{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EXA2K7IHOJOBKIVREEWOPF4AAB","short_pith_number":"pith:EXA2K7IH","schema_version":"1.0","canonical_sha256":"25c1a57d07725c1522b1212ce79780007b58b5cf4d8cd279946cb59918b93144","source":{"kind":"arxiv","id":"1807.05811","version":1},"attestation_state":"computed","paper":{"title":"Strictly hyperbolic Cauchy problems with coefficients low-regular in time and space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Lorenz","submitted_at":"2018-07-16T12:03:18Z","abstract_excerpt":"We consider the strictly hyperbolic Cauchy problem\n  \\begin{align*}\n  &D_t^m u - \\sum\\limits_{j = 0}^{m-1} \\sum\\limits_{|\\gamma|+j = m} a_{m-j,\\,\\gamma}(t,\\,x) D_x^\\gamma D_t^j u = 0, \\newline\n  &D_t^{k-1}u(0,\\,x) = g_k(x),\\,k = 1,\\,\\ldots,\\,m,\n  \\end{align*}\n  for $(t,\\,x) \\in [0,\\,T]\\times \\mathbb{R}^n$ with coefficients belonging to the Zygmund class $C^s_\\ast$ in $x$ and having a modulus of continuity below Lipschitz in $t$. Imposing additional conditions to control oscillations, we obtain a global (on $[0,\\,T]$) $L^2$ energy estimate without loss of derivatives for $s \\geq \\{1+\\varepsilon"},"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":"1807.05811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-16T12:03:18Z","cross_cats_sorted":[],"title_canon_sha256":"cd1488db0748250f311478942cfa6853ea520242d5c1238299f0a4ceefe70f80","abstract_canon_sha256":"af5a54f9069fe1ac00556a2f35d3bc7e2e3a638eb5275dfde31f618e2e158c04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:42.503601Z","signature_b64":"AZsrsHxIEMI9kSvcMRKMmL+HEfs5SLeMTi/6pO6mFUIynFN+tGLiSisonsFMaRkBTkZ1v1DuzqE5OLEsucwrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25c1a57d07725c1522b1212ce79780007b58b5cf4d8cd279946cb59918b93144","last_reissued_at":"2026-05-18T00:10:42.503086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:42.503086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strictly hyperbolic Cauchy problems with coefficients low-regular in time and space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Lorenz","submitted_at":"2018-07-16T12:03:18Z","abstract_excerpt":"We consider the strictly hyperbolic Cauchy problem\n  \\begin{align*}\n  &D_t^m u - \\sum\\limits_{j = 0}^{m-1} \\sum\\limits_{|\\gamma|+j = m} a_{m-j,\\,\\gamma}(t,\\,x) D_x^\\gamma D_t^j u = 0, \\newline\n  &D_t^{k-1}u(0,\\,x) = g_k(x),\\,k = 1,\\,\\ldots,\\,m,\n  \\end{align*}\n  for $(t,\\,x) \\in [0,\\,T]\\times \\mathbb{R}^n$ with coefficients belonging to the Zygmund class $C^s_\\ast$ in $x$ and having a modulus of continuity below Lipschitz in $t$. Imposing additional conditions to control oscillations, we obtain a global (on $[0,\\,T]$) $L^2$ energy estimate without loss of derivatives for $s \\geq \\{1+\\varepsilon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05811","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":"1807.05811","created_at":"2026-05-18T00:10:42.503170+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.05811v1","created_at":"2026-05-18T00:10:42.503170+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05811","created_at":"2026-05-18T00:10:42.503170+00:00"},{"alias_kind":"pith_short_12","alias_value":"EXA2K7IHOJOB","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EXA2K7IHOJOBKIVR","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EXA2K7IH","created_at":"2026-05-18T12:32:22.470017+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/EXA2K7IHOJOBKIVREEWOPF4AAB","json":"https://pith.science/pith/EXA2K7IHOJOBKIVREEWOPF4AAB.json","graph_json":"https://pith.science/api/pith-number/EXA2K7IHOJOBKIVREEWOPF4AAB/graph.json","events_json":"https://pith.science/api/pith-number/EXA2K7IHOJOBKIVREEWOPF4AAB/events.json","paper":"https://pith.science/paper/EXA2K7IH"},"agent_actions":{"view_html":"https://pith.science/pith/EXA2K7IHOJOBKIVREEWOPF4AAB","download_json":"https://pith.science/pith/EXA2K7IHOJOBKIVREEWOPF4AAB.json","view_paper":"https://pith.science/paper/EXA2K7IH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.05811&json=true","fetch_graph":"https://pith.science/api/pith-number/EXA2K7IHOJOBKIVREEWOPF4AAB/graph.json","fetch_events":"https://pith.science/api/pith-number/EXA2K7IHOJOBKIVREEWOPF4AAB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EXA2K7IHOJOBKIVREEWOPF4AAB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EXA2K7IHOJOBKIVREEWOPF4AAB/action/storage_attestation","attest_author":"https://pith.science/pith/EXA2K7IHOJOBKIVREEWOPF4AAB/action/author_attestation","sign_citation":"https://pith.science/pith/EXA2K7IHOJOBKIVREEWOPF4AAB/action/citation_signature","submit_replication":"https://pith.science/pith/EXA2K7IHOJOBKIVREEWOPF4AAB/action/replication_record"}},"created_at":"2026-05-18T00:10:42.503170+00:00","updated_at":"2026-05-18T00:10:42.503170+00:00"}