Analysis of Boolean functions

Aggregation module for the Fourier analysis of Boolean functions, following Ryan O'Donnell's Analysis of Boolean Functions. This subtheory grows inside the larger complexity-theory corpus, where the Fourier-analytic toolkit underpins circuit lower bounds (small-depth circuits, AC⁰), learning, property testing, and the natural-proofs barrier.

Currently formalized: Boolean functions and the Fourier expansion, with the parity functions as an orthonormal basis, Fourier coefficients and weights, Parseval/Plancherel, and the mean/variance/covariance and convolution API; Chapter 2 foundations include noise stability, the noise operator, derivatives, and coordinate and total influence. The polynomial correlation development proves the exponential XOR-of-majorities bound of Chattopadhyay, Hatami, Lee, Lovett, Tal, and Viola (2026), including its finite middle-band estimate. All definitions and theorems live under the Complexity.BooleanAnalysis namespace.