{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:QTDLDIAH6JQV34GYPJNIBPUQCK","short_pith_number":"pith:QTDLDIAH","schema_version":"1.0","canonical_sha256":"84c6b1a007f2615df0d87a5a80be9012b46cd144367fa2400eb4ec0898f17ec5","source":{"kind":"arxiv","id":"2508.17938","version":1},"attestation_state":"computed","paper":{"title":"Extremizers of a Fourier uncertainty principle related to averaging","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Miquel Saucedo, Sergey Tikhonov","submitted_at":"2025-08-25T12:06:14Z","abstract_excerpt":"We study the uncertainty principle\n  $$\\lVert\\widehat{\\mu}(\\xi) |\\xi|^\\beta\\rVert_\\infty^{\\alpha}\n  \\left(\\int |x|^\\alpha d \\mu\\right)^{\\beta} \\geq C(\\alpha,\\beta,d){\\lVert{\\mu}\\rVert_{TV}^{\\alpha+\\beta}}$$ for finite non-negative measures on $\\mathbb{R}^d $. We prove that $C(\\alpha,\\beta,d)>0$ for all $\\alpha,\\beta>0$ and that extremizers exist. Moreover, we obtain an abstract characterization of the extremizers, which allows us to describe their asymptotic behavior and, for certain parameter values, to determine them explicitly."},"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":"2508.17938","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2025-08-25T12:06:14Z","cross_cats_sorted":[],"title_canon_sha256":"e0ad074cde4fbac0dcbfad57192546b2c645e9c96cfa744ccee14ecac5f621f9","abstract_canon_sha256":"69801fd0ce38e7dd83fc08dc9bba716084aca7f07884f2dadaa7c229c3a81d88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:58:50.668703Z","signature_b64":"8HQLH7OzjJfPDedqIklZho/0R0DHr++/0jSr7OmDbqDvLb7ssdhJiBisjADWLzb7GymQNjxygZIlFejyF72kAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84c6b1a007f2615df0d87a5a80be9012b46cd144367fa2400eb4ec0898f17ec5","last_reissued_at":"2026-07-05T11:58:50.668175Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:58:50.668175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremizers of a Fourier uncertainty principle related to averaging","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Miquel Saucedo, Sergey Tikhonov","submitted_at":"2025-08-25T12:06:14Z","abstract_excerpt":"We study the uncertainty principle\n  $$\\lVert\\widehat{\\mu}(\\xi) |\\xi|^\\beta\\rVert_\\infty^{\\alpha}\n  \\left(\\int |x|^\\alpha d \\mu\\right)^{\\beta} \\geq C(\\alpha,\\beta,d){\\lVert{\\mu}\\rVert_{TV}^{\\alpha+\\beta}}$$ for finite non-negative measures on $\\mathbb{R}^d $. We prove that $C(\\alpha,\\beta,d)>0$ for all $\\alpha,\\beta>0$ and that extremizers exist. Moreover, we obtain an abstract characterization of the extremizers, which allows us to describe their asymptotic behavior and, for certain parameter values, to determine them explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17938","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.17938/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2508.17938","created_at":"2026-07-05T11:58:50.668244+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.17938v1","created_at":"2026-07-05T11:58:50.668244+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17938","created_at":"2026-07-05T11:58:50.668244+00:00"},{"alias_kind":"pith_short_12","alias_value":"QTDLDIAH6JQV","created_at":"2026-07-05T11:58:50.668244+00:00"},{"alias_kind":"pith_short_16","alias_value":"QTDLDIAH6JQV34GY","created_at":"2026-07-05T11:58:50.668244+00:00"},{"alias_kind":"pith_short_8","alias_value":"QTDLDIAH","created_at":"2026-07-05T11:58:50.668244+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/QTDLDIAH6JQV34GYPJNIBPUQCK","json":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK.json","graph_json":"https://pith.science/api/pith-number/QTDLDIAH6JQV34GYPJNIBPUQCK/graph.json","events_json":"https://pith.science/api/pith-number/QTDLDIAH6JQV34GYPJNIBPUQCK/events.json","paper":"https://pith.science/paper/QTDLDIAH"},"agent_actions":{"view_html":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK","download_json":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK.json","view_paper":"https://pith.science/paper/QTDLDIAH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.17938&json=true","fetch_graph":"https://pith.science/api/pith-number/QTDLDIAH6JQV34GYPJNIBPUQCK/graph.json","fetch_events":"https://pith.science/api/pith-number/QTDLDIAH6JQV34GYPJNIBPUQCK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/action/storage_attestation","attest_author":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/action/author_attestation","sign_citation":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/action/citation_signature","submit_replication":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/action/replication_record"}},"created_at":"2026-07-05T11:58:50.668244+00:00","updated_at":"2026-07-05T11:58:50.668244+00:00"}