Thermal Phase Noise and the Temperature Ceiling for Reliable Fifth-Coordinate Readout

Thermal agitation blurs any coordinate held in a potential, and the phase coordinate is no exception. This paper models the phase as held by a harmonic stiffness kappa = 4.142e-17 J per rad^2, calibrated so the thermal phase spread is 0.01 rad at 300 K, and computes the temperature ceiling for reliable readout. The spread reaches the 0.0667 rad budget only at 13347 K, and a stricter 0.02 rad working margin holds up to 1200 K. At 4000 K the spread is still only 0.0365 rad. Under the stated stiffness, thermal noise is therefore not the limiting factor for phase readout at any ordinary operating temperature; cryogenics are unnecessary for this purpose, and readout error budgets should be assigned to dispersion and drift instead. Computed from stated assumptions; not measured. SIMULATED, NOT MEASURED.