nx_research_flip_discover_gate.nx

nx_research_flip_discover_gate.nx -- the FLAGSHIP discovery: genuinely DISCOVER a faster matrix-multiplication scheme by SEARCH (not certify a supplied one), the modern AlphaTensor-class method done sovereignly. Exhaustive search can't reach Strassen's rank-7 for <2,2,2> (the coefficient space is astronomical). The FLIP-GRAPH local search (Kauers & Moosbauer 2022 -- how recent matmul rank records were set WITHOUT RL) can: a decomposition of the matmul tensor T over GF(2) is a multiset of rank-1 triples (u_r,v_r,w_r) summing to T. FLIP : two triples sharing one factor, e.g. (a,v1,w1)+(a,v2,w2) = (a,v1,w1+w2)+(a,v1+v2,w2) over GF(2) -- rank-preserving (2 terms -> 2 terms), a random-walk neighbor. REDUCE : when a flip makes a factor 0 (term vanishes) or two triples coincide (cancel over GF(2)), the rank DROPS. Flips never raise rank, reductions only lower it -> rank is monotone non-increasing, so the walk only needs to find ONE 8->7 reduction (easy for <2,2,2>; 6 is impossible -> floor 7). Start from the naive rank-8 scheme, random-walk with a deterministic PRNG until rank 7 is DISCOVERED, then the Brent-equation verifier (over GF(2)) certifies the discovered scheme computes <2,2,2> exactly + a random-input cross-check. LIAR-KILL: a broken scheme is rejected. HONEST SCOPE: 7 is the proven optimum for 2x2 (Hopcroft-Kerr/Winograd, cited); we discover it sovereignly -- we do NOT claim AlphaTensor's larger records. GREEN iff 7/7. license_tier: ORIGINAL