{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:EST7JHKVGUY2TGHYYNY5OY4X2S","short_pith_number":"pith:EST7JHKV","schema_version":"1.0","canonical_sha256":"24a7f49d553531a998f8c371d76397d4ae7d1cd6e78483703b74057967959577","source":{"kind":"arxiv","id":"1901.03997","version":1},"attestation_state":"computed","paper":{"title":"Long Time Boundedness of Planar Jump Discontinuities for Homogeneous Hyperbolic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jeffrey Rauch","submitted_at":"2019-01-13T15:12:06Z","abstract_excerpt":"Suppose that $L(\\partial_t,\\partial_x)$ is a homogeneous constant coefficient strongly hyperbolic partial differential operator on ${\\mathbb R}^{1+d}$ and $H$ is a characteristic hyperplane. Suppose that in a conic neighborhood of the conormal variety of $H$, the characteristic variety of $L$ is the graph of a real analytic function $\\tau(\\xi)$ with ${\\rm rank}\\,\\tau_{\\xi\\xi}$ identically equal to zero or the maximal possible value $d-1$. Suppose that the source function $f$ is compactly supported in $t\\ge 0$ and piecewise smooth with singularities only on $H$. Then the solution of $Lu=f$ with"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1901.03997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-13T15:12:06Z","cross_cats_sorted":[],"title_canon_sha256":"c2c5ab7bfd15ff6735c44dedf2e5c4ec05b408f7fb6fc50fa9591782261944c1","abstract_canon_sha256":"8dde5d9d92539f1927f20872292a084d48e6ac6b56dcf6e10f05cad9e9dad666"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:26.519514Z","signature_b64":"TFoyuKMg8OnZ77o8neSgtLFIqYK+KtiXKtim0FmliPbpzG+c2vmHYRAwjRhBnMGDA1H29qRgdPPrB+xYr9HxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24a7f49d553531a998f8c371d76397d4ae7d1cd6e78483703b74057967959577","last_reissued_at":"2026-05-17T23:56:26.519072Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:26.519072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long Time Boundedness of Planar Jump Discontinuities for Homogeneous Hyperbolic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jeffrey Rauch","submitted_at":"2019-01-13T15:12:06Z","abstract_excerpt":"Suppose that $L(\\partial_t,\\partial_x)$ is a homogeneous constant coefficient strongly hyperbolic partial differential operator on ${\\mathbb R}^{1+d}$ and $H$ is a characteristic hyperplane. Suppose that in a conic neighborhood of the conormal variety of $H$, the characteristic variety of $L$ is the graph of a real analytic function $\\tau(\\xi)$ with ${\\rm rank}\\,\\tau_{\\xi\\xi}$ identically equal to zero or the maximal possible value $d-1$. Suppose that the source function $f$ is compactly supported in $t\\ge 0$ and piecewise smooth with singularities only on $H$. Then the solution of $Lu=f$ with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03997","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1901.03997","created_at":"2026-05-17T23:56:26.519143+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.03997v1","created_at":"2026-05-17T23:56:26.519143+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03997","created_at":"2026-05-17T23:56:26.519143+00:00"},{"alias_kind":"pith_short_12","alias_value":"EST7JHKVGUY2","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"EST7JHKVGUY2TGHY","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"EST7JHKV","created_at":"2026-05-18T12:33:15.570797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EST7JHKVGUY2TGHYYNY5OY4X2S","json":"https://pith.science/pith/EST7JHKVGUY2TGHYYNY5OY4X2S.json","graph_json":"https://pith.science/api/pith-number/EST7JHKVGUY2TGHYYNY5OY4X2S/graph.json","events_json":"https://pith.science/api/pith-number/EST7JHKVGUY2TGHYYNY5OY4X2S/events.json","paper":"https://pith.science/paper/EST7JHKV"},"agent_actions":{"view_html":"https://pith.science/pith/EST7JHKVGUY2TGHYYNY5OY4X2S","download_json":"https://pith.science/pith/EST7JHKVGUY2TGHYYNY5OY4X2S.json","view_paper":"https://pith.science/paper/EST7JHKV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.03997&json=true","fetch_graph":"https://pith.science/api/pith-number/EST7JHKVGUY2TGHYYNY5OY4X2S/graph.json","fetch_events":"https://pith.science/api/pith-number/EST7JHKVGUY2TGHYYNY5OY4X2S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EST7JHKVGUY2TGHYYNY5OY4X2S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EST7JHKVGUY2TGHYYNY5OY4X2S/action/storage_attestation","attest_author":"https://pith.science/pith/EST7JHKVGUY2TGHYYNY5OY4X2S/action/author_attestation","sign_citation":"https://pith.science/pith/EST7JHKVGUY2TGHYYNY5OY4X2S/action/citation_signature","submit_replication":"https://pith.science/pith/EST7JHKVGUY2TGHYYNY5OY4X2S/action/replication_record"}},"created_at":"2026-05-17T23:56:26.519143+00:00","updated_at":"2026-05-17T23:56:26.519143+00:00"}