nx_vecmath_gate.nx

nx_vecmath_gate.nx -- THE GATE for the shared integer linear-algebra foundation (PG2, procgen.plan). GATE LAW APPLIED (CLAUDE.md "EVERY GATE YOU WRITE"): 1. returns gv_verdict so the EXIT CODE carries the verdict -- /api/gate_run derives GREEN/RED from it, and a gate that returns a bare 0 after printing RED silently blesses every failure it finds. 2. two teeth are named neg-control-* so the L2 census can SEE them. 3. every tooth is a gv_check on the shared counter, so DECLARED == EXECUTED by construction. A hand-rolled tally can print "passed 22/20"; this cannot. 4. every sweep is bound to its denominator via gv_subjects. A tooth that passes on the empty set is not a tooth, and these sweeps are the whole representable population, never a sample. 5. every tooth PRINTS ITS MEASURED VALUE. A boolean cannot say why, and both vacuous teeth this estate has caught were found in the diagnostic dump, never in the verdict vector. 6. the verdict note does NOT recite the teeth. Each gv_check name states its own strength, so adding a tooth can never make a summary sentence lie. ERROR BARS ARE DERIVED AND THE MEASUREMENT IS PRINTED BESIDE THEM. nx_itrig declares ~0.6 percent amplitude error, which at fx4096 is about 25 units of value and therefore about 25 units of ANGLE once a point is perturbed off the unit circle. The single-term atan form contributes about 20 units. The bars below sit at roughly twice their sum so a tooth fails on a REGRESSION rather than on the known approximation, and the printed maximum makes the bar ratchetable on evidence instead of by taste.