{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LWVCW3KMAZ66L5NJW6Y6KYKSDT","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":"cff390195b07548800fcd7de4d7caaf51a19590769034960c743eeeaa6307a3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-18T12:18:14Z","title_canon_sha256":"87fe51faf0e86e04b0c7a2723f7d5daac3008b37a569ea89b9726b163ec18dd3"},"schema_version":"1.0","source":{"id":"1303.4225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4225","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4225v1","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4225","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"LWVCW3KMAZ66","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LWVCW3KMAZ66L5NJ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LWVCW3KM","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:6c47203e23fa6fbb8787b965ec84300cb7242c7503dd967801b3c5f6aea6d64a","target":"graph","created_at":"2026-05-18T03:30:39Z","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":"This paper is concerned with the small smooth data problem for the 3-D nonlinear wave equation $\\partial_t^2u-\\left (1+u+\\p_t u\\right)\\Delta u=0$. This equation is prototypical of the more general equation $\\dsize\\sum_{i,j=0}^3g_{ij}(u, \\nabla u)\\partial_{ij}u=0$, where $x_0=t$ and $g_{ij}(u, \\nabla u)=c_{ij}+d_{ij}u+\\dsize\\sum_{k=0}^3e_{ij}^k\\partial_ku+O(|u|^2+|\\nabla u|^2)$ are smooth functions of their arguments, with $c_{ij}, d_{ij}$ and $e_{ij}^k$ being constants, and $d_{ij}\\neq0$ for some $(i,j)$; moreover, $\\dsize\\sum_{i,j,k=0}^3e_{ij}^k(\\partial_ku)\\p_{ij} u$ does not fulfill the nul","authors_text":"Bingbing Ding (Nanjing University), Huicheng Yin (Nanjing University), Ingo Witt (University of G\\\"ottingen)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-18T12:18:14Z","title":"Blowup of classical solutions for a class of 3-D quasilinear wave equations with small initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4225","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":"sha256:0b379f9af1a97bd564fdb99ea409a936b542c7ba4fe1d1e65e498e489302972d","target":"record","created_at":"2026-05-18T03:30:39Z","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":"cff390195b07548800fcd7de4d7caaf51a19590769034960c743eeeaa6307a3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-18T12:18:14Z","title_canon_sha256":"87fe51faf0e86e04b0c7a2723f7d5daac3008b37a569ea89b9726b163ec18dd3"},"schema_version":"1.0","source":{"id":"1303.4225","kind":"arxiv","version":1}},"canonical_sha256":"5daa2b6d4c067de5f5a9b7b1e561521cf00d4cc950089033e45907c447a78ff2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5daa2b6d4c067de5f5a9b7b1e561521cf00d4cc950089033e45907c447a78ff2","first_computed_at":"2026-05-18T03:30:39.233160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:39.233160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uQUSfE6Ta+UzxEQ8awfiqhD/oAy5PPHIjaEjGq2FEF+FXwzxVXZVzV9pcjr21TV+4UNHUKhuJhUriri/KQrGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:39.233912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b379f9af1a97bd564fdb99ea409a936b542c7ba4fe1d1e65e498e489302972d","sha256:6c47203e23fa6fbb8787b965ec84300cb7242c7503dd967801b3c5f6aea6d64a"],"state_sha256":"b0edf61d85550313161c312a494f85201755eccbf269726e87e2cbe4d2d96deb"}