nx_pow10.nx

nx_pow10.nx -- SHARED NUMERIC rung: base-10 exponential and logarithm in pure integer arithmetic. Extracted because two unrelated lanes needed the same primitive -- peptide ionisation fractions (Henderson-Hasselbalch) and thermal death kinetics (D/z values) are both decade-log physics -- and a physical primitive with two copies is a drift waiting to happen. HOW IT WORKS. A 10-entry mantissa table holds 10^0.0 .. 10^0.9 scaled by 1000; any exponent splits into whole decades (repeated x10) plus a fractional part read from the table. ilog10_milli is the same table run backwards: normalise into [1, 10), find the bracketing pair, interpolate. INTERPOLATED, AND THE ERROR IS BOUNDED AND SIGNED. Nearest-entry lookup alone is 0.1 log units granular = up to 12% error, which is far too coarse for a food-safety lethality calculation. Linear interpolation between table entries drops that to <=0.7%. Because 10^x is CONVEX, a chord lies above the curve, so interpolation always returns a value >= the true one. That sign is not incidental -- callers computing a lethality with a NEGATIVE exponent (process cooler than reference) get a slightly UNDER-stated result, which is the safe direction. A caller relying on a positive exponent should carry margin; see nx_thermal_process, which does. ⚠THAT BOUND WAS WRONG UNTIL 2026-07-25 AND SAID <=0.3%. This file had no gate of its own -- it was exercised only through its callers, so nothing ever checked its self-description. nx_pow10_test now MEASURES the bound via the functional equation 10^a*10^b = 10^(a+b), scanning the decade for the worst case: 13 permil on the doubled identity, hence ~6.5 permil on a single evaluation. That matches the closed form for a chord over a convex function, (1+r)/2/sqrt(r) - 1 with r = 10^0.1, which is 0.664%. The old figure understated the error by a factor of two. The one caller that reasons about this numerically (nx_thermal_process, botulinum cook adequacy) was re-checked against the corrected figure and its conclusion is UNCHANGED: 0.7% is still an order of magnitude inside the ~19% margin the 3.0 min industry F0 target carries over the 2.52 min 12D floor. The claim was wrong; the safety verdict it supported was not. Units: _q3 = value x 1000, _milli = value x 1000. Grounding: standard_base10_logarithm_identities (no citation needed beyond the definition; the gate checks against exact known values).