The Spectrum with the Roton in It: Landau's Fitted Constants, Priced

In 1941 Landau gave helium II a single object to hang its physics on: an excitation spectrum — phonons joined to a postulated roton minimum, eps = Delta + (p - p0)^2/2mu. From that curve the paper derives the excitation thermodynamics, the normal-fluid density, second sound, and the critical-velocity criterion, and I credit all of it at full strength — the criterion is a permanent instrument of physics, derived cleanly from whatever spectrum is supplied. What I price is the derivation status of the curve itself: the shape is asserted, the roton introduced with no microscopic derivation in the paper, and its three constants (Delta, p0, mu) are fitted to the very thermodynamic data the spectrum then organises. My bench prices the fit in its own currency: from the declared fitted parameters the roton sector returns rho_n,roton = 0.959909 / 13.777235 / 50.024352 kg/m^3 and C_r = 77.737056 / 790.583756 / 2289.384219 J kg^-1 K^-1 at 1.0 / 1.5 / 2.0 K, with Delta-elasticities at 1.5 K of -5.733365 (rho_n) and -3.917139 (C_r) — the organised outputs are exponential functions of the fit — and the fitted gap 8.600000 K stands against the first microscopic computation's 19.100000 K (ratio 2.220930), which inside the spectrum's own integrals leaves 9.118820e-04 of the fitted rho_n. Counted plainly: 1 postulated spectrum carrying 3 fitted parameters, 0 microscopic derivations in 1941. 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.