Source-relative witness continuation and native admission
Reported safe Cubical continuation theorem; exact atomic presentation excluded
This page summarizes the linked research at its stated verification level. It is not a new proof certificate or experimental confirmation.
Reported result
For the declared source-continuation interface, the selected comparison has native finite-history continuation, direct/staged coherence and recursive reuse. The theorem also covers the specified source-adapter requests and certified policy presentations, with their producer and reader hypotheses retained. The exact atomic higher package has no native derivation, but its retained E-envelope is admitted and recovers the actual higher path. The obstruction is presentation-specific, not absence of every retained higher witness.
Controls and exclusions
The source reports expected rejection of atomic-admission relabelling, hidden-filler equality and reverse execution. Opposite comparison/query presentation is not execution of inverse source edges. Native admission alone does not imply continuation-incidence preservation, and endpoint/port agreement does not equate independently chosen complete fillers. Both histories in the actual AB versus AD;DB example have active endpoint B, yet the direct carrier has distinguishable points while the indirect carrier is propositional. An equivalence would identify those distinct direct points. Their native attachment representations and original histories remain available, but generic higher machinery cannot supply this impossible carrier equivalence. This is not a universal obstruction to higher comparison.
First unresolved obligation
A proposed application outside these source families must supply its actual interface, operand derivations, complete reader and continuation binding. Generic machinery does not identify unequal attachment carriers; the AB versus AD;DB adapter has an explicit carrier-equivalence obstruction. This result supplies neither unrestricted policy closure nor physical dynamics.
Verification and sources
The source reports fresh safe Cubical dependency-closure checking and hostile-fixture rejection. These scientific checks were not rerun for this publication; their commands and receipt provenance remain in the linked packet. Continuation theorem and E-envelope · Unequal-interface counterexample.
Checker: research/voevodsky/checkers/check_witness_generator_coherence.py
Publication provenance: Versioned source/checker and historical receipt identifiers. Metadata validation is not scientific replay.