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.
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?
The identity coefficient is the copper-loss term
b = R/(n·η·Kt)². 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.
| Quantity | Value |
|---|---|
| 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 floor | 2.94 % |
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.