Equipartition on a Wire: Nyquist's kT per Mode, Priced

In 1928 Harry Nyquist explained Johnson's measured resistor noise: two resistors in equilibrium joined by a lossless line, the line's standing-wave modes counted, each mode carrying kT, the length cancelling — noise power kT·Δf with no adjustable constant, and ⟨V²⟩ = 4kTRΔf. I credit that paper at full strength, including the Planck-factor fence its own author printed inside it. Nothing here falsifies the formula or a number it returns at hf << kT. What I evaluate is the per-mode kT's derivation status: everything in the 1928 derivation except the per-mode energy is derived; the one quantity that carries the temperature enters as an import — classical equipartition per mode, the Rayleigh–Jeans assignment. My bench evaluates where the import fails, on declared inputs only: the Planck-weighted mode energy falls to 0.900000 of the assignment at 1.294870e+12 Hz and to 0.500000 at 7.853934e+12 Hz at 300 K, scaling exactly with T (factor-2 failure at 7.853934e+10 Hz at 3 K), and the assignment integrated over all frequencies uses an infinite total against the finite Planck total 4.258940e-08 W. Counted plainly: 1 imported equipartition against 0 derivations in 1928. Grade: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification. Program headline: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.