{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3QEW3LDHRQ7ERIS4ZVC3AXQANJ","short_pith_number":"pith:3QEW3LDH","canonical_record":{"source":{"id":"1609.07951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-26T12:45:42Z","cross_cats_sorted":[],"title_canon_sha256":"8f5412f1f3b674c85427702f58618ed37167b2c4d3ca0c6f47b754992f9e02c2","abstract_canon_sha256":"0e2938509ddda72be919a5844734d3629b6fb8da8757ada801cf54f084e012ad"},"schema_version":"1.0"},"canonical_sha256":"dc096dac678c3e48a25ccd45b05e006a71270a13e0173e45596333b1a4ba5f52","source":{"kind":"arxiv","id":"1609.07951","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07951","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07951v2","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07951","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"pith_short_12","alias_value":"3QEW3LDHRQ7E","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3QEW3LDHRQ7ERIS4","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3QEW3LDH","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3QEW3LDHRQ7ERIS4ZVC3AXQANJ","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-26T12:45:42Z","cross_cats_sorted":[],"title_canon_sha256":"8f5412f1f3b674c85427702f58618ed37167b2c4d3ca0c6f47b754992f9e02c2","abstract_canon_sha256":"0e2938509ddda72be919a5844734d3629b6fb8da8757ada801cf54f084e012ad"},"schema_version":"1.0"},"canonical_sha256":"dc096dac678c3e48a25ccd45b05e006a71270a13e0173e45596333b1a4ba5f52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:22.720883Z","signature_b64":"FtAWELTUZnf+KGXQEmD8NQ4BdVl6p1lyTze01teygtctNK6DUMdnAH3LvSJ2rn7aAzCkyQy+u/AwvPt7HZ+sAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc096dac678c3e48a25ccd45b05e006a71270a13e0173e45596333b1a4ba5f52","last_reissued_at":"2026-05-18T00:52:22.720243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:22.720243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07951","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jrlulW7vtSHaQOz4kwZMa7nU7uBSeVurZ9Qfz5UZqj5Y2cgY/n5hmo63+iq2sDM8IpIByj0olPYUS+hoEiboAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:22:47.475443Z"},"content_sha256":"f03c0ae42cd77081371834fd844586f22e4fdea95cf07b8776d0391ea7e0fbfc","schema_version":"1.0","event_id":"sha256:f03c0ae42cd77081371834fd844586f22e4fdea95cf07b8776d0391ea7e0fbfc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3QEW3LDHRQ7ERIS4ZVC3AXQANJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gaussian approximations for chemostat models in finite and infinite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bertrand Cloez (MISTEA), Coralie Fritsch (CMAP, IECL, TOSCA)","submitted_at":"2016-09-26T12:45:42Z","abstract_excerpt":"In a chemostat, bacteria live in a growth container of constant volume in which liquid is injected continuously. Recently, Campillo and Fritsch introduced a mass-structured individual-based model to represent this dynamics and proved its convergence to a more classic partial differential equation. In this work, we are interested in the convergence of the fluctuation process. We consider this process in some Sobolev spaces and use central limit theorems on Hilbert space to prove its convergence in law to an infinite-dimensional Gaussian process.As a consequence, we obtain a two-dimensional Gaus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07951","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UTrKBSoFDKW7rGn+XbSeJkN4hBTcDxKAQ42HyAkSU6kNRCLrU8xX3U/E1taq4VgL/0uKHWc+aqfGWCjjxZm5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:22:47.476037Z"},"content_sha256":"74322f191da784f20fe8d35eec1ddfa2dd4bb14189c936e157b66614f6150922","schema_version":"1.0","event_id":"sha256:74322f191da784f20fe8d35eec1ddfa2dd4bb14189c936e157b66614f6150922"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3QEW3LDHRQ7ERIS4ZVC3AXQANJ/bundle.json","state_url":"https://pith.science/pith/3QEW3LDHRQ7ERIS4ZVC3AXQANJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3QEW3LDHRQ7ERIS4ZVC3AXQANJ/