{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IPCAQU6HQXU6YBMQ745YOF5EK5","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":"36f638ec8de3b55fede869debb630acfb8e9355021f6487fa929ccbf96887dda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-26T21:52:23Z","title_canon_sha256":"c05b7aa247053894f388569574b189298f1544a01aff490b128ecb3fb846b558"},"schema_version":"1.0","source":{"id":"1311.6828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6828","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6828v1","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6828","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"pith_short_12","alias_value":"IPCAQU6HQXU6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IPCAQU6HQXU6YBMQ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IPCAQU6H","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:445789033cc9898d80b4e48e98b55d3624812cdf4c8a75e7babf3ffb70efaa4b","target":"graph","created_at":"2026-05-18T03:06:05Z","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":"We investigate the global time existence of smooth solutions for the Shigesada-Kawasaki-Teramoto system of cross-diffusion equations of two competing species in population dynamics. If there are self-diffusion in one species and no cross-diffusion in the other, we show that the system has a unique smooth solution for all time in bounded domains of any dimension. We obtain this result by deriving global $W^{1,p}$-estimates of Calder\\'{o}n-Zygmund type for a class of nonlinear reaction-diffusion equations with self-diffusion. These estimates are achieved by employing Caffarelli-Peral perturbatio","authors_text":"Luan T. Hoang, Truyen V. Nguyen, Tuoc V. Phan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-26T21:52:23Z","title":"Self-diffusion and cross-diffusion equations: $w^{1,p}$-estimates and global existence of smooth solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6828","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:c9dc0e6524337143ce66bbcc6e01ba8b269cc8ae468007da2c655a6aab276f15","target":"record","created_at":"2026-05-18T03:06:05Z","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":"36f638ec8de3b55fede869debb630acfb8e9355021f6487fa929ccbf96887dda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-26T21:52:23Z","title_canon_sha256":"c05b7aa247053894f388569574b189298f1544a01aff490b128ecb3fb846b558"},"schema_version":"1.0","source":{"id":"1311.6828","kind":"arxiv","version":1}},"canonical_sha256":"43c40853c785e9ec0590ff3b8717a45745ed6bc00a7ff0673ff00b6faf80c1c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43c40853c785e9ec0590ff3b8717a45745ed6bc00a7ff0673ff00b6faf80c1c4","first_computed_at":"2026-05-18T03:06:05.385560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:05.385560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+55/wnRWlUakGZX6bepQfmEkqtXU2+ocOWDK3kyMevx7uYNyEqNIskjzcMOlts0/yFkDBZIzKpGV+BGq0/IvAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:05.385982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9dc0e6524337143ce66bbcc6e01ba8b269cc8ae468007da2c655a6aab276f15","sha256:445789033cc9898d80b4e48e98b55d3624812cdf4c8a75e7babf3ffb70efaa4b"],"state_sha256":"64eb2e75aaab014d1fdd02149f698e681dbe8e5e65afaeb287c6d195e3ef4e5e"}