{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZAYXFJIOF4FREWMPYMYORSYBB5","short_pith_number":"pith:ZAYXFJIO","canonical_record":{"source":{"id":"1502.01960","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-06T17:24:09Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9cd4663da71891fa20e5475777fc65d373d3478ba97011f54315ec434e6f23bf","abstract_canon_sha256":"ae3a11ccc7973354cf3fc9d26d7be94f3bc16ea8855ca6b580cb3e3d232988fc"},"schema_version":"1.0"},"canonical_sha256":"c83172a50e2f0b12598fc330e8cb010f488d9d378a3b67a53ab1a11f378cc65d","source":{"kind":"arxiv","id":"1502.01960","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZAYXFJIOF4FREWMPYMYORSYBB5","target":"record","payload":{"canonical_record":{"source":{"id":"1502.01960","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-06T17:24:09Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9cd4663da71891fa20e5475777fc65d373d3478ba97011f54315ec434e6f23bf","abstract_canon_sha256":"ae3a11ccc7973354cf3fc9d26d7be94f3bc16ea8855ca6b580cb3e3d232988fc"},"schema_version":"1.0"},"canonical_sha256":"c83172a50e2f0b12598fc330e8cb010f488d9d378a3b67a53ab1a11f378cc65d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:50.364415Z","signature_b64":"ZU+vEqTYvX/r8cjTOhlCPamBJM/XaIvfJ0ps6bY9OskBZ9KGkwxhjs+nIla8hV38xipyKpUVUxtyxzUeZdszBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c83172a50e2f0b12598fc330e8cb010f488d9d378a3b67a53ab1a11f378cc65d","last_reissued_at":"2026-05-18T02:27:50.363986Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:50.363986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.01960","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dyw/grCsaU5hvItiHXFxDZuLL4/Z+H3aYCvjVna+4U1KfIZpQ5fDOO8Zf2I5NL3hkzOj2EToC/qHuhrXdK+QDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:28:39.438231Z"},"content_sha256":"5b37c73c2e0fd5afa1b0e2ff4b127b1e6699efe9394d5f91f8d5b2f752612d19","schema_version":"1.0","event_id":"sha256:5b37c73c2e0fd5afa1b0e2ff4b127b1e6699efe9394d5f91f8d5b2f752612d19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZAYXFJIOF4FREWMPYMYORSYBB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Collective periodicity in mean-field models of cooperative behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Francesca Collet, Marco Formentin, Paolo Dai Pra","submitted_at":"2015-02-06T17:24:09Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01960","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twla14ljAAZG7KpbNS5hLf+mo6SvAwBkjw6DytB+xPHChzWjsq7ic28PiVBOel6trbDlZCmi3/1pMRdA0IgYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:28:39.438595Z"},"content_sha256":"9df1f50fc839a07112e195207f9421e2b66dddd2739d11399e1aa5651c1192b4","schema_version":"1.0","event_id":"sha256:9df1f50fc839a07112e195207f9421e2b66dddd2739d11399e1aa5651c1192b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZAYXFJIOF4FREWMPYMYORSYBB5/bundle.json","state_url":"https://pith.science/pith/ZAYXFJIOF4FREWMPYMYORSYBB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZAYXFJIOF4FREWMPYMYORSYBB5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T23:28:39Z","links":{"resolver":"https://pith.science/pith/ZAYXFJIOF4FREWMPYMYORSYBB5","bundle":"https://pith.science/pith/ZAYXFJIOF4FREWMPYMYORSYBB5/bundle.json","state":"https://pith.science/pith/ZAYXFJIOF4FREWMPYMYORSYBB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZAYXFJIOF4FREWMPYMYORSYBB5/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UjekUWbeSjhYarazsq28uiKPos0fapxu61WKz1dyA6iQ18ohntlwvPJ9nRaobrIa9HTzU3COEYzBv4mJdzZXCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:28:39.442770Z","bundle_sha256":"b1e110fad1acc54a29887c260feb68f3f84b32174693dcb59e584e790fc79e82"}}