{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CXUN6SN5KK6YAWJIGJSW4WLSN3","short_pith_number":"pith:CXUN6SN5","canonical_record":{"source":{"id":"1210.3429","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AP","submitted_at":"2012-10-12T04:36:48Z","cross_cats_sorted":[],"title_canon_sha256":"71765c10e222afb9865195aa02eed88a6c92df86eb80a6a8aac69535e55b14d8","abstract_canon_sha256":"12da366279827d1191e3405e8e1184d8b3c58463feee6499eaeff51120838685"},"schema_version":"1.0"},"canonical_sha256":"15e8df49bd52bd80592832656e59726ed03dd2b4c4fab6e6248557b9a3c3f27a","source":{"kind":"arxiv","id":"1210.3429","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3429","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3429v1","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3429","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"pith_short_12","alias_value":"CXUN6SN5KK6Y","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CXUN6SN5KK6YAWJI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CXUN6SN5","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CXUN6SN5KK6YAWJIGJSW4WLSN3","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3429","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AP","submitted_at":"2012-10-12T04:36:48Z","cross_cats_sorted":[],"title_canon_sha256":"71765c10e222afb9865195aa02eed88a6c92df86eb80a6a8aac69535e55b14d8","abstract_canon_sha256":"12da366279827d1191e3405e8e1184d8b3c58463feee6499eaeff51120838685"},"schema_version":"1.0"},"canonical_sha256":"15e8df49bd52bd80592832656e59726ed03dd2b4c4fab6e6248557b9a3c3f27a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:19.902586Z","signature_b64":"Hqjp9Rj5jz6FDQghtkMI2ucK1TfsDe4qPkYwCwmSohQbuAAsEKyouPESlJe2YEmLWJNQL9Z3lVdjJy50UfFpCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15e8df49bd52bd80592832656e59726ed03dd2b4c4fab6e6248557b9a3c3f27a","last_reissued_at":"2026-05-18T03:43:19.900901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:19.900901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3429","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":"2026-05-18T03:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nZRx5C+3ifCwY1Yd3BBt6aP9fpXsWML/3ohIeHdqfQXcb3lOoOD22els7VKtyeNmbPH5wZy26NDVAQcWUwdqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:59:42.731353Z"},"content_sha256":"ec3b01a327bfe436e9e1bb480546f1183d8ae8645b7217bee3130be40a8b0d3b","schema_version":"1.0","event_id":"sha256:ec3b01a327bfe436e9e1bb480546f1183d8ae8645b7217bee3130be40a8b0d3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CXUN6SN5KK6YAWJIGJSW4WLSN3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Well-posedness of the Parabolic-parabolic Keller-Segel Model in $L^{1}(R^2)\\times{L}^{\\infty}(R^2)$ and $H^1_b(R^2)\\times{H}^1(R^2)$","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Deng, Congming Li","submitted_at":"2012-10-12T04:36:48Z","abstract_excerpt":"In this paper, we study global well-posedness of the two-dimensional Keller-Segel model in Lebesgue space and Sobolev space. Recall that in the paper \"Existence and uniqueness theorem on mild solutions to the Keller-Segel system in the scaling invariant space, J. Differential Equations, {252}(2012), 1213--1228\", Kozono, Sugiyama & Wachi studied global well-posedness of $n$($\\ge3$) dimensional Keller-Segel system and posted a question about the even local in time existence for the Keller-Segel system with $L^1(R^2)\\times{L}^\\infty(R^2)$ initial data. Here we give an affirmative answer to this q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3429","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":"2026-05-18T03:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5TYy3wiqAO/vTIN7rOiWlWen97YCIP0y2NMgcK7cRSbPGFBub9GBKqpSrGuetoXFzuqDgk3VSg+glSWCxIRnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:59:42.731704Z"},"content_sha256":"bdd12e7fefbb6043217a60371d33f59c47655acccfcc0e17d5cd7aeb21a59465","schema_version":"1.0","event_id":"sha256:bdd12e7fefbb6043217a60371d33f59c47655acccfcc0e17d5cd7aeb21a59465"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXUN6SN5KK6YAWJIGJSW4WLSN3/bundle.json","state_url":"https