{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:S5CWLVI3DSIZBJ3PNHUNBGTF72","short_pith_number":"pith:S5CWLVI3","canonical_record":{"source":{"id":"1802.09668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T01:15:26Z","cross_cats_sorted":["math.DS","math.PR"],"title_canon_sha256":"222c4f289f6c1360f8c77dc1588ca4634c000b6e5367b34b73d8138a8f965089","abstract_canon_sha256":"2763454aae7e962b58a9d6ec67e41f330842301a362670b8ca285a4b9e743a7c"},"schema_version":"1.0"},"canonical_sha256":"974565d51b1c9190a76f69e8d09a65fe8698777dbd6c22eacfe32c4d013a026d","source":{"kind":"arxiv","id":"1802.09668","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09668","created_at":"2026-05-18T00:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09668v2","created_at":"2026-05-18T00:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09668","created_at":"2026-05-18T00:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"S5CWLVI3DSIZ","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S5CWLVI3DSIZBJ3P","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S5CWLVI3","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:S5CWLVI3DSIZBJ3PNHUNBGTF72","target":"record","payload":{"canonical_record":{"source":{"id":"1802.09668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T01:15:26Z","cross_cats_sorted":["math.DS","math.PR"],"title_canon_sha256":"222c4f289f6c1360f8c77dc1588ca4634c000b6e5367b34b73d8138a8f965089","abstract_canon_sha256":"2763454aae7e962b58a9d6ec67e41f330842301a362670b8ca285a4b9e743a7c"},"schema_version":"1.0"},"canonical_sha256":"974565d51b1c9190a76f69e8d09a65fe8698777dbd6c22eacfe32c4d013a026d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:05.187136Z","signature_b64":"rgtmd8eVhP8afi11Rqc9z75+RZ/zgu0uMwafE5iSRQbhjDSkH0v/e0fsOWyYqhthHXpG1C7UwPJJ54MpxGJWCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"974565d51b1c9190a76f69e8d09a65fe8698777dbd6c22eacfe32c4d013a026d","last_reissued_at":"2026-05-18T00:05:05.186489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:05.186489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.09668","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":"2026-05-18T00:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IcEduC6PPpkNV49JJX8l4BXz+APEOS6JiyG26kREmg72M4bBQpR6Pk2vdSbwBU7q4AZGA6qmMKba9AYXVuL6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:25:21.652858Z"},"content_sha256":"bbcbf0070ba626ca3d33cc55f75111fe5247ee1d54fe737c15dba1f2934a0284","schema_version":"1.0","event_id":"sha256:bbcbf0070ba626ca3d33cc55f75111fe5247ee1d54fe737c15dba1f2934a0284"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:S5CWLVI3DSIZBJ3PNHUNBGTF72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Propagation of chaos for the Keller-Segel equation over bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR"],"primary_cat":"math.AP","authors_text":"Hui Huang, Razvan C. Fetecau, Weiran Sun","submitted_at":"2018-02-27T01:15:26Z","abstract_excerpt":"In this paper we rigorously justify the propagation of chaos for the parabolic-elliptic Keller-Segel equation over bounded convex domains. The boundary condition under consideration is the no-flux condition. As intermediate steps, we establish the well-posedness of the associated stochastic equation as well as the well-posedness of the Keller-Segel equation for bounded weak solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09668","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":"2026-05-18T00:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lRarn07yvIHHQKjnqT5IFhajRTmXRDYwfjzz75Om1dhsOaCvS7sAqGo+QII1mD7tmaQks2wV7eqxIJlExdoHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:25:21.653609Z"},"content_sha256":"237eecf9fc3aadfdca268c12903307335bd6c32c69a184b407f9834f02859240","schema_version":"1.0","event_id":"sha256:237eecf9fc3aadfdca268c12903307335bd6c32c69a184b407f9834f02859240"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5CWLVI3DSIZBJ3PNHUNBGTF72/bundle.json","state_url":"https://pith.science/