Manuscript En05-A@1 · En05-A.tex · section · f076e703
Separated existence obligations
A conditional continuum package with matched realizations › Separated existence obligations · lines 2039–2094
En05-A@1#conj:family, En05-A@1#conj:opcov
There exists a scaling family of admissible substrates and schedules satisfying C1–C2 with Euclidean limiting norm and admitting the directional matched relay families required by C5.
A family as in Conjecture conj:family can be equipped with realizations satisfying C3–C4 and C6, and its limit theory satisfies C7. Finite experiments in each admitted frame have complete acyclic instrument semantics.
Unrestricted device retiming closure (Hypothesis hyp:boost) is deliberately not included: Theorem thm:boostobstruction makes it incompatible with the ordinary bidirectional relay class.
| Requirement | Discrete comparison or certificate | Missing construction |
|---|---|---|
| C1–C2 | Metric envelopes; timed velocity polytopes; cardinal diamond | A Euclidean envelope together with sufficiently isotropic actual reachability. Fixed finite periodic rescaling is excluded. |
| C3–C4 | Complete local-record factorization | Matched operational realizations, convergence, and local completeness. |
| C5 | Exact relay gap ; implementation gap certificate | Boundary relays in every limiting direction with admitted total-variation limits. |
| C6 | Discrete complete supports | A localized observable realization and product-preserving algebraic limit. |
| C7 | Conditional causal-automorphism theorem | An outcome-preserving calibrated frame group for the admitted limit experiments. |