{"id":"palomar/PALOMAR-2026-09-21-000005","url":"https://github.com/GregoryMorse/unrestricted-boolean-mul/tree/c014e498e51a98529877cc256b9bcdaf5faa2e4f","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-21-000005-v2.json","repo":"https://github.com/GregoryMorse/unrestricted-boolean-mul","tags":["cs.CC","cs.DS","msc:68Q06","msc:68Q17","msc:68W30","msc:15A75","msc:94D10","computational-complexity","boolean-circuits","polynomial-multiplication"],"score":0,"title":"Unrestricted Boolean multiplicative complexity of four-term polynomial multiplication","trust":"high","domain":"cs.CC","source":"palomar","authors":["Gregory Morse"],"reviews":0,"subject":"cs.CC","summary":"Formalizes the exact minimum AND-gate counts 0, 1, 3, 6 and 9 for binary polynomial multiplication with zero through four coefficients per operand. XOR and constants are free, and AND inputs may reuse arbitrary earlier nonlinear wires. The principal result excludes eight-gate four-term circuits and matches an explicit nine-gate construction. Separate research workflows check selected n5 quadratic results and n6 upper bounds and reductions; their open unrestricted/bilinear lower bounds are not claims of this submission.","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"verified":true,"discussed":0,"published":"2026-10-20","reactions":{},"formalized":true,"formalizes":[{"title":"Unrestricted Boolean Multiplicative Complexity of Four-Term Binary Polynomial Multiplication: Rational Places, Hasse Jets, and the Failure of Nonlinear Feedback","identifier":"arXiv:2608.30238v1","relationship":"formalizes"}]}