Manuscript En08-A@1 · En08-A.tex · section · c688d76d

An audited reconstruction sequence

An audited reconstruction sequence · lines 2098–2154

The logical dependencies are:

specified event occurrences and dependency + acyclicity ⟹ partial order,

finite histories + compositional independent diamonds ⟹ schedule-independent records,

vector-space order + translation and positive-dilation invariance ⟹ convex cone order,

proper cone order + S ⟹ Lorentz cone,

full quadratic component + pointed closure and nonempty exterior ⟹ Lorentzian signature,

and

distinguishing Lorentzian realizations + chronological isomorphism ⟹ conformal diffeomorphism .

These are different conditional implications, not a chain in which each conclusion alone supplies the next set of hypotheses. Figure fig:ladder summarizes their order of presentation. No arrow is obtained by renaming an interleaving as a change of observer. We do not assert logical independence of all six results.

Displayed formulas in this passage

unlabeled · line 2101
$specified event occurrences and dependency + acyclicity ⟹ partial order,$
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$finite histories + compositional independent diamonds ⟹ schedule-independent records,$
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$vector-space order + translation and positive-dilation invariance ⟹ convex cone order,$
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$proper cone order + S ⟹ Lorentz cone,$
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$full quadratic component + pointed closure and nonempty exterior ⟹ Lorentzian signature,$
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$distinguishing Lorentzian realizations + chronological isomorphism ⟹ conformal diffeomorphism .$

Nearby in this section

figure: Figure