nx_numeric_oracle.nx

nx_numeric_oracle.nx -- the tool that verifies every future kernel. Per the "build the tools that build the systems" cardinal + user's "use the most modern research so we can really do incredible things with the math and performance" direction. Synthesises: * Csmith / EMI (Yang+ 2011, Le+ 2014) -- differential testing: feed the same input to two implementations of the same spec, refuse to ship if they disagree. * Kahan compensated (Kahan 1965) + Neumaier (1974) -- maintain summation a separate running error term so naive floating sum loss-of-precision is recovered. * Metamorphic testing (Chen+ 1998) -- when no ground-truth oracle exists, verify INVARIANTS the answer must satisfy (matmul(A, I) == A, T(T(A)) == A, sum-then-square vs square-then-sum, etc.) * Property-based (Claessen+Hughes QuickCheck 2000) -- testing generate many random inputs from a typed spec; failure produces a shrunken witness. * ULP bounds (IEEE 754 standard, 2008/2019) -- when comparing FP, count units-in-last-place distance instead of absolute / relative epsilon hacks. * Reproducible BLAS (Demmel+ 2013) -- bit-identical reduction (ReproBLAS) regardless of thread/order; achievable via deterministic accumulators. * Boldo+Melquiond formal FP verification framework that (Flocq, 2011) informs which properties are decidable. * Herbie (Panchekha+ 2015) -- given a FP expression, find an equivalent expression with smaller rounding error. Inverse direction useful for kernel optimization audits. The oracle does NOT pick ONE comparison mode -- it offers the sealed taxonomy and lets the kernel author pick the right one for the op. Substrate refuses to call something WIN unless the oracle has a structural verdict to back it.