{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JDI6RQUA3TLOADFNYBJ4BPHXDV","short_pith_number":"pith:JDI6RQUA","schema_version":"1.0","canonical_sha256":"48d1e8c280dcd6e00cadc053c0bcf71d42b3efaf9f6c52f224fcd1e518bb233d","source":{"kind":"arxiv","id":"1312.0394","version":1},"attestation_state":"computed","paper":{"title":"Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Sylvie Roelly, Wioletta Ruszel","submitted_at":"2013-12-02T10:12:03Z","abstract_excerpt":"We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of "},"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":"1312.0394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-02T10:12:03Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"1d19e9c00550b20ea1a267c3560e5941418e49adb898eff59388221338aad65b","abstract_canon_sha256":"f266c22e7cf6efef26d6f626b9137bfb0aa54f98e5ead94bbbf0b51dbfe6cf54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:45.796837Z","signature_b64":"hdAJuJcCOsVW7yHRDAregNHN/RuF2SQ71TfL0ViFwPQYc4C9ld2M+7BgPCEudH7KFIY4j1LdT277N234RNNyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48d1e8c280dcd6e00cadc053c0bcf71d42b3efaf9f6c52f224fcd1e518bb233d","last_reissued_at":"2026-05-18T03:05:45.796145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:45.796145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Sylvie Roelly, Wioletta Ruszel","submitted_at":"2013-12-02T10:12:03Z","abstract_excerpt":"We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0394","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":""},"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":"1312.0394","created_at":"2026-05-18T03:05:45.796247+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.0394v1","created_at":"2026-05-18T03:05:45.796247+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0394","created_at":"2026-05-18T03:05:45.796247+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDI6RQUA3TLO","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDI6RQUA3TLOADFN","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDI6RQUA","created_at":"2026-05-18T12:27:49.015174+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/JDI6RQUA3TLOADFNYBJ4BPHXDV","json":"https://pith.science/pith/JDI6RQUA3TLOADFNYBJ4BPHXDV.json","graph_json":"https://pith.science/api/pith-number/JDI6RQUA3TLOADFNYBJ4BPHXDV/graph.json","events_json":"https://pith.science/api/pith-number/JDI6RQUA3TLOADFNYBJ4BPHXDV/events.json","paper":"https://pith.science/paper/JDI6RQUA"},"agent_actions":{"view_html":"https://pith.science/pith/JDI6RQUA3TLOADFNYBJ4BPHXDV","download_json":"https://pith.science/pith/JDI6RQUA3TLOADFNYBJ4BPHXDV.json","view_paper":"https://pith.science/paper/JDI6RQUA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.0394&json=true","fetch_graph":"https://pith.science/api/pith-number/JDI6RQUA3TLOADFNYBJ4BPHXDV/graph.json","fetch_events":"https://pith.science/api/pith-number/JDI6RQUA3TLOADFNYBJ4BPHXDV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDI6RQUA3TLOADFNYBJ4BPHXDV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDI6RQUA3TLOADFNYBJ4BPHXDV/action/storage_attestation","attest_author":"https://pith.science/pith/JDI6RQUA3TLOADFNYBJ4BPHXDV/action/author_attestation","sign_citation":"https://pith.science/pith/JDI6RQUA3TLOADFNYBJ4BPHXDV/action/citation_signature","submit_replication":"https://pith.science/pith/JDI6RQUA3TLOADFNYBJ4BPHXDV/action/replication_record"}},"created_at":"2026-05-18T03:05:45.796247+00:00","updated_at":"2026-05-18T03:05:45.796247+00:00"}