Emergent Time as Phase Dynamics in the Logarithmic Superfluid Vacuum

This revision brings the paper into line with the rest of the program and removes one overstated prediction. The main change is to the testable-consequences section. The earlier version predicted a quadratic energy-dependent modification to photon propagation near the Planck scale. That prediction contradicts the companion light-bending paper, which shows the photon branch of the condensate dispersion is exactly linear, ω = ck, to all orders — the massive branch is gapped at the Planck scale and does not affect low-energy propagation. The revised version states the correct consequence: no energy-dependent photon dispersion at accessible energies, consistent with the gamma-ray-burst bounds on Lorentz violation and with the GW170817 constraint, so that any detection of energy-dependent photon velocity would falsify the emergent-time picture. The overclaim becomes a clean null prediction. I also made the gravitational-redshift derivation explicit about the conformal prefactor: the constant normalization common to the acoustic metric cancels in the ratio of two clocks, leaving only the field-dependent factor to carry the redshift. This closes a step that was previously silent. Smaller items: the companion no-go paper is cited under its current title, and the phrasing around the local phase rate μ(x) now states plainly that it is the chemical potential in frequency units. The core physics — time as the condensate phase counter, gravitational dilation as spatial variation of μ, the twin paradox as path-dependent phase accumulation, the arrow of time from open-system relaxation, and the horizon clock-stop — is unchanged.