{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZAYXFJIOF4FREWMPYMYORSYBB5","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":"ae3a11ccc7973354cf3fc9d26d7be94f3bc16ea8855ca6b580cb3e3d232988fc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-06T17:24:09Z","title_canon_sha256":"9cd4663da71891fa20e5475777fc65d373d3478ba97011f54315ec434e6f23bf"},"schema_version":"1.0","source":{"id":"1502.01960","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01960","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01960v1","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01960","created_at":"2026-05-18T02:27:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZAYXFJIOF4FR","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZAYXFJIOF4FREWMP","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZAYXFJIO","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:9df1f50fc839a07112e195207f9421e2b66dddd2739d11399e1aa5651c1192b4","target":"graph","created_at":"2026-05-18T02:27:50Z","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 propose a way to break symmetry in stochastic dynamics by introducing a dissipation term. We show in a specific mean-field model, that if the reversible model undergoes a phase transition of ferromagnetic type, then its dissipative counterpart exhibits periodic orbits in the thermodynamic limit.","authors_text":"Francesca Collet, Marco Formentin, Paolo Dai Pra","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-06T17:24:09Z","title":"Collective periodicity in mean-field models of cooperative behavior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01960","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":"sha256:5b37c73c2e0fd5afa1b0e2ff4b127b1e6699efe9394d5f91f8d5b2f752612d19","target":"record","created_at":"2026-05-18T02:27:50Z","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":"ae3a11ccc7973354cf3fc9d26d7be94f3bc16ea8855ca6b580cb3e3d232988fc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-06T17:24:09Z","title_canon_sha256":"9cd4663da71891fa20e5475777fc65d373d3478ba97011f54315ec434e6f23bf"},"schema_version":"1.0","source":{"id":"1502.01960","kind":"arxiv","version":1}},"canonical_sha256":"c83172a50e2f0b12598fc330e8cb010f488d9d378a3b67a53ab1a11f378cc65d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c83172a50e2f0b12598fc330e8cb010f488d9d378a3b67a53ab1a11f378cc65d","first_computed_at":"2026-05-18T02:27:50.363986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:50.363986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZU+vEqTYvX/r8cjTOhlCPamBJM/XaIvfJ0ps6bY9OskBZ9KGkwxhjs+nIla8hV38xipyKpUVUxtyxzUeZdszBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:50.364415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01960","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b37c73c2e0fd5afa1b0e2ff4b127b1e6699efe9394d5f91f8d5b2f752612d19","sha256:9df1f50fc839a07112e195207f9421e2b66dddd2739d11399e1aa5651c1192b4"],"state_sha256":"72c7d46a6f2c3466a9108c918b76d864dd5a76f9052267305c3312ab3734848a"}