Unrestricted Boolean multiplicative complexity of four-term polynomial multiplication
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.
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