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GF(2) Möbius / zeta transform in o(N log N) XOR gates, the first asymptotic improvement over Yates (1937) for circuits with cancellation: proofs, certificates, Lean 4 checks, and closed ideas. Asymptotic only, AI-checked, not yet human-refereed.
Exact GPU zeta/Möbius/Walsh–Hadamard transforms on the subset lattice - one templated Metal kernel via MLX. Exact over Z/2³² & Z/2⁶⁴, bandwidth-bound on Apple Silicon: n = 29 in 174 ms, ~96% of copy.