{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XHYCVQTAKFB7T33RJCDYLYPRAX","short_pith_number":"pith:XHYCVQTA","schema_version":"1.0","canonical_sha256":"b9f02ac2605143f9ef71488785e1f105faa65d9dc8ea489d5a65081572f19ae3","source":{"kind":"arxiv","id":"1705.01418","version":1},"attestation_state":"computed","paper":{"title":"Wave equation for operators with discrete spectrum and irregular propagation speed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Michael Ruzhansky, Niyaz Tokmagambetov","submitted_at":"2017-05-03T13:29:18Z","abstract_excerpt":"Given a Hilbert space, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with discrete non-negative spectrum acting on it. We consider the cases when the time-dependent propagation speed is regular, H\\\"older, and distributional. We also consider cases when it it is strictly positive (strictly hyperbolic case) and when it is non-negative (weakly hyperbolic case). When the propagation speed is a distribution, we introduce the notion of \"very weak solutions\" to the Cauchy problem. We show that the Cauchy problem for the wave equation with the distribution"},"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":"1705.01418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-03T13:29:18Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"86dbef0eeec85b278c47c886eceba8c43cba4bb0b754cd761304a9aca25e7502","abstract_canon_sha256":"21644b3f7a46baf53564ee20669f4e420a305844af56a58263a1bc92fd22f888"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:50.781203Z","signature_b64":"Kc5AZZM2tAKdePkvxYrGs8JM/CjKF85UVfLnVZel6sINYTPcgmXO+eKp/C4DoGFHoWzLvF7xn+YafEMtRAsVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9f02ac2605143f9ef71488785e1f105faa65d9dc8ea489d5a65081572f19ae3","last_reissued_at":"2026-05-18T00:32:50.780615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:50.780615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wave equation for operators with discrete spectrum and irregular propagation speed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Michael Ruzhansky, Niyaz Tokmagambetov","submitted_at":"2017-05-03T13:29:18Z","abstract_excerpt":"Given a Hilbert space, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with discrete non-negative spectrum acting on it. We consider the cases when the time-dependent propagation speed is regular, H\\\"older, and distributional. We also consider cases when it it is strictly positive (strictly hyperbolic case) and when it is non-negative (weakly hyperbolic case). When the propagation speed is a distribution, we introduce the notion of \"very weak solutions\" to the Cauchy problem. We show that the Cauchy problem for the wave equation with the distribution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01418","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":"1705.01418","created_at":"2026-05-18T00:32:50.780703+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.01418v1","created_at":"2026-05-18T00:32:50.780703+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01418","created_at":"2026-05-18T00:32:50.780703+00:00"},{"alias_kind":"pith_short_12","alias_value":"XHYCVQTAKFB7","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"XHYCVQTAKFB7T33R","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"XHYCVQTA","created_at":"2026-05-18T12:31:53.515858+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/XHYCVQTAKFB7T33RJCDYLYPRAX","json":"https://pith.science/pith/XHYCVQTAKFB7T33RJCDYLYPRAX.json","graph_json":"https://pith.science/api/pith-number/XHYCVQTAKFB7T33RJCDYLYPRAX/graph.json","events_json":"https://pith.science/api/pith-number/XHYCVQTAKFB7T33RJCDYLYPRAX/events.json","paper":"https://pith.science/paper/XHYCVQTA"},"agent_actions":{"view_html":"https://pith.science/pith/XHYCVQTAKFB7T33RJCDYLYPRAX","download_json":"https://pith.science/pith/XHYCVQTAKFB7T33RJCDYLYPRAX.json","view_paper":"https://pith.science/paper/XHYCVQTA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.01418&json=true","fetch_graph":"https://pith.science/api/pith-number/XHYCVQTAKFB7T33RJCDYLYPRAX/graph.json","fetch_events":"https://pith.science/api/pith-number/XHYCVQTAKFB7T33RJCDYLYPRAX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XHYCVQTAKFB7T33RJCDYLYPRAX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XHYCVQTAKFB7T33RJCDYLYPRAX/action/storage_attestation","attest_author":"https://pith.science/pith/XHYCVQTAKFB7T33RJCDYLYPRAX/action/author_attestation","sign_citation":"https://pith.science/pith/XHYCVQTAKFB7T33RJCDYLYPRAX/action/citation_signature","submit_replication":"https://pith.science/pith/XHYCVQTAKFB7T33RJCDYLYPRAX/action/replication_record"}},"created_at":"2026-05-18T00:32:50.780703+00:00","updated_at":"2026-05-18T00:32:50.780703+00:00"}