When is a system's temperature its own, and in which frame is that a fact? The fifteenth grouping of this series answered the first half: Paper 52 made local equilibrium a checkable per-sector gate and temperature something a sector qualifies for; Paper 53 made the balance a per-sector, per-boundary account. Both ran, by declaration, in the device rest frame. Paper 54 then covariantized the account — with the composition seated separately at the charter's dynamics panel — and refused one question by name: G-LE's covariance as a qualification — KMS in which frame, temperature under boosts, the Planck–Ott controversy's temperature half. The presumed authority under audit here is the Global Equilibrium Surface — the assumption that thermodynamic standing is fixed by one preferred simultaneity or equilibrium frame. This paper — the fifty-sixth in the sequence, the standing panel completing the Covariant Completion Program's audit (corpus-level grouping closure follows Paper 55's publication) — poses exactly the refused question. Delivered: a patch type — a declared region with its own rest-frame field, sector algebra, and sector state — with its flow defined as a precise dynamical object (the one-parameter automorphism group generated by the sector's declared patch-frame Hamiltonian in the patch's own proper time, together with the patch-frame Davies generator), and the covariant gate G-LE-cov: Paper 52's six components re-typed to patch proper time, the temperature tier's algebraic type (KMS, at the Haag–Hugenholtz–Winnink seat) separated in print from the finite-mode instance actually evaluated (quantum detailed balance of the declared discrete-mode Davies generator), the anti-circularity certificate carried whole. A qualification-invariance theorem is stated at its exact strength: coordinate/re-description invariance of the declared patch-relative gate — a transformation lemma shows how admissible re-descriptions act on the state, generator, and flow (by conjugation), so the temperature tier consumes only conjugation-invariant spectral data and every verdict is constant on re-description orbits; the gate never forms a frame temperature, so the Planck–Ott question is dissolved for this gate by typing, and the rival reading (a physically preferred frame temperature) is declined as architecture, never refuted. Also delivered: a three-layer classification — patch admissibility, the sector-instance verdict admitted / refused / nonequilibrium-defective with the tier sequencing fixed, and the combined product table: four declared sector instances across three declared patch geometries, twelve cells computed at the frozen corners. The laboratory-acceleration Rindler column is conditionally classified under an explicitly displayed hypothesis list H-R (each hypothesis graded declared / imported-form / computed), with the Unruh occupancy bound (about exp (-7x10¹8) at the declared corner) consumed only for the residual vacuum contribution, and the lapse variation (about 10^-18) the other computed row; the finite-duration diamond column runs on Paper 54's window floor, consumed. Paper 53's no-fail range is shown covariantly stable — the identity lemma's hypotheses are patch-frame facts, so the recorded zeros transfer by typing, and no balance is re-evaluated. Eling–Guedens–Jacobson-type nonequilibrium terms are typed to the defective cell, never imported as dynamics. An exact rest-frame recovery returns Paper 52's gate form to form, corner arithmetic unchanged (separation 1. 2x10^-3 / 2. 8x10^-2; geometric ratio 0. 0196; licensed local temperature about 73 mK). The realized ceiling is scoped: conjuncts (s1) - (s4) close on the declared classes; (s5) — strong acceleration (where particle content itself is description-relative), curved patches (the Tolman–Ehrenfest import is read only against uniform inheritance, never as a curved-patch construction), off-class and device-grade evaluation, nonequilibrium evaluation beyond typing, and the background-independent frontier — remains the named residue, scored open here and built elsewhere. Verdict: CovStatus (standing) = scoped at model grade. No new physics is adopted; no calibration is spent; no datum is scored; no band moves — and this panel completes the grouping's audit: all three charter scaffolds are now audited (boundary published and scoped; the dynamics panel reported as a pipeline status at the time of writing; standing scoped here), with one shared frontier named.
Tomoyuki Uchida (Sun,) studied this question.