nx_vec_kernel.nx

nx_vec_kernel.nx -- R-VEC-0 of the onsite-search S-class ladder: the SOVEREIGN vector-math kernel (LIBRARY), the lowest (silicon) rung every semantic-search capability stands on. Pure INTEGER fixed-point -- deterministic, byte-reproducible, no-float (operator doctrine) -- so a cosine is a known-answer test, not a flaky measurement. KAT lives in nx_vec_kernel_gate.nx (imports this), matching the nx_bm25 / nx_bm25f library+gate split. cosine(a,b) = dot(a,b) / (||a|| * ||b||), bounded in [-1,1] (cited srch_cosine.raw); at scale = a matrix-matrix multiply = BLAS Level 3 / GEMM (cited srch_blas.raw), the kernel the CUDA-exceed roadmap climbs on the RTX 5080. PRECISION TRICK: integer sqrt of small norms collapses (isqrt(2)=1) and would make every short vector look identical. So compute cos SQUARED in a scaled domain and isqrt THAT: cos_milli = sign(dot) * isqrt( dot^2 * 1e6 / (||a||^2 * ||b||^2) ) -> cosine scaled to [-1000,1000] By Cauchy-Schwarz dot^2 <= ||a||^2*||b||^2, so the ratio is in [0,1e6] and isqrt lands in [0,1000] exactly. OVERFLOW CONTRACT (honest boundary): dot^2 * 1e6 must fit i64 (< 9.2e18) => |dot| < ~3e6. Satisfied by L2-normalized int8/int16 embeddings (R-VEC-1 feeds these; R-VEC-4 quantizes to keep norms small). exports: vr_dot, vr_isqrt, vr_cos_milli license_tier: ORIGINAL