An exactly solvable minisuperspace model with a proven observational-equivalence theorem, a complete signature classification, and an ultralight-relic test

Abstract

We study an exactly solvable minisuperspace model class in which mass plays the role of the time variable, constructed from established elements: the Compton clock, the timelike character of the conformal factor in the DeWitt supermetric, and relational (Page–Wootters) time. The model admits a single free boundary datum at the endpoint of the mass variable. We prove an operator identity showing that, under a stated set of premises, every record functional, meaning the reduced state of any recorder chain for arbitrary couplings and durations, is independent of that datum. The model class is therefore observationally equivalent to standard physics. The premises admit four classes of violation, which we enumerate and bound individually. All are closed for known matter: the adiabaticity parameter Λ = H(T_gen)/m of every Standard Model mass-generation event lies at least 2.3 orders of magnitude below the required threshold, and every species is in thermal equilibrium at its own mass genesis. The one surviving configuration, a decoupled species with mass genesis at its own Hubble scale, coincides with the misalignment-onset locus of ultralight relics. For such a species we derive a conditional signature: a scale-localized, phase-coherent modulation of the transfer function carrying a single anomalous global phase, which can be fit to existing survey data. All claims are graded as established physics, exact results of the model class, or stated assumptions.