular constraint.

Durable verification

• Packet: research/flavor/flavor-auxiliary-square-portal-gram-no-go.md
• Checker: research/flavor/checkers/wp718_auxiliary_square_portal_gram_no_go.py
• Result: research/flavor/results/wp718_auxiliary_square_portal_gram_no_go.json
• Sequence claim: seqclaim-a7eb524ac0195559c6a77ec5
• Epistemic graph event: ev-000000006941-2be5dba8-5f76-4f18-869e-de5de65d36ed

View source on GitHub