nx_kubelka_gate.nx

nx_kubelka_gate.nx -- THE GATE FOR THE KUBELKA-MUNK CHROMOPHORE SUBSTRATE, 2026-09-03. SUBJECT: km_r_from_ks / km_ks_from_r / km_ks_mix / km_r_of_mix in-process (the lib has no main). WHAT MAKES THESE TEETH NON-VACUOUS. This model needs no external table to be falsifiable: it carries its own oracle. The forward and the inverse are independent closed forms, so a ROUND TRIP over a ladder of reflectances convicts either one of them being wrong -- a mistyped forward cannot invert back to where it started. The physical checks are the ones that matter for skin: more melanin must be DARKER, more haemoglobin must be DARKER, and reflectance must stay inside [0,1] for every input on the ladder. Teeth, in order: T1 zero absorption is unit reflectance, EXACTLY (not within a tolerance -- the algebra is exact there). T2 the ladder is NON-DEGENERATE: it spans real range. Without this, T3 and T4 could pass on a constant. T3 ROUND TRIP r -> K/S -> r over the whole ladder, every rung, no sampling. T4 monotone: reflectance falls as K/S rises, strictly, across every adjacent pair. T5 bounds: every reflectance on the ladder lies in [0,1]. T6 PHYSICAL: more melanin is strictly darker. T7 PHYSICAL: more haemoglobin is strictly darker. T8 NEG-CONTROL: a non-positive scattering coefficient REFUSES rather than dividing by zero. T9 NEG-CONTROL: inverting a reflectance of zero REFUSES rather than returning an infinity as a number. T10 NEG-CONTROL: inverting a reflectance above one REFUSES (outside the model's domain). PROVEN 10/10 GREEN on the laptop build farm 2026-09-03 while the NAS build lane was storm-refused. license_tier: ORIGINAL No hw writes (Rule 26). expect_exit: 0