{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:YU3MFQKD5DFUTZJOMNCUDPBIQB","short_pith_number":"pith:YU3MFQKD","canonical_record":{"source":{"id":"2209.13188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-27T06:44:06Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b20a9633f2a4e254701b660534048b190a7e6dbac8c069e31dc52f65fd6b35c9","abstract_canon_sha256":"76ecbc0259579b93326ab2cb72480b5c02c1569ee60173c780ace3d671e2b8be"},"schema_version":"1.0"},"canonical_sha256":"c536c2c143e8cb49e52e634541bc28806c612c0985a28b4c727e7501c9df325b","source":{"kind":"arxiv","id":"2209.13188","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.13188","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"arxiv_version","alias_value":"2209.13188v1","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.13188","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_12","alias_value":"YU3MFQKD5DFU","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_16","alias_value":"YU3MFQKD5DFUTZJO","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_8","alias_value":"YU3MFQKD","created_at":"2026-07-05T05:01:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:YU3MFQKD5DFUTZJOMNCUDPBIQB","target":"record","payload":{"canonical_record":{"source":{"id":"2209.13188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-27T06:44:06Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b20a9633f2a4e254701b660534048b190a7e6dbac8c069e31dc52f65fd6b35c9","abstract_canon_sha256":"76ecbc0259579b93326ab2cb72480b5c02c1569ee60173c780ace3d671e2b8be"},"schema_version":"1.0"},"canonical_sha256":"c536c2c143e8cb49e52e634541bc28806c612c0985a28b4c727e7501c9df325b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:01:07.593110Z","signature_b64":"5YCVCChCsFpnAY1F6H3s7We6NNodsaNPd/FwAqioDq5QeQ/K9xPLZBx9DjzBY3eojijYEHDCMeN6SLPF/gW4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c536c2c143e8cb49e52e634541bc28806c612c0985a28b4c727e7501c9df325b","last_reissued_at":"2026-07-05T05:01:07.592689Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:01:07.592689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.13188","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":"2026-07-05T05:01:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GyFyeOk1iY4bQOsnAI0sTfwBu42IOWwuGAPCNqqDkchXR+0SkdTTI2hl1uureF1W57Rp75p3qmWm+dQrCU9nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:34:08.187495Z"},"content_sha256":"00fe7ea663b174bef79d9f7fa233888b329c3a4b87999d8a3ba87fed1650f7e0","schema_version":"1.0","event_id":"sha256:00fe7ea663b174bef79d9f7fa233888b329c3a4b87999d8a3ba87fed1650f7e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:YU3MFQKD5DFUTZJOMNCUDPBIQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of the stochastic Keller-Segel model in one dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Debopriya Mukherjee, Erika Hausenblas, Thanh Tran","submitted_at":"2022-09-27T06:44:06Z","abstract_excerpt":"In a recent paper (J. Differential Equations, 310: 506-554, 2022), the authors proved the existence of martingale solutions to a stochastic version of the classical Patlak-Keller-Segel system in 1 dimension (1D), driven by time-homogeneous spatial Wiener processes. The current paper is a continuation and consists of two results about the stochastic Patlak-Keller-Segel system in 1D. First, we establish some additional regularity results of the solutions. The additional regularity is, e.g. important for its numerical modeling. Then, as a second result, we obtain the pathwise uniqueness of the so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.13188","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.13188/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:01:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1vMETvqUxJH2ltfpitGRbBwL9Sqw8sHa9PMXsJM+11SbTu8R6V4T80r2H8ZY43oKZaMrLv1jeYRjMp2JqFhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:34:08.188412Z"},"content_sha256":"e6918f958ccb1c92d0633c979dc9e05a3f58c51cd07eb7616a290b62b04e56bb","schema_version":"1.0","event_id":"sha256:e6918f958ccb1c92d0633c979dc9e05a3f58c51cd07eb7616a290b62b04e56bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YU3MFQKD5DFUTZJOMNCUDPBIQB/bundle.json","state_url":"https://pith.science/pith/YU3