{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Y2BY3HKFCKZQPDW2RUNGV4SXKR","short_pith_number":"pith:Y2BY3HKF","canonical_record":{"source":{"id":"2602.01138","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-02-01T10:20:50Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"24937445e634595116318f8815a8a285bc5020f776cbccbb41a9d1d9d39deeb8","abstract_canon_sha256":"b2f778282f7426dae40b7e66a8c09038d5507d714f577d555100acc5c325e96c"},"schema_version":"1.0"},"canonical_sha256":"c6838d9d4512b3078eda8d1a6af25754536d7ddcd9287518fa2b88945751723f","source":{"kind":"arxiv","id":"2602.01138","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.01138","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"arxiv_version","alias_value":"2602.01138v2","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.01138","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"pith_short_12","alias_value":"Y2BY3HKFCKZQ","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"pith_short_16","alias_value":"Y2BY3HKFCKZQPDW2","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"pith_short_8","alias_value":"Y2BY3HKF","created_at":"2026-05-20T00:05:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Y2BY3HKFCKZQPDW2RUNGV4SXKR","target":"record","payload":{"canonical_record":{"source":{"id":"2602.01138","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-02-01T10:20:50Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"24937445e634595116318f8815a8a285bc5020f776cbccbb41a9d1d9d39deeb8","abstract_canon_sha256":"b2f778282f7426dae40b7e66a8c09038d5507d714f577d555100acc5c325e96c"},"schema_version":"1.0"},"canonical_sha256":"c6838d9d4512b3078eda8d1a6af25754536d7ddcd9287518fa2b88945751723f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:41.249195Z","signature_b64":"cq+lcnkVNFQaH300efpoAccIfyYJ9mPRgD8IhGhdxeqkUrIC3XThRt9Vrpg1IdVMPxL//a8cXBmaORNV6D/PCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6838d9d4512b3078eda8d1a6af25754536d7ddcd9287518fa2b88945751723f","last_reissued_at":"2026-05-20T00:05:41.248687Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:41.248687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.01138","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":"2026-05-20T00:05:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VCadsqFx/LKSO8X6CUY0mss1vXsb1jVEZeFnU04tNA+ncjfjkZKv0tmx1lTRg/e+oc4XJYHZgytUrDqrCiZLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:41:37.272991Z"},"content_sha256":"6815143f2ed584100eaee6726d606687d665f715efbc2b2b2dad771913694238","schema_version":"1.0","event_id":"sha256:6815143f2ed584100eaee6726d606687d665f715efbc2b2b2dad771913694238"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Y2BY3HKFCKZQPDW2RUNGV4SXKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigorous derivation of the mean-field limit for the signal-dependent Keller-Segel system","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Hui Huang, Jinhuan Wang, Keyu Li","submitted_at":"2026-02-01T10:20:50Z","abstract_excerpt":"We rigorously derive a two-dimensional Keller-Segel type system with signal-dependent sensitivity from a stochastic interacting particle model. By employing suitably defined stopping times, we prove that the convergence of the interacting particle system towards the corresponding mean-field limit equations in probability under an algebraic scaling regime which improves upon existing results with logarithmic scaling. Building on this, we apply the relative-entropy method to obtain strong $L^1$ propagation of chaos, and establish an algebraic convergence rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.01138","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.01138/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":"2026-05-20T00:05:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MoZIKXrj5GmQ8Q2TyNoMM6tpR9j/gAiwJ/HkC41ikz0/Y2QGGA0KeyuXw1MaujzK8Ekk/WIVBz68bUufKn9zAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:41:37.273500Z"},"content_sha256":"a2faedf510a65c18851969eac4652aeeda4467400febf5b61e67b5cf63d273fa","schema_version":"1.0","event_id":"sha256:a2faedf510a65c18851969eac4652aeeda4467400febf5b61e67b5cf63d273fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2BY3HKFCKZQPDW2RUNGV4SXKR/bundle.json","state_url":"https://pith.science/pith/Y2BY3HKFCKZQPDW2RUNGV4SXKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2BY3HKFCKZQPDW2RUNGV4SXKR/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":"2026-05-25T19:41:37Z","links":{"resolver":"https://pith.science/pith/Y2BY3HKFCKZQPDW2RUNGV4SXKR","bundle":"https://pith.science/pith/Y2BY3HKFCKZQPDW2RUNGV4SXKR/bundle.json","state":"https://pith.science/pith/Y2BY3HKFCKZQPDW2RUNGV4SXKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2BY3HKFCKZQPDW2RUNGV4SXKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Y2BY3HKFCKZQPDW2RUNGV4SXKR","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":"b2f778282f7426dae40b7e66a8c09038d5507d714f577d555100acc5c325e96c","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-02-01T10:20:50Z","title_canon_sha256":"24937445e634595116318f8815a8a285bc5020f776cbccbb41a9d1d9d39deeb8"},"schema_version":"1.0","source":{"id":"2602.01138","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.01138","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"arxiv_version","alias_value":"2602.01138v2","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.01138","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"pith_short_12","alias_value":"Y2BY3HKFCKZQ","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"pith_short_16","alias_value":"Y2BY3HKFCKZQPDW2","created_at":"2026-05-20T00:05:41Z"},{"alias_kind":"pith_short_8","alias_value":"Y2BY3HKF","created_at":"2026-05-20T00:05:41Z"}],"graph_snapshots":[{"event_id":"sha256:a2faedf510a65c18851969eac4652aeeda4467400febf5b61e67b5cf63d273fa","target":"graph","created_at":"2026-05-20T00:05:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2602.01138/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We rigorously derive a two-dimensional Keller-Segel type system with signal-dependent sensitivity from a stochastic interacting particle model. By employing suitably defined stopping times, we prove that the convergence of the interacting particle system towards the corresponding mean-field limit equations in probability under an algebraic scaling regime which improves upon existing results with logarithmic scaling. Building on this, we apply the relative-entropy method to obtain strong $L^1$ propagation of chaos, and establish an algebraic convergence rate.","authors_text":"Hui Huang, Jinhuan Wang, Keyu Li","cross_cats":["math.AP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-02-01T10:20:50Z","title":"Rigorous derivation of the mean-field limit for the signal-dependent Keller-Segel system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.01138","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":"sha256:6815143f2ed584100eaee6726d606687d665f715efbc2b2b2dad771913694238","target":"record","created_at":"2026-05-20T00:05:41Z","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":"b2f778282f7426dae40b7e66a8c09038d5507d714f577d555100acc5c325e96c","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-02-01T10:20:50Z","title_canon_sha256":"24937445e634595116318f8815a8a285bc5020f776cbccbb41a9d1d9d39deeb8"},"schema_version":"1.0","source":{"id":"2602.01138","kind":"arxiv","version":2}},"canonical_sha256":"c6838d9d4512b3078eda8d1a6af25754536d7ddcd9287518fa2b88945751723f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6838d9d4512b3078eda8d1a6af25754536d7ddcd9287518fa2b88945751723f","first_computed_at":"2026-05-20T00:05:41.248687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:41.248687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cq+lcnkVNFQaH300efpoAccIfyYJ9mPRgD8IhGhdxeqkUrIC3XThRt9Vrpg1IdVMPxL//a8cXBmaORNV6D/PCA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:41.249195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.01138","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6815143f2ed584100eaee6726d606687d665f715efbc2b2b2dad771913694238","sha256:a2faedf510a65c18851969eac4652aeeda4467400febf5b61e67b5cf63d273fa"],"state_sha256":"7de7964bc867080381e05d4133fbc763e04bb4429e4cae94bbe7925792076aeb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lyIbT8NA3oNbLUaP9yaEw+xUdL5d7eu2qBD+1CwseyDMLksQgix6NSELWr/UIl7Uo1XiczuOx1VOdV8oUptMCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:41:37.277172Z","bundle_sha256":"f42ad8b5ec3bf9bbe8451e191e237588da86a8b208a638e90425557f361ed22f"}}