{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:TSMWNAEZK3DSYQD7NZQVUYCVSF","short_pith_number":"pith:TSMWNAEZ","schema_version":"1.0","canonical_sha256":"9c9966809956c72c407f6e615a6055914da1c5cc86c2d1e42160e682f16f758d","source":{"kind":"arxiv","id":"1206.3691","version":1},"attestation_state":"computed","paper":{"title":"Stochastic models for a chemostat and long time behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jaime San Martin, Pierre Collet (CPHT), Servet Martinez, Sylvie Meleard (CMAP)","submitted_at":"2012-06-16T18:47:47Z","abstract_excerpt":"We introduce two stochastic chemostat models consisting in a coupled population-nutrient process reflecting the interaction between the nutrient and the bacterias in the chemostat with finite volume. The nutrient concentration evolves continuously but depending on the population size, while the population size is a birth and death process with coefficients depending on time through the nutrient concentration. The nutrient is shared by the bacteria and creates a regulation of the bacterial population size. The latter and the fluctuations due to the random births and deaths of individuals make t"},"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":"1206.3691","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-16T18:47:47Z","cross_cats_sorted":[],"title_canon_sha256":"8d0dd49a3005db8dea9f52963d5fe14da581b354ab8b99bd037406410dafb0b4","abstract_canon_sha256":"5afd585df2838dd366a74cad000d5845b981cdabf8496bb584f0b6b609950745"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:19.079860Z","signature_b64":"V8GbIIsU+jYBWJ2iMdWHTuvCmWpbPpuajbWcxOTToLOOK7Apor45ivDsd+TYYCn+qJ9aN9P6rD3IaHB822WCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c9966809956c72c407f6e615a6055914da1c5cc86c2d1e42160e682f16f758d","last_reissued_at":"2026-05-18T03:53:19.079172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:19.079172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic models for a chemostat and long time behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jaime San Martin, Pierre Collet (CPHT), Servet Martinez, Sylvie Meleard (CMAP)","submitted_at":"2012-06-16T18:47:47Z","abstract_excerpt":"We introduce two stochastic chemostat models consisting in a coupled population-nutrient process reflecting the interaction between the nutrient and the bacterias in the chemostat with finite volume. The nutrient concentration evolves continuously but depending on the population size, while the population size is a birth and death process with coefficients depending on time through the nutrient concentration. The nutrient is shared by the bacteria and creates a regulation of the bacterial population size. The latter and the fluctuations due to the random births and deaths of individuals make t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3691","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":"1206.3691","created_at":"2026-05-18T03:53:19.079274+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.3691v1","created_at":"2026-05-18T03:53:19.079274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3691","created_at":"2026-05-18T03:53:19.079274+00:00"},{"alias_kind":"pith_short_12","alias_value":"TSMWNAEZK3DS","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"TSMWNAEZK3DSYQD7","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"TSMWNAEZ","created_at":"2026-05-18T12:27:23.164592+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/TSMWNAEZK3DSYQD7NZQVUYCVSF","json":"https://pith.science/pith/TSMWNAEZK3DSYQD7NZQVUYCVSF.json","graph_json":"https://pith.science/api/pith-number/TSMWNAEZK3DSYQD7NZQVUYCVSF/graph.json","events_json":"https://pith.science/api/pith-number/TSMWNAEZK3DSYQD7NZQVUYCVSF/events.json","paper":"https://pith.science/paper/TSMWNAEZ"},"agent_actions":{"view_html":"https://pith.science/pith/TSMWNAEZK3DSYQD7NZQVUYCVSF","download_json":"https://pith.science/pith/TSMWNAEZK3DSYQD7NZQVUYCVSF.json","view_paper":"https://pith.science/paper/TSMWNAEZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.3691&json=true","fetch_graph":"https://pith.science/api/pith-number/TSMWNAEZK3DSYQD7NZQVUYCVSF/graph.json","fetch_events":"https://pith.science/api/pith-number/TSMWNAEZK3DSYQD7NZQVUYCVSF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TSMWNAEZK3DSYQD7NZQVUYCVSF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TSMWNAEZK3DSYQD7NZQVUYCVSF/action/storage_attestation","attest_author":"https://pith.science/pith/TSMWNAEZK3DSYQD7NZQVUYCVSF/action/author_attestation","sign_citation":"https://pith.science/pith/TSMWNAEZK3DSYQD7NZQVUYCVSF/action/citation_signature","submit_replication":"https://pith.science/pith/TSMWNAEZK3DSYQD7NZQVUYCVSF/action/replication_record"}},"created_at":"2026-05-18T03:53:19.079274+00:00","updated_at":"2026-05-18T03:53:19.079274+00:00"}