"""Reproduce the TE1–TE15 proof mechanism diagram.""" from pathlib import Path SVG='\nConstructing normal traces on every finite von Neumann algebraTrace-free projection comparison makes the unitary orbit hull uniformly small on decreasing projections. Positive compactness puts its closure in the normal predual. Countable subgroup fixed points and compactness give a fixed point for the full unitary group. It is a normal trace with unchanged central values.\n\nNormal traces from a positive functional\'s unitary orbit hull\nM finite; φ positive normal; Kφ is its norm-closed convex unitary orbit hull.\n\nTrace-free projection control\neⱼ orthogonal, fⱼ ∼ eⱼ⇒ fⱼ → 0 σ-strongly\nUniform decreasing-tail boundTE10–TE11\n\nPositive weak compactness\npMp derived from supportsAll closure points normal\nKφ weakly compactTE1–TE6\n\nFull-group fixed point\nCountable subgroup firstCompact finite intersections\nInvariance ⇒ normal trace τφTE7–TE9, TE12\n\n\nτφ(a) = φ(a) for a ∈ Z(M); normal traces separate every nonzero x ∈ M⁺.\nNonzero finite factor: τ(1) = 1; τ faithful and unique among all tracial states. TE13–TE15.\nArrows are proved implications. No separability or cardinality assumption on M or its representation.\n\n' Path(__file__).with_suffix(".svg").write_text(SVG,encoding="utf-8")