| 13.24); no-signaling by algebra preservation (Thm
| 13.17); a candidate cosmic-time completion and
| its gapless-pointer variant (§13.11, not
| adopted); covariant, matter-localizing, and
| interacting cases open.
Temporal quantum reference frames? | Generation, readings, and conditional descriptions
| distinguished (Def. 14.1, Prop. 14.2); criterion
| for overlapping descriptions (Def. 14.3), proved
| for late-record instruments with ideal clocks
| (Prop. 14.5); imperfect clocks open (Conj. 14.4).
Quantum gravity? | Generative order distinguished from classical cosmic
| time; conditions Q1–Q5, obstructions R1–R4, and
| test problems G1–G3 (§15).
Table 5. The open questions and where they are answered.
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19. Conclusion
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The present world is represented here by a perspective-neutral quantum state together with a
Lucretian truth profile drawn from an exactly specified space of admissible histories. The
generative law is a relational, single-outcome instrument in discrete stages, or equivalently a
relational GRW-type jump process in continuous time. Its primitive events are occurrences whose
probabilities the law fixes, not sharp values of observables. Frame descriptions are unitary
reductions of the neutral state, and two descriptions describe one complete state exactly when they
lie in one description orbit. The interpretive thesis that such an orbit is one realized world with
one history is what CTGP adds, and it is stated as a thesis, not presented as a theorem.
The truth profile does work that the quantum state cannot do. With finite-width collapse, any
present state can be reached along any sequence of events from a suitable initial state, so nothing
in the present physical state settles what happened; what settles it is what the present world has
been. That is the Lucretian thesis, given an exact form. The same results separate what is true
about the past from what can be recovered about it and from what still influences the future: the
past is definite, it may be unrecoverable, and it acts on the future only through the present.
Beyond the finite model, the same structure points to a definite program. The distinction that
matters most is between agreement about states and agreement about realized histories: theories can
agree on every density operator and still disagree about what happened, so single-outcome
compatibility with relativity must be proved at the level of histories. For causally local
instruments in finite models it holds, and the choice of generative foliation is then empirically
invisible, as CTGP’s observational equivalence requires. For gapless detectors on a free
relativistic field it holds as well, with operational no-signaling even in Sorkin’s configuration,
and it extends to spontaneous Gaussian collapses of smeared fields on a fixed family of regions and
to collapses at Poisson-distributed locations on every causally orderable configuration. Beyond
that, a covariant law needs structure at each event: orderability is lost in large volumes,
interfering collapses then depend on their order, and no Lorentz-invariant smearing law exists.
Within CTGP, cosmological time can supply that structure consistently, as a candidate extension, but
only by giving the generative order a dynamical role, which is a decision for the framework rather
than a result. Realizing each collapse by a gapless pointer coupled to the field removes the need to
order the collapses, although cosmological time still fixes their smearings and the definite pointer
readings must still be postulated. A covariant spontaneous-collapse theory that localizes matter
remains to be established. Quantum clocks may repeat readings, delocalize events, and order them
differently from generation without touching event identity, and for two ideal clocks with the
interventions inside the constraint, late-record events are clock-neutral even when the order of the
interactions that write them is superposed, and that superposition has observable consequences for
offset-coherent measurements. Deriving a definite generative order from clock-neutral data, treating
realistic clocks, and carrying generation into quantum gravity remain open.
The law generates the history, and the truth profile records it. Frames describe the result
differently, but they never disagree about what happened.
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