://pith.science/pith/CXUN6SN5KK6YAWJIGJSW4WLSN3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXUN6SN5KK6YAWJIGJSW4WLSN3/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":"2026-06-01T18:59:42Z","links":{"resolver":"https://pith.science/pith/CXUN6SN5KK6YAWJIGJSW4WLSN3","bundle":"https://pith.science/pith/CXUN6SN5KK6YAWJIGJSW4WLSN3/bundle.json","state":"https://pith.science/pith/CXUN6SN5KK6YAWJIGJSW4WLSN3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXUN6SN5KK6YAWJIGJSW4WLSN3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CXUN6SN5KK6YAWJIGJSW4WLSN3","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":"12da366279827d1191e3405e8e1184d8b3c58463feee6499eaeff51120838685","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AP","submitted_at":"2012-10-12T04:36:48Z","title_canon_sha256":"71765c10e222afb9865195aa02eed88a6c92df86eb80a6a8aac69535e55b14d8"},"schema_version":"1.0","source":{"id":"1210.3429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3429","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3429v1","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3429","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"pith_short_12","alias_value":"CXUN6SN5KK6Y","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CXUN6SN5KK6YAWJI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CXUN6SN5","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:bdd12e7fefbb6043217a60371d33f59c47655acccfcc0e17d5cd7aeb21a59465","target":"graph","created_at":"2026-05-18T03:43:19Z","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 study global well-posedness of the two-dimensional Keller-Segel model in Lebesgue space and Sobolev space. Recall that in the paper \"Existence and uniqueness theorem on mild solutions to the Keller-Segel system in the scaling invariant space, J. Differential Equations, {252}(2012), 1213--1228\", Kozono, Sugiyama & Wachi studied global well-posedness of $n$($\\ge3$) dimensional Keller-Segel system and posted a question about the even local in time existence for the Keller-Segel system with $L^1(R^2)\\times{L}^\\infty(R^2)$ initial data. Here we give an affirmative answer to this q","authors_text":"Chao Deng, Congming Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AP","submitted_at":"2012-10-12T04:36:48Z","title":"Global Well-posedness of the Parabolic-parabolic Keller-Segel Model in $L^{1}(R^2)\\times{L}^{\\infty}(R^2)$ and $H^1_b(R^2)\\times{H}^1(R^2)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3429","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:ec3b01a327bfe436e9e1bb480546f1183d8ae8645b7217bee3130be40a8b0d3b","target":"record","created_at":"2026-05-18T03:43:19Z","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":"12da366279827d1191e3405e8e1184d8b3c58463feee6499eaeff51120838685","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AP","submitted_at":"2012-10-12T04:36:48Z","title_canon_sha256":"71765c10e222afb9865195aa02eed88a6c92df86eb80a6a8aac69535e55b14d8"},"schema_version":"1.0","source":{"id":"1210.3429","kind":"arxiv","version":1}},"canonical_sha256":"15e8df49bd52bd80592832656e59726ed03dd2b4c4fab6e6248557b9a3c3f27a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15e8df49bd52bd80592832656e59726ed03dd2b4c4fab6e6248557b9a3c3f27a","first_computed_at":"2026-05-18T03:43:19.900901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:19.900901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hqjp9Rj5jz6FDQghtkMI2ucK1TfsDe4qPkYwCwmSohQbuAAsEKyouPESlJe2YEmLWJNQL9Z3lVdjJy50UfFpCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:19.902586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec3b01a327bfe436e9e1bb480546f1183d8ae8645b7217bee3130be40a8b0d3b","sha256:bdd12e7fefbb6043217a60371d33f59c47655acccfcc0e17d5cd7aeb21a59465"],"state_sha256":"635e590f84872da2bf0c4a3411aed8871a747a42713c3b69eddfc31d3e87dd24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Jxz6DdHeUqMAVLxTBbpAy9gWhtb1C1xkb3gpooX7h2E7eOXNDzYJyUoqAk3ZBbt6jOvR2kyXBwh1DJuxhXODQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:59:42.734529Z","bundle_sha256":"d9f1adf6e809a1ee0a54fbfb7eb53c19b8e090c182e69a9c2ceacd4252239d20"}}