{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:A2N46DXW6GCWQMEFXLIC4XGKZO","short_pith_number":"pith:A2N46DXW","schema_version":"1.0","canonical_sha256":"069bcf0ef6f185683085bad02e5ccacba9b9e473b7a82b68b3880a23361ec47d","source":{"kind":"arxiv","id":"1711.02339","version":2},"attestation_state":"computed","paper":{"title":"Sparse bounds for pseudodifferential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"David Beltran, Laura Cladek","submitted_at":"2017-11-07T08:55:26Z","abstract_excerpt":"We prove sparse bounds for pseudodifferential operators associated to H\\\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates for pseudodifferential operators. The results naturally apply to the context of oscillatory Fourier multipliers, with applications to dispersive equations and oscillatory convolution kernels."},"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":"1711.02339","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-07T08:55:26Z","cross_cats_sorted":[],"title_canon_sha256":"568b04da75799296e607f4c31587189bc5e61cda237ba08e0d81a04d24eec5d9","abstract_canon_sha256":"8439ce48a2dda5bba83c9170ad2b0a9297cc057114b751de494e5863e69b367e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:24.170488Z","signature_b64":"oWeObScMmlLuvyrouM3uPW8WK/MwnC4n2/1H3iOXC0iCGH4+KchCpTMUj1ls9R+xuJhYlbgHQNNMJ8Sb0U0KCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"069bcf0ef6f185683085bad02e5ccacba9b9e473b7a82b68b3880a23361ec47d","last_reissued_at":"2026-05-18T00:20:24.169642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:24.169642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse bounds for pseudodifferential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"David Beltran, Laura Cladek","submitted_at":"2017-11-07T08:55:26Z","abstract_excerpt":"We prove sparse bounds for pseudodifferential operators associated to H\\\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates for pseudodifferential operators. The results naturally apply to the context of oscillatory Fourier multipliers, with applications to dispersive equations and oscillatory convolution kernels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02339","kind":"arxiv","version":2},"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":"1711.02339","created_at":"2026-05-18T00:20:24.169831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.02339v2","created_at":"2026-05-18T00:20:24.169831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02339","created_at":"2026-05-18T00:20:24.169831+00:00"},{"alias_kind":"pith_short_12","alias_value":"A2N46DXW6GCW","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"A2N46DXW6GCWQMEF","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"A2N46DXW","created_at":"2026-05-18T12:31:05.417338+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/A2N46DXW6GCWQMEFXLIC4XGKZO","json":"https://pith.science/pith/A2N46DXW6GCWQMEFXLIC4XGKZO.json","graph_json":"https://pith.science/api/pith-number/A2N46DXW6GCWQMEFXLIC4XGKZO/graph.json","events_json":"https://pith.science/api/pith-number/A2N46DXW6GCWQMEFXLIC4XGKZO/events.json","paper":"https://pith.science/paper/A2N46DXW"},"agent_actions":{"view_html":"https://pith.science/pith/A2N46DXW6GCWQMEFXLIC4XGKZO","download_json":"https://pith.science/pith/A2N46DXW6GCWQMEFXLIC4XGKZO.json","view_paper":"https://pith.science/paper/A2N46DXW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.02339&json=true","fetch_graph":"https://pith.science/api/pith-number/A2N46DXW6GCWQMEFXLIC4XGKZO/graph.json","fetch_events":"https://pith.science/api/pith-number/A2N46DXW6GCWQMEFXLIC4XGKZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A2N46DXW6GCWQMEFXLIC4XGKZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A2N46DXW6GCWQMEFXLIC4XGKZO/action/storage_attestation","attest_author":"https://pith.science/pith/A2N46DXW6GCWQMEFXLIC4XGKZO/action/author_attestation","sign_citation":"https://pith.science/pith/A2N46DXW6GCWQMEFXLIC4XGKZO/action/citation_signature","submit_replication":"https://pith.science/pith/A2N46DXW6GCWQMEFXLIC4XGKZO/action/replication_record"}},"created_at":"2026-05-18T00:20:24.169831+00:00","updated_at":"2026-05-18T00:20:24.169831+00:00"}