{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MW6GXNIDR4G4SD3XW3PD5ICUI6","short_pith_number":"pith:MW6GXNID","schema_version":"1.0","canonical_sha256":"65bc6bb5038f0dc90f77b6de3ea054478f01f8a240ddfc5496833760bbcbba5e","source":{"kind":"arxiv","id":"1309.2872","version":2},"attestation_state":"computed","paper":{"title":"Random transitions described by the stochastic Smoluchowski-Poisson system and by the stochastic Keller-Segel model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"L. Delfini, P.H. Chavanis","submitted_at":"2013-09-11T16:02:39Z","abstract_excerpt":"We study random transitions between two metastable states that appear below a critical temperature in a one dimensional self-gravitating Brownian gas with a modified Poisson equation experiencing a second order phase transition from a homogeneous phase to an inhomogeneous phase. We numerically solve the $N$-body Langevin equations and the stochastic Smoluchowski-Poisson system which takes fluctuations (finite $N$ effects) into account. The system switches back and forth between the two metastable states (bistability) and the particles accumulate successively at the center or at the boundary 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":"1309.2872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-11T16:02:39Z","cross_cats_sorted":[],"title_canon_sha256":"ba2e7a6b432dc4aca55cc1cf673df570ae1c5ace331b42dee00647b97ed8f43b","abstract_canon_sha256":"d74e846ad972857408214eeb1cdc82903123f986cb4a45c3d96185c9d8b445e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:41.094255Z","signature_b64":"Kyp3Zb2RiCUAksffwb3Ll1S53+tV//k8JYzASayZHV/csf4xwWek+7Va5a0IFD4cKg9kTaUoTpHSVc8fdQHBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65bc6bb5038f0dc90f77b6de3ea054478f01f8a240ddfc5496833760bbcbba5e","last_reissued_at":"2026-05-18T02:53:41.093661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:41.093661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random transitions described by the stochastic Smoluchowski-Poisson system and by the stochastic Keller-Segel model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"L. Delfini, P.H. Chavanis","submitted_at":"2013-09-11T16:02:39Z","abstract_excerpt":"We study random transitions between two metastable states that appear below a critical temperature in a one dimensional self-gravitating Brownian gas with a modified Poisson equation experiencing a second order phase transition from a homogeneous phase to an inhomogeneous phase. We numerically solve the $N$-body Langevin equations and the stochastic Smoluchowski-Poisson system which takes fluctuations (finite $N$ effects) into account. The system switches back and forth between the two metastable states (bistability) and the particles accumulate successively at the center or at the boundary of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2872","kind":"arxiv","version":2},"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":"1309.2872","created_at":"2026-05-18T02:53:41.093747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.2872v2","created_at":"2026-05-18T02:53:41.093747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2872","created_at":"2026-05-18T02:53:41.093747+00:00"},{"alias_kind":"pith_short_12","alias_value":"MW6GXNIDR4G4","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MW6GXNIDR4G4SD3X","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MW6GXNID","created_at":"2026-05-18T12:27:52.871228+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/MW6GXNIDR4G4SD3XW3PD5ICUI6","json":"https://pith.science/pith/MW6GXNIDR4G4SD3XW3PD5ICUI6.json","graph_json":"https://pith.science/api/pith-number/MW6GXNIDR4G4SD3XW3PD5ICUI6/graph.json","events_json":"https://pith.science/api/pith-number/MW6GXNIDR4G4SD3XW3PD5ICUI6/events.json","paper":"https://pith.science/paper/MW6GXNID"},"agent_actions":{"view_html":"https://pith.science/pith/MW6GXNIDR4G4SD3XW3PD5ICUI6","download_json":"https://pith.science/pith/MW6GXNIDR4G4SD3XW3PD5ICUI6.json","view_paper":"https://pith.science/paper/MW6GXNID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.2872&json=true","fetch_graph":"https://pith.science/api/pith-number/MW6GXNIDR4G4SD3XW3PD5ICUI6/graph.json","fetch_events":"https://pith.science/api/pith-number/MW6GXNIDR4G4SD3XW3PD5ICUI6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MW6GXNIDR4G4SD3XW3PD5ICUI6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MW6GXNIDR4G4SD3XW3PD5ICUI6/action/storage_attestation","attest_author":"https://pith.science/pith/MW6GXNIDR4G4SD3XW3PD5ICUI6/action/author_attestation","sign_citation":"https://pith.science/pith/MW6GXNIDR4G4SD3XW3PD5ICUI6/action/citation_signature","submit_replication":"https://pith.science/pith/MW6GXNIDR4G4SD3XW3PD5ICUI6/action/replication_record"}},"created_at":"2026-05-18T02:53:41.093747+00:00","updated_at":"2026-05-18T02:53:41.093747+00:00"}