A Temperature Priced by Acceleration: The Unruh and Hawking Toll, Priced

An accelerated observer in empty space finds the vacuum warm. That is the Unruh effect (1976), and its gravitational twin is the Hawking temperature of a black hole (1974–75): two of the deepest results in modern theory, each a temperature *derived* — not fitted, not postulated — from quantum field theory on a spacetime with a horizon. I credit both derivations at full strength: inside their premises they are theorems, the detector analysis is permanent, and the flat-space/horizon analogy Unruh drew is one of the great clarifying moves of the century. Nothing in this paper falsifies a digit of either result. What I price is the toll's exchange rate and its one declared premise. On declared inputs only, my bench returns the Unruh coefficient hbar/(2 pi c k_B) = 4.055014e-21 K per (m/s^2): at Earth gravity the vacuum warms by 3.976610e-20 K; one kelvin costs an acceleration of 2.466083e+20 m/s^2 (2.514705e+19 g); room temperature costs 7.398249e+22 m/s^2. The Hawking side returns its coefficient 1.226901e+23 K kg: a solar-mass hole sits at 6.170074e-08 K, a 1e12 kg hole at 1.226901e+11 K with a fixed-background evaporation time of 2.665437e+12 yr, and the hole whose temperature equals the microwave background's stated 2.725 K masses 4.502388e+22 kg. Every one of those numbers is derived — inside a premise the bench prints on its own face and this paper prints at full size: a horizon exists for the observer whose temperature this is. The horizon is the premise; the temperature is the toll it charges; and the premise itself is derived nowhere in either paper — counted by my bench as: temperatures derived inside the horizon premise = all of them; the horizon premise itself derived = 0. Grade for this census entry, printed at full size: REASON FOUND / STILL TURNING — a pricing of a derivation's premise and exchange rate, explicitly not a kill and not a falsification. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.