The Banach-Butterfly Invariant μ(f) is a Schur-convex algebraic quantity defined from influence-adaptive exponents on the Walsh-Hadamard butterfly that distinguishes functions with equal total influence and exhibits n-dependent correlations with minimum polynomial threshold support.
Atn= 4, this is2 4 ×2 4 = 256integer multiplications per function, with65,536functions total: approximately16.8×10 6 operations, completing in under 1 second on any modern CPU
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The Banach-Butterfly Invariant: Influence-Adaptive Walsh Geometry for Ternary Polynomial Threshold Functions
The Banach-Butterfly Invariant μ(f) is a Schur-convex algebraic quantity defined from influence-adaptive exponents on the Walsh-Hadamard butterfly that distinguishes functions with equal total influence and exhibits n-dependent correlations with minimum polynomial threshold support.