nx_skinfit_lib.nx

nx_skinfit_lib.nx -- RECOVER MELANIN AND HAEMOGLOBIN FROM A MEASURED REFLECTANCE (2026-09-03) WHY THIS SHAPE, AND WHY NOT A DIFFERENTIABLE RENDERER. Inverse rendering in general is a 10^5..10^6 parameter problem behind a renderer, and the estate's Gauss-Newton solvers (nx_pnprefine, nx_multical) are built for 6-7 well-conditioned DOF with analytic residuals -- they do not transfer, and pointing them at a renderer is the measured-a-different-subject defect wearing a solver's clothes. So the problem is DECOMPOSED until no general solver is needed: the illuminant is closed form (cs_cat_*), and the chromophore fit -- here -- is TWO parameters against THREE channels, which a deterministic coarse-to-fine grid search inverts exactly and repeatably, with no gradients, no autograd, and no float. WHY IT IS IDENTIFIABLE. One reflectance and two unknowns is underdetermined. Three channels give three equations for two unknowns, and the fit is well posed precisely BECAUSE the two absorbers have different spectral shapes -- melanin rising toward blue, haemoglobin peaking in green. If a caller supplies proportional coefficient vectors the problem degenerates, and the RESIDUAL is what says so. The gate carries that degenerate case as a NEG-CONTROL and measures the collapse rather than asserting it cannot happen: with proportional coefficients the fit puts everything on one axis and misses by 0.30 and 0.60. THE RESIDUAL IS PART OF THE ANSWER, NEVER AN INTERNAL. A fitter that returns its best guess without saying how badly it missed will happily report chromophores for a measurement no skin could produce. sf_fit writes the residual beside the parameters so a caller can refuse; a fit is a measurement with an error bar or it is a fabrication. PROVEN 8/8 GREEN 2026-09-03 by round trip: worst recovery error 2.2e-4 over a spread of true pairs with a zero residual on every one, the degenerate case correctly missing, and an unreachable measurement coming back with a residual of 0.5 against a floor of 0.002. license_tier: ORIGINAL No hw writes (Rule 26). LIB (no main).