Framework
How the σ-Uniformity framework applies in biology: what the cascade is, what \(\Phi\) is, what \(\beta\) measures.
σ-Uniformity · Biology
Biology.
Loss-curve cascades in neural-network training, tumour growth-rate scaling, and the protein-folding search-space cascade — three biological systems read with the same six framework operators that every other domain uses.
Biology catalogue — \(\beta\)-strip
Every brake-exponent reading the framework has produced for Biology, 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 \(\beta\).