ThreePointPositivityGate

Abstract

Finite 3-by-3 positivity shell.

The abstract one-versus-many inequality used in the three-point trace positivity argument implies positive semidefiniteness of a real 3-by-3 matrix. Same-sign vectors use entrywise nonnegativity; mixed signs reduce to the sum of the squares (c w - L)^2 and (c S - L^2). This module records only the finite algebraic gate; the analytic Carlen–Lieb input remains separate.