Framework
How the σ-Uniformity framework applies in pure math: what the cascade is, what \(\Phi\) is, what \(\beta\) measures.
σ-Uniformity · Pure Math
Pure Math.
Universality classes in pure mathematics — Ising critical exponents, random-matrix spacing, Ricci-flow neckpinch, homogenisation limits, and the KPZ-vs-EW anti-shadow — read against the framework's universal threshold beta = 1.
Pure Math catalogue — \(\beta\)-strip
Every brake-exponent reading the framework has produced for Pure Math, on a single \(\beta\)-axis. The vertical line at \(\beta = 1\) is Theorem 1's intrinsic threshold — the only universal threshold the framework admits.
\(\beta < 0\): shrinking
\(0 \le \beta < 1\): sub-rate
\(1 \le \beta < 2\): super-rate
\(\beta \ge 2\): deeply super-rate
Click any point for the full reading: instance, \(\beta\) value, and a link to the source code.
Findings
Headline cases, validated cascades, and the honest limits of what the framework can decide.
Methodology
Data sources, measurement pipeline, and a worked-example trace from raw signal to \(\beta\).