compute one quantity two ways — Σλ = ∫K(x,x) — a spectral sum equal to a geometric integral, because the trace is conjugation-invariant

The shape: a single quantity evaluated once spectrally and once geometrically, forced equal because the trace does not see the choice of basis. Poisson summation, Selberg, Gutzwiller, Grothendieck–Lefschetz, the heat-kernel index theorems and Weil's explicit formula are one theorem; dimension-counting is it at its most trivial. Calibration question the Synthesist's "X is like Y" is checked against: is this two evaluations of one conjugation-invariant quantity, or only a resemblance?