evt-max-bound-subgaussian

IN premise — summaries/2026/08/24/aristotelian-2026-sR-references-chunk-2.md

Created 2026-08-24T17:10:51+00:00

The expected maximum similarity over M layer pairs is bounded by μ + 3σ√(log M) under sub-Gaussian tail conditions, requiring no independence assumptions

Summary

Even when you scan a large number of layer pairs, the most similar pair you'll find is guaranteed to stay close to the average, growing only as the square root of the log of the pair count. This matters because the bound holds without assuming the pairs are independent, so it applies directly to real layered systems where components are heavily correlated, giving a clean ceiling for how much spurious alignment can appear just from looking at many candidates.