{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KGCZRDSMK6JGMPNNVP43KC2YVF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2e27a072cf429d10aec962272f7dcb1df852448dbb8c4e163ef1b49956398279","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-04T19:17:45Z","title_canon_sha256":"bde9311e6b5f0c7a70d7a3a91489708668694a32eae319497c5e535635fa7e07"},"schema_version":"1.0","source":{"id":"1310.1378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1378","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1378v1","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1378","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"KGCZRDSMK6JG","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KGCZRDSMK6JGMPNN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KGCZRDSM","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:8c4c521a112cc509beee27d18c3e78cb7f1424f6cf55e13a975111ff8d9ad15d","target":"graph","created_at":"2026-05-18T03:11:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider lattices of regular sets of non negative integers, i.e. of sets definable in Presbuger arithmetic. We prove that if such a lattice is closed under decrement then it is also closed under many other functions: quotients by an integer, roots, etc.","authors_text":"Ir\\`ene Guessarian, Patrick C\\'egielski, Serge Grigorieff","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-04T19:17:45Z","title":"On Lattices of Regular Sets of Natural Integers Closed under Decrementation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1378","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1b05e5428c8bc38ef58efbd65c14f7bd77f5a045e25519e352b539b71be232b3","target":"record","created_at":"2026-05-18T03:11:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2e27a072cf429d10aec962272f7dcb1df852448dbb8c4e163ef1b49956398279","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-04T19:17:45Z","title_canon_sha256":"bde9311e6b5f0c7a70d7a3a91489708668694a32eae319497c5e535635fa7e07"},"schema_version":"1.0","source":{"id":"1310.1378","kind":"arxiv","version":1}},"canonical_sha256":"5185988e4c5792663dadabf9b50b58a96f054489c951b21a4d64c9e3eb2d7709","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5185988e4c5792663dadabf9b50b58a96f054489c951b21a4d64c9e3eb2d7709","first_computed_at":"2026-05-18T03:11:22.525018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:22.525018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xMB4HEvg+H6Q0JA50Jd++Ktewi3p4JoyCJmx5w/cvr9Apj9L0QN0MtbffirfO33PKxK2SEk6jHYRZZz9kvw3Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:22.525520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b05e5428c8bc38ef58efbd65c14f7bd77f5a045e25519e352b539b71be232b3","sha256:8c4c521a112cc509beee27d18c3e78cb7f1424f6cf55e13a975111ff8d9ad15d"],"state_sha256":"b0e32fde12763e041c14f725167eb7002b057670cf1164c2720db7bc7e779139"}