{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4PXEKWB53S2CWSLUH7IQA3SXQO","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":"8215433ab84508498399c913bf26bcc409e188cf12ed2623a27b9e778b0d370d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-09T19:19:29Z","title_canon_sha256":"9e0e72736fab0dca8c82b960dbc7c532513a82c4224b37cb73b0120ea7ef476c"},"schema_version":"1.0","source":{"id":"1502.02611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02611","created_at":"2026-05-18T02:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02611v1","created_at":"2026-05-18T02:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02611","created_at":"2026-05-18T02:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"4PXEKWB53S2C","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4PXEKWB53S2CWSLU","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4PXEKWB5","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:f058aa740fe31fb0dc5fce1167fe5144a878d14800423a8cc9986b933fae459c","target":"graph","created_at":"2026-05-18T02:27:41Z","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 concerned with conservative solutions to the nonlinear wave equation $u_{tt} - c(u)\\big(c(u) u_x\\big)_x = 0$. For an open dense set of $C^3$ initial data, we prove that the solution is piecewise smooth in the $t$-$x$ plane, while the gradient $u_x$ can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem.","authors_text":"Alberto Bressan, Geng Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-09T19:19:29Z","title":"Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02611","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:ce99866798249785eea835bc95242bffb9a6e68bb07f82e8bae1b2d67b7239b0","target":"record","created_at":"2026-05-18T02:27:41Z","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":"8215433ab84508498399c913bf26bcc409e188cf12ed2623a27b9e778b0d370d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-09T19:19:29Z","title_canon_sha256":"9e0e72736fab0dca8c82b960dbc7c532513a82c4224b37cb73b0120ea7ef476c"},"schema_version":"1.0","source":{"id":"1502.02611","kind":"arxiv","version":1}},"canonical_sha256":"e3ee45583ddcb42b49743fd1006e5783b0fc724dc96c7bab772f077aca22ddb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3ee45583ddcb42b49743fd1006e5783b0fc724dc96c7bab772f077aca22ddb5","first_computed_at":"2026-05-18T02:27:41.714489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:41.714489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FjeFhoU6J2+o/vINS4X+nvCuLqhGPvctfg3TQbkCDejngS8NjIhP3siptu6OrRkpb4XfQgwRaSuwI97G3KT3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:41.715345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce99866798249785eea835bc95242bffb9a6e68bb07f82e8bae1b2d67b7239b0","sha256:f058aa740fe31fb0dc5fce1167fe5144a878d14800423a8cc9986b933fae459c"],"state_sha256":"07a8bf19de1d6b9c9fe29a7196234417befbde778f5b91dddb0b6b1158e2be49"}