MFQKD5DFUTZJOMNCUDPBIQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YU3MFQKD5DFUTZJOMNCUDPBIQB/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":"2026-08-11T06:34:08Z","links":{"resolver":"https://pith.science/pith/YU3MFQKD5DFUTZJOMNCUDPBIQB","bundle":"https://pith.science/pith/YU3MFQKD5DFUTZJOMNCUDPBIQB/bundle.json","state":"https://pith.science/pith/YU3MFQKD5DFUTZJOMNCUDPBIQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YU3MFQKD5DFUTZJOMNCUDPBIQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YU3MFQKD5DFUTZJOMNCUDPBIQB","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":"76ecbc0259579b93326ab2cb72480b5c02c1569ee60173c780ace3d671e2b8be","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-27T06:44:06Z","title_canon_sha256":"b20a9633f2a4e254701b660534048b190a7e6dbac8c069e31dc52f65fd6b35c9"},"schema_version":"1.0","source":{"id":"2209.13188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.13188","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"arxiv_version","alias_value":"2209.13188v1","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.13188","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_12","alias_value":"YU3MFQKD5DFU","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_16","alias_value":"YU3MFQKD5DFUTZJO","created_at":"2026-07-05T05:01:07Z"},{"alias_kind":"pith_short_8","alias_value":"YU3MFQKD","created_at":"2026-07-05T05:01:07Z"}],"graph_snapshots":[{"event_id":"sha256:e6918f958ccb1c92d0633c979dc9e05a3f58c51cd07eb7616a290b62b04e56bb","target":"graph","created_at":"2026-07-05T05:01:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.13188/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a recent paper (J. Differential Equations, 310: 506-554, 2022), the authors proved the existence of martingale solutions to a stochastic version of the classical Patlak-Keller-Segel system in 1 dimension (1D), driven by time-homogeneous spatial Wiener processes. The current paper is a continuation and consists of two results about the stochastic Patlak-Keller-Segel system in 1D. First, we establish some additional regularity results of the solutions. The additional regularity is, e.g. important for its numerical modeling. Then, as a second result, we obtain the pathwise uniqueness of the so","authors_text":"Debopriya Mukherjee, Erika Hausenblas, Thanh Tran","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-27T06:44:06Z","title":"Uniqueness of the stochastic Keller-Segel model in one dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.13188","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":"sha256:00fe7ea663b174bef79d9f7fa233888b329c3a4b87999d8a3ba87fed1650f7e0","target":"record","created_at":"2026-07-05T05:01:07Z","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":"76ecbc0259579b93326ab2cb72480b5c02c1569ee60173c780ace3d671e2b8be","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-09-27T06:44:06Z","title_canon_sha256":"b20a9633f2a4e254701b660534048b190a7e6dbac8c069e31dc52f65fd6b35c9"},"schema_version":"1.0","source":{"id":"2209.13188","kind":"arxiv","version":1}},"canonical_sha256":"c536c2c143e8cb49e52e634541bc28806c612c0985a28b4c727e7501c9df325b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c536c2c143e8cb49e52e634541bc28806c612c0985a28b4c727e7501c9df325b","first_computed_at":"2026-07-05T05:01:07.592689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:01:07.592689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5YCVCChCsFpnAY1F6H3s7We6NNodsaNPd/FwAqioDq5QeQ/K9xPLZBx9DjzBY3eojijYEHDCMeN6SLPF/gW4Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:01:07.593110Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.13188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00fe7ea663b174bef79d9f7fa233888b329c3a4b87999d8a3ba87fed1650f7e0","sha256:e6918f958ccb1c92d0633c979dc9e05a3f58c51cd07eb7616a290b62b04e56bb"],"state_sha256":"bd0eb33edba89735ec9a0c61250b4b769f82f6556c1a2ec8be7b54f9b82c23ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"smVPCApqRDpj/KboXbu+RFz+WdOPmS7ZzrKxJ6qY3eBvtREmsdgJorf88JWydYd2dpw8tuuM/dPrF1i4rLxbDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T06:34:08.195214Z","bundle_sha256":"fc7e5371dfdb5cece53084164f18ed46f1a27de552b2f99fb499e0bd31340fb7"}}