{"paper":{"title":"Remarks on Primitive Regulation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Milan Rosko","submitted_at":"2026-05-18T12:05:45Z","abstract_excerpt":"We prove, and mechanize in Rocq, an abstract obstruction theorem for primitive closure predicates, defined as $C : \\mathsf{Form} \\to \\mathsf{Prop}$ over the closed implication-falsity fragment $A,B ::= \\bot \\mid A \\to B$. Two structurally distinct completeness principles for $C$ enter the result. Evaluation completeness $\\mathsf{Eval}(C)$ is generative: every formula-valued behavior of codes admits a representing code, up to closure equivalence $A \\simeq_C B \\triangleq C(A \\to B) \\land C(B \\to A)$. Excluded-middle completeness $\\mathsf{LEM}(C)$ is decisional: every formula is accepted, or its "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18924","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18924/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}