{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ILUVGABJEWEYAUIOQMEXOWDZNL","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":"682f8f02e6fa1bdd3359adc7f463def2e016ad3d335a66bff55bf7145499d806","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-08T01:12:57Z","title_canon_sha256":"69d4d912639b1206c789dfedac7cfe36a3a4689dbd3c1e05d89cc4d33135133d"},"schema_version":"1.0","source":{"id":"1408.1741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1741","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1741v1","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1741","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"pith_short_12","alias_value":"ILUVGABJEWEY","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ILUVGABJEWEYAUIO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ILUVGABJ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:b62b182c6017bf754b6e204898da0fd8dea58ea8484284e0ada0499b038d0bbf","target":"graph","created_at":"2026-05-18T02:45:39Z","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 wave breaking for the Dullin-Gottwald-Holm equation and the two-component Dullin-Gottwald-Holm system. We establish a new blow-up criterion for the general case $\\gamma+c_0\\alpha^2 \\geq 0$ involving local-in-space conditions on the initial data.","authors_text":"Duc-Trung Hoang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-08T01:12:57Z","title":"The local criteria for blowup of the Dullin-Gottwald-Holm equation and the two-component Dullin-Gottwald-Holm system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1741","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":"sha256:2478faf28ed4f01b8aa1aa29bd6a65eab47deb0384651b062ca947f87e05c845","target":"record","created_at":"2026-05-18T02:45:39Z","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":"682f8f02e6fa1bdd3359adc7f463def2e016ad3d335a66bff55bf7145499d806","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-08T01:12:57Z","title_canon_sha256":"69d4d912639b1206c789dfedac7cfe36a3a4689dbd3c1e05d89cc4d33135133d"},"schema_version":"1.0","source":{"id":"1408.1741","kind":"arxiv","version":1}},"canonical_sha256":"42e9530029258980510e83097758796ad42fe88b86798b2603633ec17ecf5628","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42e9530029258980510e83097758796ad42fe88b86798b2603633ec17ecf5628","first_computed_at":"2026-05-18T02:45:39.142199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:39.142199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2a++cJrIiEvNMmmDBDrJ+rXVatTM6Iacxt8eyhPUr1HABrurEj8PzmGge1dCs9Pw8CaYCFHL6r+1kD/zMrMZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:39.142893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2478faf28ed4f01b8aa1aa29bd6a65eab47deb0384651b062ca947f87e05c845","sha256:b62b182c6017bf754b6e204898da0fd8dea58ea8484284e0ada0499b038d0bbf"],"state_sha256":"796901cff2bc5a6d8ae2807635d90e40a61c3ea38c31a807035859752c36f878"}