nx_icecream_balance.nx

nx_icecream_balance.nx -- FOOD-SCIENCE SUITE / MIX BALANCING rung. nx_icecream ANALYSES a mix that already exists. This SOLVES for the mix: given targets, it returns the grams of each ingredient to weigh out. That inversion is the formulator's actual job, and it is the difference between a calculator and a design tool. THREE SOLVERS, EACH EXACT -- no iteration, no search, no float. 1. THE DAIRY BALANCE is a TRIANGULAR system, so it solves in one pass. Fat comes only from cream, so cream is determined first; cream drags MSNF in with it, so the powder only makes up the shortfall; sugar and stabiliser are direct; added water is whatever is left. Solving it as a general matrix would be wrong-headed -- the dependency order IS the dairy chemistry. 2. THE SUGAR BLEND is a 2x2 with a closed form. Two sugars, two constraints (total mass, target PAC), so g_lo = (PAC_hi * S - P) / (PAC_hi - PAC_lo) and the PAC figures come from ic_pac_from_mw, not from constants, so the solver works for ANY sugar pair rather than the one it was written against. 3. THE SERVE-TEMPERATURE INVERSION runs the freezing curve backwards: pick the temperature you want to scoop at and the ice fraction you want there, and it returns the grams of sweetener that produce it. This is where the dextrose lever becomes a number instead of an opinion -- scooping at -12 C takes ~248 g of sucrose or ~130 g of dextrose per kg, because PAC is inverse in molar mass. EVERY SOLVER REFUSES RATHER THAN RETURNS A BAD MIX. Cream that already overshoots the MSNF target, a PAC target outside what the two sugars can reach, negative added water -- all set feasible = 0. A formulation that cannot exist must not come back as numbers a person would then weigh out. ROUNDING IS TO NEAREST, NOT TRUNCATED. Truncation cost a whole PAC unit in nx_icecream (dextrose 190.009 read as 189); here it would silently miss the MSNF target by a gram per stage. Grounding (cited; researcher-groundable): goff_hartel_ice_cream_mix_calculation_serum_point