{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6OMNOATUBHWIKVA4E3RPAS2M6Z","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":"c26c6427318ec2b1e795285dbdd06f22a9209e401aca13a4ac1b03431a255fe1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-15T13:49:31Z","title_canon_sha256":"446f9ead528b98d9f4cca5116f58e1bded872672d045a601c77a6e00d827ed25"},"schema_version":"1.0","source":{"id":"1908.05539","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05539","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05539v4","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05539","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"pith_short_12","alias_value":"6OMNOATUBHWI","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"pith_short_16","alias_value":"6OMNOATUBHWIKVA4","created_at":"2026-07-05T01:17:57Z"},{"alias_kind":"pith_short_8","alias_value":"6OMNOATU","created_at":"2026-07-05T01:17:57Z"}],"graph_snapshots":[{"event_id":"sha256:a4c4c69ff4ee946021c3460a7e88c84e11ba7b74afb7f45cbe3089a4158f4274","target":"graph","created_at":"2026-07-05T01:17:57Z","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/1908.05539/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one and the other is a native one or both are invasive species. Our results seem to be the first that provide a precise spreading speed and profile for such a strong competition system. Among other things, our analysis relies on the construction of new types of supersolution and subsolution, which are optimal in certain sense.","authors_text":"Chang-Hong Wu, Maolin Zhou, Rui Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-15T13:49:31Z","title":"Sharp estimates for the spreading speed of the Lotka-Volterra diffusion system with strong competition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05539","kind":"arxiv","version":4},"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:f0229e4d8fe2f28c202d54633cf58657838cba04ab2d8e2dea93cb4ff3f38de8","target":"record","created_at":"2026-07-05T01:17:57Z","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":"c26c6427318ec2b1e795285dbdd06f22a9209e401aca13a4ac1b03431a255fe1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-15T13:49:31Z","title_canon_sha256":"446f9ead528b98d9f4cca5116f58e1bded872672d045a601c77a6e00d827ed25"},"schema_version":"1.0","source":{"id":"1908.05539","kind":"arxiv","version":4}},"canonical_sha256":"f398d7027409ec85541c26e2f04b4cf678d86683185782b38511930aa46fe8f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f398d7027409ec85541c26e2f04b4cf678d86683185782b38511930aa46fe8f3","first_computed_at":"2026-07-05T01:17:57.511968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:57.511968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sZOrE7WzhcXhOBepR3YxslxcehdlcwPUNs/ZVCxP/BtpwSlwk8jgIaA2jJEUScEHjk62Ag24NY82h9f9MDUIAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:57.512540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05539","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0229e4d8fe2f28c202d54633cf58657838cba04ab2d8e2dea93cb4ff3f38de8","sha256:a4c4c69ff4ee946021c3460a7e88c84e11ba7b74afb7f45cbe3089a4158f4274"],"state_sha256":"08110f3bb3bf2fd97ab2a3df91218ed312c0c01a580259f3727b83522b15a01c"}