{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:V7JGUGFJXYPCFDJ5JIK54ZQCFY","short_pith_number":"pith:V7JGUGFJ","schema_version":"1.0","canonical_sha256":"afd26a18a9be1e228d3d4a15de66022e0f53aee85dda48b8bf5cc3f5c6b384f0","source":{"kind":"arxiv","id":"1411.0953","version":1},"attestation_state":"computed","paper":{"title":"Measures of localization and quantitative Nyquist densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jo\\~ao M. Pereira, Lu\\'is Daniel Abreu","submitted_at":"2014-11-04T16:11:15Z","abstract_excerpt":"We obtain a refinement of the degrees of freedom estimate of Landau and Pollak. More precisely, we estimate, in terms of $\\epsilon$, the increase in the degrees of freedom resulting upon allowing the functions to contain a certain prescribed amount of energy $\\epsilon $ outside a region delimited by a set $T$ in time and a set $\\Omega $ in frequency. In this situation, the lower asymptotic Nyquist density $\\vert T\\vert \\vert \\Omega \\vert /2\\pi$ is increased to $(1+\\epsilon)\\vert T\\vert \\vert \\Omega \\vert /2\\pi$. At the technical level, we prove a pseudospectra version of the classical spectral"},"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":"1411.0953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-04T16:11:15Z","cross_cats_sorted":[],"title_canon_sha256":"b01bfc5cdf62ec1e2734e360c2098221f89d8160f0c90964fe69659cee841a56","abstract_canon_sha256":"891c67eedcfecc86a2eafb3c5e171a15f8f4a65affa666571f9b2b78cdc38720"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:37.834805Z","signature_b64":"MeDrLFQCizZP5jq0cBYa8oqkxqPTcT/8EXkD0aYE8qc96IhUTJ9Xt7fQEaN9Yk5ogs521POOFBZZq20FVurzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afd26a18a9be1e228d3d4a15de66022e0f53aee85dda48b8bf5cc3f5c6b384f0","last_reissued_at":"2026-05-18T02:38:37.834140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:37.834140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Measures of localization and quantitative Nyquist densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jo\\~ao M. Pereira, Lu\\'is Daniel Abreu","submitted_at":"2014-11-04T16:11:15Z","abstract_excerpt":"We obtain a refinement of the degrees of freedom estimate of Landau and Pollak. More precisely, we estimate, in terms of $\\epsilon$, the increase in the degrees of freedom resulting upon allowing the functions to contain a certain prescribed amount of energy $\\epsilon $ outside a region delimited by a set $T$ in time and a set $\\Omega $ in frequency. In this situation, the lower asymptotic Nyquist density $\\vert T\\vert \\vert \\Omega \\vert /2\\pi$ is increased to $(1+\\epsilon)\\vert T\\vert \\vert \\Omega \\vert /2\\pi$. At the technical level, we prove a pseudospectra version of the classical spectral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0953","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":"1411.0953","created_at":"2026-05-18T02:38:37.834235+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.0953v1","created_at":"2026-05-18T02:38:37.834235+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0953","created_at":"2026-05-18T02:38:37.834235+00:00"},{"alias_kind":"pith_short_12","alias_value":"V7JGUGFJXYPC","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"V7JGUGFJXYPCFDJ5","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"V7JGUGFJ","created_at":"2026-05-18T12:28:52.271510+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/V7JGUGFJXYPCFDJ5JIK54ZQCFY","json":"https://pith.science/pith/V7JGUGFJXYPCFDJ5JIK54ZQCFY.json","graph_json":"https://pith.science/api/pith-number/V7JGUGFJXYPCFDJ5JIK54ZQCFY/graph.json","events_json":"https://pith.science/api/pith-number/V7JGUGFJXYPCFDJ5JIK54ZQCFY/events.json","paper":"https://pith.science/paper/V7JGUGFJ"},"agent_actions":{"view_html":"https://pith.science/pith/V7JGUGFJXYPCFDJ5JIK54ZQCFY","download_json":"https://pith.science/pith/V7JGUGFJXYPCFDJ5JIK54ZQCFY.json","view_paper":"https://pith.science/paper/V7JGUGFJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.0953&json=true","fetch_graph":"https://pith.science/api/pith-number/V7JGUGFJXYPCFDJ5JIK54ZQCFY/graph.json","fetch_events":"https://pith.science/api/pith-number/V7JGUGFJXYPCFDJ5JIK54ZQCFY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V7JGUGFJXYPCFDJ5JIK54ZQCFY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V7JGUGFJXYPCFDJ5JIK54ZQCFY/action/storage_attestation","attest_author":"https://pith.science/pith/V7JGUGFJXYPCFDJ5JIK54ZQCFY/action/author_attestation","sign_citation":"https://pith.science/pith/V7JGUGFJXYPCFDJ5JIK54ZQCFY/action/citation_signature","submit_replication":"https://pith.science/pith/V7JGUGFJXYPCFDJ5JIK54ZQCFY/action/replication_record"}},"created_at":"2026-05-18T02:38:37.834235+00:00","updated_at":"2026-05-18T02:38:37.834235+00:00"}