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":"2026-05-31T23:22:47Z","links":{"resolver":"https://pith.science/pith/3QEW3LDHRQ7ERIS4ZVC3AXQANJ","bundle":"https://pith.science/pith/3QEW3LDHRQ7ERIS4ZVC3AXQANJ/bundle.json","state":"https://pith.science/pith/3QEW3LDHRQ7ERIS4ZVC3AXQANJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3QEW3LDHRQ7ERIS4ZVC3AXQANJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3QEW3LDHRQ7ERIS4ZVC3AXQANJ","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":"0e2938509ddda72be919a5844734d3629b6fb8da8757ada801cf54f084e012ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-26T12:45:42Z","title_canon_sha256":"8f5412f1f3b674c85427702f58618ed37167b2c4d3ca0c6f47b754992f9e02c2"},"schema_version":"1.0","source":{"id":"1609.07951","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07951","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07951v2","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07951","created_at":"2026-05-18T00:52:22Z"},{"alias_kind":"pith_short_12","alias_value":"3QEW3LDHRQ7E","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3QEW3LDHRQ7ERIS4","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3QEW3LDH","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:74322f191da784f20fe8d35eec1ddfa2dd4bb14189c936e157b66614f6150922","target":"graph","created_at":"2026-05-18T00:52:22Z","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":"In a chemostat, bacteria live in a growth container of constant volume in which liquid is injected continuously. Recently, Campillo and Fritsch introduced a mass-structured individual-based model to represent this dynamics and proved its convergence to a more classic partial differential equation. In this work, we are interested in the convergence of the fluctuation process. We consider this process in some Sobolev spaces and use central limit theorems on Hilbert space to prove its convergence in law to an infinite-dimensional Gaussian process.As a consequence, we obtain a two-dimensional Gaus","authors_text":"Bertrand Cloez (MISTEA), Coralie Fritsch (CMAP, IECL, TOSCA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-26T12:45:42Z","title":"Gaussian approximations for chemostat models in finite and infinite dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07951","kind":"arxiv","version":2},"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:f03c0ae42cd77081371834fd844586f22e4fdea95cf07b8776d0391ea7e0fbfc","target":"record","created_at":"2026-05-18T00:52:22Z","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":"0e2938509ddda72be919a5844734d3629b6fb8da8757ada801cf54f084e012ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-26T12:45:42Z","title_canon_sha256":"8f5412f1f3b674c85427702f58618ed37167b2c4d3ca0c6f47b754992f9e02c2"},"schema_version":"1.0","source":{"id":"1609.07951","kind":"arxiv","version":2}},"canonical_sha256":"dc096dac678c3e48a25ccd45b05e006a71270a13e0173e45596333b1a4ba5f52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc096dac678c3e48a25ccd45b05e006a71270a13e0173e45596333b1a4ba5f52","first_computed_at":"2026-05-18T00:52:22.720243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:22.720243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FtAWELTUZnf+KGXQEmD8NQ4BdVl6p1lyTze01teygtctNK6DUMdnAH3LvSJ2rn7aAzCkyQy+u/AwvPt7HZ+sAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:22.720883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07951","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f03c0ae42cd77081371834fd844586f22e4fdea95cf07b8776d0391ea7e0fbfc","sha256:74322f191da784f20fe8d35eec1ddfa2dd4bb14189c936e157b66614f6150922"],"state_sha256":"c827e7ea42ee6d90af61034abdd1f6f289637ee18a78b5e37f5af4a9b1445ed6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lidGzEst1BTrY6sMmPWVcTHq08yT6lolfUbsOMCM+timFNIn0BMrN+QvOCPsat/6lYR1tBroodkK+yEqJ/HMAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:22:47.479253Z","bundle_sha256":"4f507e6c3536a8ece66b629280923b2c9fc276e5cec1f0253b6cfc5b9c1693a7"}}