nx_ferment_kinetics.nx

nx_ferment_kinetics.nx -- R3 science rung: predictive fermentation model. "All the science": predict a ferment's acidification curve pH(t) from first principles -- culture population growth + temperature-scaled lactic-acid production -- so a recipe can be SIMULATED before a drop of milk is warmed, and so the generative rung (R5) can predict whether a NOVEL ferment will reach a safe pH. THE MODEL (fixed-point, integer-exact, deterministic): 1. Population N(t): logistic growth dN = r*N*(K-N)/K r = r_base * temp_factor(T) -- warmer culture grows faster 2. Acid A(t): produced in proportion to population AND metabolic rate dA = acid_yield * temp_factor(T) * N/K (the lactose -> lactic-acid flux; warmer bacteria metabolise faster, so the temperature effect COMPOUNDS through both N and A) 3. pH(t) = pH0 - A (acid accumulation drops pH from milk's 6.5) TEMPERATURE -> RATE via the biological Q10 coefficient (van't Hoff): rate(T) / rate(T_ref) = Q10 ^ ((T - T_ref)/10) computed as exp( ln(Q10)/10 * (T - T_ref) ) using the canonical nx_exp substrate. Q10 ~ 2.5 for lactic-acid bacteria. NOTE: nx_arrhenius's reciprocal-of-Kelvin form was evaluated and is UNUSABLE here -- 1/T in its Q10(1024) fixed-point rounds a 13 C span to delta 0 (1048576/310426 = 3). The biological-Q10 exponential is both the correct microbiology model for this range AND precision- safe, so we compose nx_exp directly. The measured exceed: a $40 yogurt maker holds 43 C but PREDICTS nothing. This rung predicts the set-time curve and proves, by construction, that warmer ferments (within range) acidify faster -- the quantitative Q10 claim, gate-checked, not asserted. genealogy_id: vant_hoff_1884_q10 + verhulst_1838_logistic + monod_1949_growth + nishi_exp_q10_substrate_2026