theorem total_spread_eq_endpoint_ratio (spec : OrderedSpectrum M)
(hM : 1 < M) :
spec.rate ⟨0, by omega⟩ / spec.rate ⟨M - 1, by omega⟩ =
timescaleFromRate (spec.rate ⟨M - 1, by omega⟩) /
timescaleFromRate (spec.rate ⟨0, by omega⟩) := by
simp only [timescaleFromRate]
field_simpEndogenous Hierarchy: Why N Levels?