{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZG54X6IMYVQLIK3HRIJ4WSGVR2","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":"534fc1bef174f1994178ab939142e7c9cf0d01dc4fb537e75c32ec6eff86ea3a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-11T21:48:50Z","title_canon_sha256":"1894d098cf7b8c1bb5e0e96e3055f7bdc13da3ec46fe96f32f37179a4ff6d900"},"schema_version":"1.0","source":{"id":"1404.3232","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3232","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3232v4","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3232","created_at":"2026-05-18T00:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZG54X6IMYVQL","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZG54X6IMYVQLIK3H","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZG54X6IM","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:77a9ff631ed1366c1d0b2328ab72dc55c3471b179ff2188ae3b2d1a65a54fdd8","target":"graph","created_at":"2026-05-18T00:40:08Z","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":"In this paper, we describe several different meanings for the concept of Gibbs measure on the lattice $\\mathbb{N}$ in the context of finite alphabets (or state space). We compare and analyze these \"in principle\" distinct notions: DLR-Gibbs measures, Thermodynamic Limit and eigenprobabilities for the dual of the Ruelle operator (also called conformal measures).\n  Among other things we extended the classical notion of a Gibbsian specification on $\\mathbb{N}$ in such way that the similarity of many results in Statistical Mechanics and Dynamical System becomes apparent. One of our main result clai","authors_text":"Artur O. Lopes, Leandro Cioletti","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-11T21:48:50Z","title":"Interactions, Specifications, DLR probabilities and the Ruelle Operator in the One-Dimensional Lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3232","kind":"arxiv","version":4},"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":"sha256:9c7307ccb9c157eac4d7095c638c7fb2309ef7fc7fd64c61a3d5d4557864dde8","target":"record","created_at":"2026-05-18T00:40:08Z","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":"534fc1bef174f1994178ab939142e7c9cf0d01dc4fb537e75c32ec6eff86ea3a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-11T21:48:50Z","title_canon_sha256":"1894d098cf7b8c1bb5e0e96e3055f7bdc13da3ec46fe96f32f37179a4ff6d900"},"schema_version":"1.0","source":{"id":"1404.3232","kind":"arxiv","version":4}},"canonical_sha256":"c9bbcbf90cc560b42b678a13cb48d58e82adef92825851bc62cc0bda2e0d51ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9bbcbf90cc560b42b678a13cb48d58e82adef92825851bc62cc0bda2e0d51ba","first_computed_at":"2026-05-18T00:40:08.748172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:08.748172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HutRE69dbNl3xsWljRYb1o3syoilBO/xCqEfBaV/fhKq1AWMv8h7KNFCovX30H/jGZpTr7R3ZcWxDwv2YEtMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:08.748619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3232","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c7307ccb9c157eac4d7095c638c7fb2309ef7fc7fd64c61a3d5d4557864dde8","sha256:77a9ff631ed1366c1d0b2328ab72dc55c3471b179ff2188ae3b2d1a65a54fdd8"],"state_sha256":"138ea17188f75557c5fb35c5dbcd4f6746e5057ba7c77eec9a87b4592b218066"}