{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IPTRSAWON7GXKWULRPNIODRWVM","short_pith_number":"pith:IPTRSAWO","schema_version":"1.0","canonical_sha256":"43e71902ce6fcd755a8b8bda870e36ab2fdd6e035b954753912b39e95c759a47","source":{"kind":"arxiv","id":"1605.06401","version":1},"attestation_state":"computed","paper":{"title":"Sparse bilinear forms for Bochner Riesz multipliers and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Cristina Benea (LMJL), Frederic Bernicot (LMJL), Teresa Luque (LMJL)","submitted_at":"2016-05-20T15:22:09Z","abstract_excerpt":"We use the very recent approach developed by Lacey in [23] and extended by Bernicot-Frey-Petermichl in [3], in order to control Bochner-Riesz operators by a sparse bilinear form. In this way, new quantitative weighted estimates, as well as vector-valued inequalities are deduced."},"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":"1605.06401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-20T15:22:09Z","cross_cats_sorted":[],"title_canon_sha256":"e42ffe82cfac663a5897348f3c3820dcef5ae22c34e82f441d11156977582461","abstract_canon_sha256":"f7886118a1ee22de609bd4d9b2076225ace118cac260487e8e3c52d52a3c1f0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:06.566800Z","signature_b64":"bRaC8UpXENFz0ys6D0Hex5cWbC72iuuP4iyuFjPYO0TwYf09EoCAzSiJq5xWhvFEGS3Uz1wQ3yDZ1H3wonpgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43e71902ce6fcd755a8b8bda870e36ab2fdd6e035b954753912b39e95c759a47","last_reissued_at":"2026-05-18T00:45:06.566454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:06.566454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse bilinear forms for Bochner Riesz multipliers and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Cristina Benea (LMJL), Frederic Bernicot (LMJL), Teresa Luque (LMJL)","submitted_at":"2016-05-20T15:22:09Z","abstract_excerpt":"We use the very recent approach developed by Lacey in [23] and extended by Bernicot-Frey-Petermichl in [3], in order to control Bochner-Riesz operators by a sparse bilinear form. In this way, new quantitative weighted estimates, as well as vector-valued inequalities are deduced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06401","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":"1605.06401","created_at":"2026-05-18T00:45:06.566509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.06401v1","created_at":"2026-05-18T00:45:06.566509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06401","created_at":"2026-05-18T00:45:06.566509+00:00"},{"alias_kind":"pith_short_12","alias_value":"IPTRSAWON7GX","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IPTRSAWON7GXKWUL","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IPTRSAWO","created_at":"2026-05-18T12:30:22.444734+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/IPTRSAWON7GXKWULRPNIODRWVM","json":"https://pith.science/pith/IPTRSAWON7GXKWULRPNIODRWVM.json","graph_json":"https://pith.science/api/pith-number/IPTRSAWON7GXKWULRPNIODRWVM/graph.json","events_json":"https://pith.science/api/pith-number/IPTRSAWON7GXKWULRPNIODRWVM/events.json","paper":"https://pith.science/paper/IPTRSAWO"},"agent_actions":{"view_html":"https://pith.science/pith/IPTRSAWON7GXKWULRPNIODRWVM","download_json":"https://pith.science/pith/IPTRSAWON7GXKWULRPNIODRWVM.json","view_paper":"https://pith.science/paper/IPTRSAWO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.06401&json=true","fetch_graph":"https://pith.science/api/pith-number/IPTRSAWON7GXKWULRPNIODRWVM/graph.json","fetch_events":"https://pith.science/api/pith-number/IPTRSAWON7GXKWULRPNIODRWVM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IPTRSAWON7GXKWULRPNIODRWVM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IPTRSAWON7GXKWULRPNIODRWVM/action/storage_attestation","attest_author":"https://pith.science/pith/IPTRSAWON7GXKWULRPNIODRWVM/action/author_attestation","sign_citation":"https://pith.science/pith/IPTRSAWON7GXKWULRPNIODRWVM/action/citation_signature","submit_replication":"https://pith.science/pith/IPTRSAWON7GXKWULRPNIODRWVM/action/replication_record"}},"created_at":"2026-05-18T00:45:06.566509+00:00","updated_at":"2026-05-18T00:45:06.566509+00:00"}