The fingerprint that melts

Two motors off the same production line are not identical, and the difference is measurable. That difference could serve as an identity — a machine proving it is the machine it claims to be, from physics its software cannot author. Then the motor warms up.

Predict first

Manufacturing makes two identical-model motors differ by about 21% in one measurable coefficient. How much does that same coefficient change when one motor simply warms up by 40 °C during normal use?

Operating condition

Do you measure winding temperature?

The identity coefficient is the copper-loss term b = R/(n·η·Kt. Copper resistance rises with heat at +0.393 %/°C; magnet remanence, and so Kt, falls at −0.12 %/°C. Because Kt is squared and in the denominator, the two effects compound: +0.633 %/°C.

Where these numbers come from
QuantityValue
Copper resistivity coeff.+0.393 %/°C
NdFeB remanence coeff.−0.08 to −0.12 %/°C
Kt unit tolerance±10 %
Resistance unit tolerance±8 %
Model resolution floor2.94 %

Institute working note, Security · provenance. The identity claim itself is not ours: silicon PUFs own per-unit identity from manufacturing variance, and motor current signature analysis already learns per-motor baselines. What is drawn here is the physics of whether it survives a duty cycle.

Thermal drift
Unit separation
Drift / separation
Crossover