Thermodynamic cooling profile vs. Sensory Sweet Spot & Thermal Risk Threshold
The saved cooling example uses initial eighty-eight and ambient twenty-one Celsius. Initial excess is sixty-seven; target fifty-eight point five has excess thirty-seven point five. Bars share zero at eight pixels per excess degree, explicitly using differences rather than absolute temperatures. These are model inputs and a source target, not a guarantee of safe drinking or a medical recommendation. For baseline material and volume, rate is point zero zero one seven zero six eight eight per second. The source multiplies initial excess by exponential negative rate times seconds, then adds ambient. Around three hundred forty seconds, excess reaches thirty-seven point five. Bars compare initial and target excess at the same scale. Real cups, evaporation, mixing and measured temperature can differ; this is a calibrated teaching model. The source solves target time by logarithm of initial-excess over target-excess, divided by cooling rate, then rounds seconds. Baseline target is about three hundred forty seconds. A hypothetical rate eighty percent of baseline increases time to about four hundred twenty-five. Bars label the hypothetical comparison at one pixel per second. Targets at or below ambient return no finite crossing. Full native JSON and original controls remain preserved; real thermal safety is unverified.