{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HG4Z5YZWK2Z4WYZSY7J27GAVJC","short_pith_number":"pith:HG4Z5YZW","schema_version":"1.0","canonical_sha256":"39b99ee33656b3cb6332c7d3af981548a4ad21f1756c4c12de5698dbc611eb80","source":{"kind":"arxiv","id":"1808.01389","version":1},"attestation_state":"computed","paper":{"title":"Dispersive estimates for the wave equation on Riemannian manifolds of bounded curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hart F. Smith, Yuanlong Chen","submitted_at":"2018-08-03T23:29:50Z","abstract_excerpt":"We establish space-time dispersive estimates for solutions to the wave equation on compact Riemannian manifolds with bounded sectional curvature, with the same exponents as for $C^\\infty$ metrics. The estimates are for bounded time intervals, so by finite propagation velocity the results apply also on non-compact manifolds under appropriate uniform conditions. We assume a priori that in local coordinates the metric tensor components satisfy ${\\rm g}_{ij}\\in W^{1,p}$ for some $p>d$, which ensures that the curvature tensor is well defined in the weak sense, but this can be relaxed to any assumpt"},"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":"1808.01389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-03T23:29:50Z","cross_cats_sorted":[],"title_canon_sha256":"1225acf57238f54d541aa51bec69294dffda839739002acb12b9b12d34b8a62f","abstract_canon_sha256":"c86b7e81fb6c28979b23097aee0478a0157aeeef18977f12ce5fe0d83b212921"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:52.023812Z","signature_b64":"lB5XSK2zmA20UJBsVOCPwSuORbT0EfGAmFi+jeb8k5nY9in9h44+dvHtB0iJmMUNon9/bN2JiTerepv/IckoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39b99ee33656b3cb6332c7d3af981548a4ad21f1756c4c12de5698dbc611eb80","last_reissued_at":"2026-05-17T23:59:52.023365Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:52.023365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dispersive estimates for the wave equation on Riemannian manifolds of bounded curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hart F. Smith, Yuanlong Chen","submitted_at":"2018-08-03T23:29:50Z","abstract_excerpt":"We establish space-time dispersive estimates for solutions to the wave equation on compact Riemannian manifolds with bounded sectional curvature, with the same exponents as for $C^\\infty$ metrics. The estimates are for bounded time intervals, so by finite propagation velocity the results apply also on non-compact manifolds under appropriate uniform conditions. We assume a priori that in local coordinates the metric tensor components satisfy ${\\rm g}_{ij}\\in W^{1,p}$ for some $p>d$, which ensures that the curvature tensor is well defined in the weak sense, but this can be relaxed to any assumpt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01389","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":"1808.01389","created_at":"2026-05-17T23:59:52.023432+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.01389v1","created_at":"2026-05-17T23:59:52.023432+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01389","created_at":"2026-05-17T23:59:52.023432+00:00"},{"alias_kind":"pith_short_12","alias_value":"HG4Z5YZWK2Z4","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HG4Z5YZWK2Z4WYZS","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HG4Z5YZW","created_at":"2026-05-18T12:32:28.185984+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/HG4Z5YZWK2Z4WYZSY7J27GAVJC","json":"https://pith.science/pith/HG4Z5YZWK2Z4WYZSY7J27GAVJC.json","graph_json":"https://pith.science/api/pith-number/HG4Z5YZWK2Z4WYZSY7J27GAVJC/graph.json","events_json":"https://pith.science/api/pith-number/HG4Z5YZWK2Z4WYZSY7J27GAVJC/events.json","paper":"https://pith.science/paper/HG4Z5YZW"},"agent_actions":{"view_html":"https://pith.science/pith/HG4Z5YZWK2Z4WYZSY7J27GAVJC","download_json":"https://pith.science/pith/HG4Z5YZWK2Z4WYZSY7J27GAVJC.json","view_paper":"https://pith.science/paper/HG4Z5YZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.01389&json=true","fetch_graph":"https://pith.science/api/pith-number/HG4Z5YZWK2Z4WYZSY7J27GAVJC/graph.json","fetch_events":"https://pith.science/api/pith-number/HG4Z5YZWK2Z4WYZSY7J27GAVJC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HG4Z5YZWK2Z4WYZSY7J27GAVJC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HG4Z5YZWK2Z4WYZSY7J27GAVJC/action/storage_attestation","attest_author":"https://pith.science/pith/HG4Z5YZWK2Z4WYZSY7J27GAVJC/action/author_attestation","sign_citation":"https://pith.science/pith/HG4Z5YZWK2Z4WYZSY7J27GAVJC/action/citation_signature","submit_replication":"https://pith.science/pith/HG4Z5YZWK2Z4WYZSY7J27GAVJC/action/replication_record"}},"created_at":"2026-05-17T23:59:52.023432+00:00","updated_at":"2026-05-17T23:59:52.023432+00:00"}