{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:JLNSPEC7QAMZ3VTBEPRT3MJ7FF","short_pith_number":"pith:JLNSPEC7","schema_version":"1.0","canonical_sha256":"4adb27905f80199dd66123e33db13f294f3637f1126afb9bf82551a394ca8253","source":{"kind":"arxiv","id":"2010.07771","version":1},"attestation_state":"computed","paper":{"title":"Spacetime integral bounds for the energy-critical nonlinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Dodson","submitted_at":"2020-10-15T14:07:25Z","abstract_excerpt":"In this paper we prove a global spacetime bound for the quintic, nonlinear wave equation in three dimensions. This bound depends on the $L_{t}^{\\infty} L_{x}^{2}$ and $L_{t}^{\\infty} \\dot{H}^{2}$ norms of the solution to the quintic problem."},"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":"2010.07771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-10-15T14:07:25Z","cross_cats_sorted":[],"title_canon_sha256":"fb68b1d033c55b00d2a4d36707821ba067a61aee23e68f7ea815f85dcccad4a9","abstract_canon_sha256":"8e851d66da7e72bea8544b72b7b3cce33fc2ba1b01c88a2d3b12affb600e19f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:43:20.436398Z","signature_b64":"hdbWeTxmz52w/mJ2t02HydTaudJEAMgVgRbfr6iLPJPt0bNBnqb2icu2bnE9lRFekmdwroWSIq0vzqxBxOk5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4adb27905f80199dd66123e33db13f294f3637f1126afb9bf82551a394ca8253","last_reissued_at":"2026-07-05T01:43:20.435913Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:43:20.435913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spacetime integral bounds for the energy-critical nonlinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Dodson","submitted_at":"2020-10-15T14:07:25Z","abstract_excerpt":"In this paper we prove a global spacetime bound for the quintic, nonlinear wave equation in three dimensions. This bound depends on the $L_{t}^{\\infty} L_{x}^{2}$ and $L_{t}^{\\infty} \\dot{H}^{2}$ norms of the solution to the quintic problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.07771","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.07771/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2010.07771","created_at":"2026-07-05T01:43:20.435970+00:00"},{"alias_kind":"arxiv_version","alias_value":"2010.07771v1","created_at":"2026-07-05T01:43:20.435970+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.07771","created_at":"2026-07-05T01:43:20.435970+00:00"},{"alias_kind":"pith_short_12","alias_value":"JLNSPEC7QAMZ","created_at":"2026-07-05T01:43:20.435970+00:00"},{"alias_kind":"pith_short_16","alias_value":"JLNSPEC7QAMZ3VTB","created_at":"2026-07-05T01:43:20.435970+00:00"},{"alias_kind":"pith_short_8","alias_value":"JLNSPEC7","created_at":"2026-07-05T01:43:20.435970+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/JLNSPEC7QAMZ3VTBEPRT3MJ7FF","json":"https://pith.science/pith/JLNSPEC7QAMZ3VTBEPRT3MJ7FF.json","graph_json":"https://pith.science/api/pith-number/JLNSPEC7QAMZ3VTBEPRT3MJ7FF/graph.json","events_json":"https://pith.science/api/pith-number/JLNSPEC7QAMZ3VTBEPRT3MJ7FF/events.json","paper":"https://pith.science/paper/JLNSPEC7"},"agent_actions":{"view_html":"https://pith.science/pith/JLNSPEC7QAMZ3VTBEPRT3MJ7FF","download_json":"https://pith.science/pith/JLNSPEC7QAMZ3VTBEPRT3MJ7FF.json","view_paper":"https://pith.science/paper/JLNSPEC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2010.07771&json=true","fetch_graph":"https://pith.science/api/pith-number/JLNSPEC7QAMZ3VTBEPRT3MJ7FF/graph.json","fetch_events":"https://pith.science/api/pith-number/JLNSPEC7QAMZ3VTBEPRT3MJ7FF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JLNSPEC7QAMZ3VTBEPRT3MJ7FF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JLNSPEC7QAMZ3VTBEPRT3MJ7FF/action/storage_attestation","attest_author":"https://pith.science/pith/JLNSPEC7QAMZ3VTBEPRT3MJ7FF/action/author_attestation","sign_citation":"https://pith.science/pith/JLNSPEC7QAMZ3VTBEPRT3MJ7FF/action/citation_signature","submit_replication":"https://pith.science/pith/JLNSPEC7QAMZ3VTBEPRT3MJ7FF/action/replication_record"}},"created_at":"2026-07-05T01:43:20.435970+00:00","updated_at":"2026-07-05T01:43:20.435970+00:00"}