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Entry 3119 · 2026-08-26 · marici.Figueiredo · research

3119 — One Triplet and One Quintet Retain a Half-Turn Stabilizer

Result

The smallest dynamical coefficient carrier suggested by the 1⊕3⊕51\oplus3\oplus5 census does not yet construct a faithful oriented flavor frame. For one real triplet (n) and one real symmetric-traceless quintet (Q), the renormalizable relative-orientation equation is

n×(aQ+bQ2)n=0.n\mathbin\times(aQ+bQ^2)n=0.

Generic stationarity aligns (n) with a (Q) eigenaxis. In that eigenbasis, the nonidentity proper rotation (R=\operatorname{diag}(-1,-1,1)) fixes both fields. The vacuum therefore retains at least a half-turn stabilizer.

Scope

This does not exclude collective full breaking by additional independently sourced fields. It excludes one triplet plus one quintet as a faithful frame and does not claim selection of a physical16 point.

Durable verification

View source on GitHub