pith/S5CWLVI3DSIZBJ3PNHUNBGTF72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5CWLVI3DSIZBJ3PNHUNBGTF72/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":"2026-06-09T02:25:21Z","links":{"resolver":"https://pith.science/pith/S5CWLVI3DSIZBJ3PNHUNBGTF72","bundle":"https://pith.science/pith/S5CWLVI3DSIZBJ3PNHUNBGTF72/bundle.json","state":"https://pith.science/pith/S5CWLVI3DSIZBJ3PNHUNBGTF72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5CWLVI3DSIZBJ3PNHUNBGTF72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S5CWLVI3DSIZBJ3PNHUNBGTF72","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":"2763454aae7e962b58a9d6ec67e41f330842301a362670b8ca285a4b9e743a7c","cross_cats_sorted":["math.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T01:15:26Z","title_canon_sha256":"222c4f289f6c1360f8c77dc1588ca4634c000b6e5367b34b73d8138a8f965089"},"schema_version":"1.0","source":{"id":"1802.09668","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09668","created_at":"2026-05-18T00:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09668v2","created_at":"2026-05-18T00:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09668","created_at":"2026-05-18T00:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"S5CWLVI3DSIZ","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S5CWLVI3DSIZBJ3P","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S5CWLVI3","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:237eecf9fc3aadfdca268c12903307335bd6c32c69a184b407f9834f02859240","target":"graph","created_at":"2026-05-18T00:05:05Z","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 this paper we rigorously justify the propagation of chaos for the parabolic-elliptic Keller-Segel equation over bounded convex domains. The boundary condition under consideration is the no-flux condition. As intermediate steps, we establish the well-posedness of the associated stochastic equation as well as the well-posedness of the Keller-Segel equation for bounded weak solutions.","authors_text":"Hui Huang, Razvan C. Fetecau, Weiran Sun","cross_cats":["math.DS","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T01:15:26Z","title":"Propagation of chaos for the Keller-Segel equation over bounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09668","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:bbcbf0070ba626ca3d33cc55f75111fe5247ee1d54fe737c15dba1f2934a0284","target":"record","created_at":"2026-05-18T00:05:05Z","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":"2763454aae7e962b58a9d6ec67e41f330842301a362670b8ca285a4b9e743a7c","cross_cats_sorted":["math.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-27T01:15:26Z","title_canon_sha256":"222c4f289f6c1360f8c77dc1588ca4634c000b6e5367b34b73d8138a8f965089"},"schema_version":"1.0","source":{"id":"1802.09668","kind":"arxiv","version":2}},"canonical_sha256":"974565d51b1c9190a76f69e8d09a65fe8698777dbd6c22eacfe32c4d013a026d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"974565d51b1c9190a76f69e8d09a65fe8698777dbd6c22eacfe32c4d013a026d","first_computed_at":"2026-05-18T00:05:05.186489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:05.186489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgtmd8eVhP8afi11Rqc9z75+RZ/zgu0uMwafE5iSRQbhjDSkH0v/e0fsOWyYqhthHXpG1C7UwPJJ54MpxGJWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:05.187136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.09668","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbcbf0070ba626ca3d33cc55f75111fe5247ee1d54fe737c15dba1f2934a0284","sha256:237eecf9fc3aadfdca268c12903307335bd6c32c69a184b407f9834f02859240"],"state_sha256":"54f7eb4e184907c6eb00bc17e7459355d0771536fb445b464a2cb0d0d8ed9345"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YcbjKSX2D4grad/Me/W9tc8g/KOppR/cpleuD8eTg6PF2mB3N8M1idrJXLDWx2NsMd1dKLIgFRADPQP7LymECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:25:21.657963Z","bundle_sha256":"bfef3bf601b61e1aa402d758578fd9ab527a4ef857373f752edcc83e169c1413"}}