nx_icecream.nx

nx_icecream.nx -- FOOD-SCIENCE SUITE / FROZEN DESSERT rung. Computes what a frozen dessert mix will actually DO -- where it starts to freeze, how much of its water is ice at any serving temperature, whether it will go sandy, and whether it is legally ice cream -- from composition and physical chemistry, instead of trusting a recipe's "churn until thick". THE CORE IS ONE EQUATION, HONESTLY APPLIED. Freezing-point depression is colligative: dT = Kf * molality. Everything expensive follows from it: - As water freezes OUT, the remaining solution CONCENTRATES, so the freezing point keeps dropping. At equilibrium at temperature T, the unfrozen water is exactly the amount whose freezing point IS T. Since depression is inversely proportional to water for fixed solute: frozen_fraction = 1 - FPD_initial / |T| That is derived, not tabulated -- ic_frozen_water_permil. - Inverting it answers the question a recipe cannot: what cabinet temperature gives the scoopable ~72% ice I want, FOR THIS MIX? -- ic_serve_temp_for_frozen_permil. MEASURED against published freezing curves for a typical mix (FPD ~2.5 C): this model gives 51% frozen at -5 C (lit ~50%), 81% at -13 C (lit ~80%), 86% at -18 C (lit ~90%). It tracks well through the scooping range and runs ~4 points LOW in the deep-freeze tail, where ideal-solution theory stops holding (activity coefficients depart from 1 in a highly concentrated serum). Stated, not hidden. PAC IS DERIVED, POD CANNOT BE. The gelato trade's anti-freezing power index (PAC, sucrose = 100) is just a molecular-weight ratio, so this COMPUTES it -- ic_pac_from_mw reproduces the trade table exactly for the crystalline sugars (sucrose 100, dextrose 190, fructose 190, lactose 100). Sweetening power (POD) is psychophysical -- a measured human response, not a colligative property -- so it stays a cited table. Confusing the two is the classic formulation error: dextrose has ~1.9x the freezing power of sucrose but only ~0.7x the sweetness, which is exactly why it is the lever for a softer product without a sweeter one. All INTEGER. Suffixes: _q1 = x10, _q2 = x100, _q3 = x1000, _permil = x1000 (fraction), _milli_c = temperature x1000 in Celsius. Grounding (cited; researcher-groundable):