{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SJKS4IESAJDE6JHC7IE5JDZZGF","short_pith_number":"pith:SJKS4IES","schema_version":"1.0","canonical_sha256":"92552e209202464f24e2fa09d48f393166076fc034b1d3cd1037c48a6d3f2ebf","source":{"kind":"arxiv","id":"2605.18924","version":1},"attestation_state":"computed","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.18924","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-05-18T12:05:45Z","cross_cats_sorted":[],"title_canon_sha256":"bcae6989fe34fa543c8b165ddcd2959d80d056af45ca1d28d0d507988b62f2e7","abstract_canon_sha256":"66278cc7830e3a7d3bfb0d76e2e3d398c9cace6e2da20ab98cd972a5624ac434"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:06:32.384238Z","signature_b64":"vZZAxrbh66r4dHLJUy1tGouvJ62c3zmuY2muOE/MPUO9WH3d3ua6x8X2/P1CS5QCgrceDF/XVxpRWt0zO4ETCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92552e209202464f24e2fa09d48f393166076fc034b1d3cd1037c48a6d3f2ebf","last_reissued_at":"2026-05-20T00:06:32.383447Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:06:32.383447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.18924","created_at":"2026-05-20T00:06:32.383577+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.18924v1","created_at":"2026-05-20T00:06:32.383577+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18924","created_at":"2026-05-20T00:06:32.383577+00:00"},{"alias_kind":"pith_short_12","alias_value":"SJKS4IESAJDE","created_at":"2026-05-20T00:06:32.383577+00:00"},{"alias_kind":"pith_short_16","alias_value":"SJKS4IESAJDE6JHC","created_at":"2026-05-20T00:06:32.383577+00:00"},{"alias_kind":"pith_short_8","alias_value":"SJKS4IES","created_at":"2026-05-20T00:06:32.383577+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SJKS4IESAJDE6JHC7IE5JDZZGF","json":"https://pith.science/pith/SJKS4IESAJDE6JHC7IE5JDZZGF.json","graph_json":"https://pith.science/api/pith-number/SJKS4IESAJDE6JHC7IE5JDZZGF/graph.json","events_json":"https://pith.science/api/pith-number/SJKS4IESAJDE6JHC7IE5JDZZGF/events.json","paper":"https://pith.science/paper/SJKS4IES"},"agent_actions":{"view_html":"https://pith.science/pith/SJKS4IESAJDE6JHC7IE5JDZZGF","download_json":"https://pith.science/pith/SJKS4IESAJDE6JHC7IE5JDZZGF.json","view_paper":"https://pith.science/paper/SJKS4IES","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.18924&json=true","fetch_graph":"https://pith.science/api/pith-number/SJKS4IESAJDE6JHC7IE5JDZZGF/graph.json","fetch_events":"https://pith.science/api/pith-number/SJKS4IESAJDE6JHC7IE5JDZZGF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SJKS4IESAJDE6JHC7IE5JDZZGF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SJKS4IESAJDE6JHC7IE5JDZZGF/action/storage_attestation","attest_author":"https://pith.science/pith/SJKS4IESAJDE6JHC7IE5JDZZGF/action/author_attestation","sign_citation":"https://pith.science/pith/SJKS4IESAJDE6JHC7IE5JDZZGF/action/citation_signature","submit_replication":"https://pith.science/pith/SJKS4IESAJDE6JHC7IE5JDZZGF/action/replication_record"}},"created_at":"2026-05-20T00:06:32.383577+00:00","updated_at":"2026-05-20T00:06:32.383577+00:00"}