nx_appliedmath_gate.nx

nx_appliedmath_gate.nx -- THE APPLIED MATHEMATICS THE ESTATE ALREADY COMPUTES, PROVED BY IDENTITY. WHY THIS EXISTS (measured 2026-09-03): a capability census found real applied mathematics scattered across this estate and presented as MATHEMATICS NOWHERE -- a Weibull wear-and-tear core in pure integer fixed point, loan amortization whose header claims "conservation-proven" with no gate to prove it, single-pass streaming statistics with a parallel MERGE, and general matrix algebra. /compare/computational grades only the SYMBOLIC stack against Wolfram and SymPy; none of these organs appear on any board, and none had a gate. THE FIELD'S OWN COMPLAINT IS THE OPPORTUNITY. The mathematics community's documented grievance against computer algebra is not breadth, it is TRUST: a published account records Mathematica computing a determinant wrongly and returning DIFFERENT answers for the same determinant on two evaluations, inside a system whose source cannot be inspected. Meanwhile numerical analysis is the branch largely ABSENT from mathlib, so the applied half of mathematics has almost no machine-checked corpus at all. This estate's applied math is integer-exact and bit-reproducible by construction, which is worth nothing until something CHECKS it. This gate is that check. EVERY TOOTH IS AN IDENTITY OR A CONSERVATION LAW, TRUE INDEPENDENTLY OF ANY IMPLEMENTATION: money -- the principal repaid over the schedule equals the principal borrowed, to the penny survival -- ln and exp are inverses; ln(1)=0; exp(0)=1; a longer exposure cannot lower failure probability statistics -- merging two streams gives the mean, count and extrema of the single stream over their union matrices -- transpose is an involution, (AB)^T = B^T A^T, a repeated row makes the determinant vanish Tolerances are DECLARED, never implied: the fixed-point transcendentals are checked to a stated number of Q20 units, and the tolerance is named in the tooth so a reader cannot mistake approximate for exact. license_tier: ORIGINAL