{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5J2EOWW5JJRCILSDLGF4VXL2FV","short_pith_number":"pith:5J2EOWW5","canonical_record":{"source":{"id":"1601.08026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-29T10:14:39Z","cross_cats_sorted":[],"title_canon_sha256":"b87b407a7d398330584388ead6ca8e6f55f03709a70b2e67c81c42b0e19a906d","abstract_canon_sha256":"71b71003149527d4891e64a5201c994847a63392c6f10f580a26942c79070ed7"},"schema_version":"1.0"},"canonical_sha256":"ea74475add4a62242e43598bcadd7a2d5712c4fb71392a993eff19647e70e67c","source":{"kind":"arxiv","id":"1601.08026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08026","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08026v1","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08026","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"pith_short_12","alias_value":"5J2EOWW5JJRC","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5J2EOWW5JJRCILSD","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5J2EOWW5","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5J2EOWW5JJRCILSDLGF4VXL2FV","target":"record","payload":{"canonical_record":{"source":{"id":"1601.08026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-29T10:14:39Z","cross_cats_sorted":[],"title_canon_sha256":"b87b407a7d398330584388ead6ca8e6f55f03709a70b2e67c81c42b0e19a906d","abstract_canon_sha256":"71b71003149527d4891e64a5201c994847a63392c6f10f580a26942c79070ed7"},"schema_version":"1.0"},"canonical_sha256":"ea74475add4a62242e43598bcadd7a2d5712c4fb71392a993eff19647e70e67c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:41.199637Z","signature_b64":"zK4Up1DQRTgMtDtFcG5WRZkFu0bljpjPn/HB7lcLLpp4y/vyWVig+dtDFFW1bnvcazfjCaN3yDRML2+6yeJvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea74475add4a62242e43598bcadd7a2d5712c4fb71392a993eff19647e70e67c","last_reissued_at":"2026-05-18T01:21:41.198970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:41.198970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.08026","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":"2026-05-18T01:21:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5QCQULqh4YBJRYTi2tDb+xrD3wgwtDOu4zGsME2JWqd0lSHQ/GXsiK22W+WNRANOqf+8J2sJeywmiBfFqZwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:47:34.622219Z"},"content_sha256":"d0255cc17aebcc1e6dab604152bb0bc3e09d2719eebb39ab196b7943227c2cc0","schema_version":"1.0","event_id":"sha256:d0255cc17aebcc1e6dab604152bb0bc3e09d2719eebb39ab196b7943227c2cc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5J2EOWW5JJRCILSDLGF4VXL2FV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The 2-D stochastic Keller-Segel particle model : existence and uniqueness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laure P\\'ed\\`eches (IMT), Patrick Cattiaux (IMT)","submitted_at":"2016-01-29T10:14:39Z","abstract_excerpt":"We introduce a stochastic system of interacting particles which is expected to furnish as the number of particles goes to infinity a stochastic approach of the 2-D Keller-Segel model. In this note, we prove existence and some uniqueness for the stochastic model for the parabolic-elliptic Keller-Segel equation, for all regimes under the critical mass. Prior results for existence and weak uniqueness have been very recently obtained by N. Fournier and B. Jourdain [6]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08026","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":"2026-05-18T01:21:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q/hOychflFmJ+gbAExTp1WehZ7axVmPAFBXgb1Ib5H3DhRTDRBMi5kN/DnAcZiqZDKUlRkPGG0gFGrVe8BTCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:47:34.622811Z"},"content_sha256":"b5baba465a7d045740997bf4bfd708b6b450c4bf2dc33436e81fdbfd36b87f78","schema_version":"1.0","event_id":"sha256:b5baba465a7d045740997bf4bfd708b6b450c4bf2dc33436e81fdbfd36b87f78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5J2EOWW5JJRCILSDLGF4VXL2FV/bundle.json","state_url":"https://pith.science/pith/5J2EOWW5JJRCILSDLGF4VXL2FV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5J2EOWW5JJRCILSDLGF4VXL2FV/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":"2026-08-17T14:47:34Z","links":{"resolver":"https://pith.science/pith/5J2EOWW5JJRCILSDLGF4VXL2FV","bundle":"https://pith.science/pith/5J2EOWW5JJRCILSDLGF4VXL2FV/bundle.json","state":"https://pith.science/pith/5J2EOWW5JJRCILSDLGF4VXL2FV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5J2EOWW5JJRCILSDLGF4VXL2FV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5J2EOWW5JJRCILSDLGF4VXL2FV","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":"71b71003149527d4891e64a5201c994847a63392c6f10f580a26942c79070ed7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-29T10:14:39Z","title_canon_sha256":"b87b407a7d398330584388ead6ca8e6f55f03709a70b2e67c81c42b0e19a906d"},"schema_version":"1.0","source":{"id":"1601.08026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08026","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08026v1","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08026","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"pith_short_12","alias_value":"5J2EOWW5JJRC","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5J2EOWW5JJRCILSD","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5J2EOWW5","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:b5baba465a7d045740997bf4bfd708b6b450c4bf2dc33436e81fdbfd36b87f78","target":"graph","created_at":"2026-05-18T01:21:41Z","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 introduce a stochastic system of interacting particles which is expected to furnish as the number of particles goes to infinity a stochastic approach of the 2-D Keller-Segel model. In this note, we prove existence and some uniqueness for the stochastic model for the parabolic-elliptic Keller-Segel equation, for all regimes under the critical mass. Prior results for existence and weak uniqueness have been very recently obtained by N. Fournier and B. Jourdain [6].","authors_text":"Laure P\\'ed\\`eches (IMT), Patrick Cattiaux (IMT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-29T10:14:39Z","title":"The 2-D stochastic Keller-Segel particle model : existence and uniqueness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08026","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:d0255cc17aebcc1e6dab604152bb0bc3e09d2719eebb39ab196b7943227c2cc0","target":"record","created_at":"2026-05-18T01:21:41Z","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":"71b71003149527d4891e64a5201c994847a63392c6f10f580a26942c79070ed7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-29T10:14:39Z","title_canon_sha256":"b87b407a7d398330584388ead6ca8e6f55f03709a70b2e67c81c42b0e19a906d"},"schema_version":"1.0","source":{"id":"1601.08026","kind":"arxiv","version":1}},"canonical_sha256":"ea74475add4a62242e43598bcadd7a2d5712c4fb71392a993eff19647e70e67c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea74475add4a62242e43598bcadd7a2d5712c4fb71392a993eff19647e70e67c","first_computed_at":"2026-05-18T01:21:41.198970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:41.198970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zK4Up1DQRTgMtDtFcG5WRZkFu0bljpjPn/HB7lcLLpp4y/vyWVig+dtDFFW1bnvcazfjCaN3yDRML2+6yeJvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:41.199637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.08026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0255cc17aebcc1e6dab604152bb0bc3e09d2719eebb39ab196b7943227c2cc0","sha256:b5baba465a7d045740997bf4bfd708b6b450c4bf2dc33436e81fdbfd36b87f78"],"state_sha256":"0c68a0cbbbdeb5beec5828f6630a86982dd6e4b10d13ac1524cab699562ba842"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ijm+uZc58RPNf4M9c3/xFccgK2ZWFlpiuqK2EJNe7h4wL3JTukpVBcJN627LbXndbzmAA7GFR49h4s2vXyleCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T14:47:34.706714Z","bundle_sha256":"34ef8b3cf2e86f0f75fba58c2ce3b57a99a15debff2aeda7f7577710c93435c2"}}