{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:SKQXN4J5PDO4IDUAGORSTHBTRC","short_pith_number":"pith:SKQXN4J5","schema_version":"1.0","canonical_sha256":"92a176f13d78ddc40e8033a3299c33889a5ef889d6183e225c0e623510e078ea","source":{"kind":"arxiv","id":"1907.08131","version":1},"attestation_state":"computed","paper":{"title":"Uniform $L^p$ Resolvent Estimates on the Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Jonathan Hickman","submitted_at":"2019-07-18T16:09:15Z","abstract_excerpt":"A new range of uniform $L^p$ resolvent estimates is obtained in the setting of the flat torus, improving previous results of Bourgain, Shao, Sogge and Yao. The arguments rely on the $\\ell^2$-decoupling theorem and multidimensional Weyl sum estimates."},"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":"1907.08131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T16:09:15Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"82a870efe9a22f2e9fd55b39374e7f18a6c98be66bc8981351205270652cb111","abstract_canon_sha256":"755853299672693d26d77e994167a9fad8f3cb4da71a9ca08b61a405a8ee250c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:15.014565Z","signature_b64":"K2wBsDM+BiCoxZUYKh1JJwMOR289VyxyD8ZyU4aUFXpwUiGstEys658YHZiv8OqJ/SQtq4sNzjpxljMHRRDqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92a176f13d78ddc40e8033a3299c33889a5ef889d6183e225c0e623510e078ea","last_reissued_at":"2026-05-17T23:40:15.013805Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:15.013805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform $L^p$ Resolvent Estimates on the Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Jonathan Hickman","submitted_at":"2019-07-18T16:09:15Z","abstract_excerpt":"A new range of uniform $L^p$ resolvent estimates is obtained in the setting of the flat torus, improving previous results of Bourgain, Shao, Sogge and Yao. The arguments rely on the $\\ell^2$-decoupling theorem and multidimensional Weyl sum estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08131","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":"1907.08131","created_at":"2026-05-17T23:40:15.013913+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.08131v1","created_at":"2026-05-17T23:40:15.013913+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08131","created_at":"2026-05-17T23:40:15.013913+00:00"},{"alias_kind":"pith_short_12","alias_value":"SKQXN4J5PDO4","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"SKQXN4J5PDO4IDUA","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"SKQXN4J5","created_at":"2026-05-18T12:33:27.125529+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/SKQXN4J5PDO4IDUAGORSTHBTRC","json":"https://pith.science/pith/SKQXN4J5PDO4IDUAGORSTHBTRC.json","graph_json":"https://pith.science/api/pith-number/SKQXN4J5PDO4IDUAGORSTHBTRC/graph.json","events_json":"https://pith.science/api/pith-number/SKQXN4J5PDO4IDUAGORSTHBTRC/events.json","paper":"https://pith.science/paper/SKQXN4J5"},"agent_actions":{"view_html":"https://pith.science/pith/SKQXN4J5PDO4IDUAGORSTHBTRC","download_json":"https://pith.science/pith/SKQXN4J5PDO4IDUAGORSTHBTRC.json","view_paper":"https://pith.science/paper/SKQXN4J5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.08131&json=true","fetch_graph":"https://pith.science/api/pith-number/SKQXN4J5PDO4IDUAGORSTHBTRC/graph.json","fetch_events":"https://pith.science/api/pith-number/SKQXN4J5PDO4IDUAGORSTHBTRC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SKQXN4J5PDO4IDUAGORSTHBTRC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SKQXN4J5PDO4IDUAGORSTHBTRC/action/storage_attestation","attest_author":"https://pith.science/pith/SKQXN4J5PDO4IDUAGORSTHBTRC/action/author_attestation","sign_citation":"https://pith.science/pith/SKQXN4J5PDO4IDUAGORSTHBTRC/action/citation_signature","submit_replication":"https://pith.science/pith/SKQXN4J5PDO4IDUAGORSTHBTRC/action/replication_record"}},"created_at":"2026-05-17T23:40:15.013913+00:00","updated_at":"2026-05-17T23:40:15.013913+00:00"}