{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M4AK74AAC3NTJJWR2NO2QPVLL4","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":"3ed9b8762157111f1f76f5576227ef48a140c0c885d700b3ee340352aa0a0acf","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-24T16:15:13Z","title_canon_sha256":"53b19165170db64d947f2e43f9829bd73da9e9ba68f6bf47f010a8d6a71cfdb5"},"schema_version":"1.0","source":{"id":"1505.06453","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06453","created_at":"2026-05-18T01:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06453v2","created_at":"2026-05-18T01:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06453","created_at":"2026-05-18T01:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"M4AK74AAC3NT","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M4AK74AAC3NTJJWR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M4AK74AA","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:1bae5eceaa17bd618fba55cbb1a4b1470860ec4a40c15d927567ffd74e7ba314","target":"graph","created_at":"2026-05-18T01:12:20Z","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 dispersionless Kadomtsev-Petviashvili (dKP) equation $(u_t+uu_x)_x=u_{yy}$ is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation $u_t+uu_x=0$. We show numerically that the solutions to the transformed equation do not develop shocks. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape reg","authors_text":"C. Klein, J. Eggers, T. Grava","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-24T16:15:13Z","title":"Shock formation in the dispersionless Kadomtsev-Petviashvili equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06453","kind":"arxiv","version":2},"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":"sha256:9b56d93d2cbf3442ed9789509c05f772cdc11ccf70c8109ff4f201e6ca696306","target":"record","created_at":"2026-05-18T01:12:20Z","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":"3ed9b8762157111f1f76f5576227ef48a140c0c885d700b3ee340352aa0a0acf","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-24T16:15:13Z","title_canon_sha256":"53b19165170db64d947f2e43f9829bd73da9e9ba68f6bf47f010a8d6a71cfdb5"},"schema_version":"1.0","source":{"id":"1505.06453","kind":"arxiv","version":2}},"canonical_sha256":"6700aff00016db34a6d1d35da83eab5f2980a2025e6e55f210c5364480306cf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6700aff00016db34a6d1d35da83eab5f2980a2025e6e55f210c5364480306cf5","first_computed_at":"2026-05-18T01:12:20.034009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:20.034009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ps+X5jYTUgdR9clGjbMKJVWqOu9ffQWMoqWfx9LgGzW44mIzoZuab/qz47NJAVwGPaYmqhpZcAEY2MwPV2s3Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:20.034418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06453","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b56d93d2cbf3442ed9789509c05f772cdc11ccf70c8109ff4f201e6ca696306","sha256:1bae5eceaa17bd618fba55cbb1a4b1470860ec4a40c15d927567ffd74e7ba314"],"state_sha256":"6eef715285f62aa9d727ec649b46bf297cfb54ad3a98aa26af9d27754a06ca8d"}