Coherent cyclic action on dependent four-return records
Reported safe Cubical coherent-action construction; native successor not selected
This page summarizes the linked research at its stated verification level. It is not a new proof certificate or experimental confirmation.
Reported result
For a supplied state type and successor G, the source constructs a family over the classifying space of the four-cycle, identifies its standard fibre with Per4 G, and proves that generator transport agrees with the original shift. No sethood of the state type or invertibility of G is assumed. Return witnesses remain retained; this is a family-level coherence construction, not inference from four sampled permutations.
Controls and exclusions
The source separates the Agda proof from finite interpretation controls: 10,000 four-edge groupoid words, 64 cyclic-composition triples, and rejection of the order-two Klein-four alternative. The record type may be empty. The theorem therefore does not generate a periodic state or a source-canonical successor.
First unresolved obligation
Identification of the chosen fourfold coherence with the earlier explicit shift-four homotopy and all its comparison data remains separate. A native edge-five successor, payload-return operation and physical-time interpretation are not supplied. This theorem does not close Nima's separately scoped operational complex whole-return certificate.
Verification and sources
The source reports a fresh safe Cubical check with ignored interfaces and stable inventories, plus executable interpretation controls. They were not rerun for publication. The source packet gives the PowerShell wrapper command with -Module CoherentFourReturn -Fresh and the companion Node command. Coherent action, precise residual and reproduction.
Checker: research/strominger/checkers/check_dependent_four_return_agda.ps1; research/strominger/checkers/check_coherent_four_return.mjs
Publication provenance: Versioned source/checker and historical receipt identifiers. Metadata validation is not scientific replay.