Circuits, Proofs, and Algebra: research papers and reproducible code on complexity lower bounds, motivated by P vs NP and VP vs VNP.
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.
Lean formalization of support-two VNP₁ characteristic-two compilers and class bridges
Machine-checkable exact matrix-multiplication circuits and scalable shared-preprocessing constructions
Lean 4 formalization of matrix-multiplication exponent bounds: Strassen to Coppersmith–Winograd to Duan–Wu–Zhou's ω < 2.374631, plus rank lower bounds and the Alman–Vassilevska Williams barriers
Rectangular matrix multiplication over arbitrary and noncommutative rings: exponent 9/4 (2.25), dual exponent >= 1/2, shared-leg entropy, Lean 4 formal proofs. 任意环与非交换环上的矩阵乘法形式化证明。
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