{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JABD6AQZ5YP5PFEJ66KKVNN5OA","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":"ab69ea6a7e4b29e64bb3c4c0909c84a36fbf599a26a8ebe9d718d5f814335fd7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-09T19:19:00Z","title_canon_sha256":"3308adf3bd012c6b61a66ff8604ffe0d27f8d89bff52e858610376136313e8f0"},"schema_version":"1.0","source":{"id":"1412.3058","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3058","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3058v4","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3058","created_at":"2026-05-18T01:02:31Z"},{"alias_kind":"pith_short_12","alias_value":"JABD6AQZ5YP5","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JABD6AQZ5YP5PFEJ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JABD6AQZ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:303e3f5b6c2e1b4a58f989a12f6adbed152047075dfcdc8bfd71a6d17e8b2290","target":"graph","created_at":"2026-05-18T01:02:31Z","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":"The paper is devoted to the study of shock formation of the 3-dimensional quasilinear wave equation \\begin{equation}\\label{Main Equation}\n  - \\big(1+3G^{\\prime\\prime}(0) (\\partial_t\\phi)^2\\big)\\partial^2_t \\phi +\\Delta\\phi=0,\\tag{\\textbf{$\\star$}} \\end{equation} where $G^{\\prime\\prime}(0)$ is a non-zero constant. We will exhibit a family of smooth initial data and show that the foliation of the incoming characteristic hypersurfaces collapses. Similar to 1-dimensional conservational laws, we refer this specific type breakdown of smooth solutions as shock formation. Since $(\\star)$ satisfies the","authors_text":"Pin Yu, Shuang Miao","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-09T19:19:00Z","title":"On the formation of shocks for quasilinear wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3058","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:fdc009b6402af9b624cd5a4cdf1bfa7fa73646c9b098c216286dcd6676247fc5","target":"record","created_at":"2026-05-18T01:02:31Z","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":"ab69ea6a7e4b29e64bb3c4c0909c84a36fbf599a26a8ebe9d718d5f814335fd7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-09T19:19:00Z","title_canon_sha256":"3308adf3bd012c6b61a66ff8604ffe0d27f8d89bff52e858610376136313e8f0"},"schema_version":"1.0","source":{"id":"1412.3058","kind":"arxiv","version":4}},"canonical_sha256":"48023f0219ee1fd79489f794aab5bd701ab6f65810394c8d161886405a41b2ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48023f0219ee1fd79489f794aab5bd701ab6f65810394c8d161886405a41b2ab","first_computed_at":"2026-05-18T01:02:31.228363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:31.228363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kgPmsOBZH/p+och9OOXwAgXZD26LblWwBWIxgJyHeWpJPRbRqqVGRCUBPYdxd8Nin1T9IdF2l4hawgMmzhNTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:31.228890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3058","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdc009b6402af9b624cd5a4cdf1bfa7fa73646c9b098c216286dcd6676247fc5","sha256:303e3f5b6c2e1b4a58f989a12f6adbed152047075dfcdc8bfd71a6d17e8b2290"],"state_sha256":"f4a33571606cc84e0e10a968ca87f2f444a20051f2b7e22bfadc9b12cf45d6d1"}