{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MLRL5LOIPIPU5TGZBJCY6DJAD2","short_pith_number":"pith:MLRL5LOI","schema_version":"1.0","canonical_sha256":"62e2beadc87a1f4eccd90a458f0d201eb171c77b285afc95f041209d925d5618","source":{"kind":"arxiv","id":"1704.03586","version":1},"attestation_state":"computed","paper":{"title":"Bilinear Spherical Maximal Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Danqing He, J. A. Barrionevo, Loukas Grafakos, Lucas Oliveira, Petr Honz\\'ik","submitted_at":"2017-04-12T01:18:45Z","abstract_excerpt":"We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of $L^p$ with $p<1$. We also obtain counterexamples that are asymptotically optimal with our positive results on certain indices as the dimension tends to infinity."},"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":"1704.03586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-12T01:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"a0dab353012ccc88ad1788f931d201ba86bf6659f789a505718412ac4adc6eea","abstract_canon_sha256":"4822c55efaaad6a923237126c177c01456ec4f560ca5fb4191fe3308b8f8df80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:27.430242Z","signature_b64":"pD1NnY8SOlXTY9fqCQ3MkB/ujlk6Bk5n2Ks/ozHHL6s25WvnyKVQXywOHgPK4c2RalX43Xw3p2VPhLmvJXwlCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62e2beadc87a1f4eccd90a458f0d201eb171c77b285afc95f041209d925d5618","last_reissued_at":"2026-05-18T00:46:27.429619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:27.429619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bilinear Spherical Maximal Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Danqing He, J. A. Barrionevo, Loukas Grafakos, Lucas Oliveira, Petr Honz\\'ik","submitted_at":"2017-04-12T01:18:45Z","abstract_excerpt":"We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of $L^p$ with $p<1$. We also obtain counterexamples that are asymptotically optimal with our positive results on certain indices as the dimension tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03586","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":"1704.03586","created_at":"2026-05-18T00:46:27.429729+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.03586v1","created_at":"2026-05-18T00:46:27.429729+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03586","created_at":"2026-05-18T00:46:27.429729+00:00"},{"alias_kind":"pith_short_12","alias_value":"MLRL5LOIPIPU","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MLRL5LOIPIPU5TGZ","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MLRL5LOI","created_at":"2026-05-18T12:31:31.346846+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/MLRL5LOIPIPU5TGZBJCY6DJAD2","json":"https://pith.science/pith/MLRL5LOIPIPU5TGZBJCY6DJAD2.json","graph_json":"https://pith.science/api/pith-number/MLRL5LOIPIPU5TGZBJCY6DJAD2/graph.json","events_json":"https://pith.science/api/pith-number/MLRL5LOIPIPU5TGZBJCY6DJAD2/events.json","paper":"https://pith.science/paper/MLRL5LOI"},"agent_actions":{"view_html":"https://pith.science/pith/MLRL5LOIPIPU5TGZBJCY6DJAD2","download_json":"https://pith.science/pith/MLRL5LOIPIPU5TGZBJCY6DJAD2.json","view_paper":"https://pith.science/paper/MLRL5LOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.03586&json=true","fetch_graph":"https://pith.science/api/pith-number/MLRL5LOIPIPU5TGZBJCY6DJAD2/graph.json","fetch_events":"https://pith.science/api/pith-number/MLRL5LOIPIPU5TGZBJCY6DJAD2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MLRL5LOIPIPU5TGZBJCY6DJAD2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MLRL5LOIPIPU5TGZBJCY6DJAD2/action/storage_attestation","attest_author":"https://pith.science/pith/MLRL5LOIPIPU5TGZBJCY6DJAD2/action/author_attestation","sign_citation":"https://pith.science/pith/MLRL5LOIPIPU5TGZBJCY6DJAD2/action/citation_signature","submit_replication":"https://pith.science/pith/MLRL5LOIPIPU5TGZBJCY6DJAD2/action/replication_record"}},"created_at":"2026-05-18T00:46:27.429729+00:00","updated_at":"2026-05-18T00:46:27.429729+00:00"}