nx_mathcore_gate.nx

nx_mathcore_gate.nx -- THE MATH CORE HAD NO GATE AT ALL (measured 2026-09-03). nx_catalog says it plainly: nx_bigint_gate, nx_rational_gate, nx_complex_gate and nx_derive_gate are ALL ABSENT -- no source, no binary, nothing promoted. So the estate's exact arithmetic (arbitrary-precision integers and exact rationals), which /compare/computational claims presence on in its very first rows and which the no-float determinism doctrine rests on, carried ZERO executable proof. That is why the board reads CLAIM-ONLY on the honesty census: it asserts coverage with no evidence a referee can run. EVERY TOOTH HERE IS AN ALGEBRAIC IDENTITY, WHICH IS ITS OWN ORACLE. A test that compares an implementation against a number a human typed proves only that the human agreed with the code. An identity -- a*(b+c) = a*b + a*c, (a+b)-b = a, 1/3 + 1/6 = 1/2 -- is true independently of any implementation, so a wrong add, a wrong carry or a wrong normalisation cannot satisfy it. The distributivity teeth are the load-bearing ones: they multiply and add the SAME operands two different ways and demand the same bytes. NON-VACUITY IS ASSERTED, NOT ASSUMED: the carry teeth assert the carry actually FIRED (a round-trip through a shift that never carried would pass while proving nothing), and both comparators are bite-proven -- each must REPORT a difference on values that differ and stay SILENT on values that are equal. A comparator that answers "equal" to everything would pass every identity above and is exactly what the bite catches. license_tier: ORIGINAL