nx_research_discover_matmul_gate.nx

nx_research_discover_matmul_gate.nx -- DISCOVERY widened to the matrix-multiplication family, the direct AlphaTensor analog (operator: "widen discovery ... search candidate low-mult MATMUL schemes a la AlphaTensor"). A fast matmul = a LOW-RANK BILINEAR TENSOR DECOMPOSITION. For an R-term scheme {(u_r,v_r,w_r)}: m_r = (u_r . a)(v_r . b) (R scalar multiplications) c_k = sum_r w_r[k] * m_r (only +/- of the m_r when coeffs are in {-1,0,1}) It computes the bilinear map exactly <=> Brent's equations hold: for all i,j,k: sum_r u_r[i] v_r[j] w_r[k] == T[i][j][k] (T = the problem's tensor) R = the multiplication count. Naive 2x2 matmul is rank 8; Strassen is rank 7. This gate: SUBSTRATE : a sovereign Brent-equation VERIFIER -- the exact certifier a discovery search rides on. MATMUL : the verifier certifies naive 2x2 (rank 8) AND Strassen (rank 7) as correct <2,2,2> schemes, and REJECTS a broken Strassen (liar-kill). Ties the substrate to real matrix multiplication. DISCOVERY : on a TRACTABLE bilinear problem -- complex multiplication, tensor (a+bi)(c+di) -- an EXHAUSTIVE {-1,0,1} search DISCOVERS a rank-3 scheme (3 mults < naive 4: the Gauss/Karatsuba speedup) it was never given, proves it MINIMAL (no rank-2 exists), and the same verifier + random-input check certify it exact. A broken rank-3 is rejected. HONEST SCOPE: the SEARCH discovers on the small problem; for <2,2,2> matmul we CERTIFY the known rank-7 via the same verifier -- we do NOT claim a blind AlphaTensor-scale rank-7 search. Pure integer, no float, deterministic, reproducible. GREEN iff 8/8. license_tier: ORIGINAL