{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QTDLDIAH6JQV34GYPJNIBPUQCK","short_pith_number":"pith:QTDLDIAH","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"},"canonical_sha256":"84c6b1a007f2615df0d87a5a80be9012b46cd144367fa2400eb4ec0898f17ec5","source":{"kind":"arxiv","id":"2508.17938","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17938","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17938v1","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17938","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"pith_short_12","alias_value":"QTDLDIAH6JQV","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"pith_short_16","alias_value":"QTDLDIAH6JQV34GY","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"pith_short_8","alias_value":"QTDLDIAH","created_at":"2026-07-05T11:58:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QTDLDIAH6JQV34GYPJNIBPUQCK","target":"record","payload":{"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"},"canonical_sha256":"84c6b1a007f2615df0d87a5a80be9012b46cd144367fa2400eb4ec0898f17ec5","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"},"source_kind":"arxiv","source_id":"2508.17938","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:58:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eTlYJcuQG05+d5EXVVJ8DlF0/UwnpHJPxz2xi5tCKWUyi6T7r81IV3O/ap1d7uc7ldSLEiVlDHjtCeu1DTQ6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:36:43.759552Z"},"content_sha256":"4a8b6caddf218ea88fe20391eda3465f9711518a7f7a468dccba659aacfc61c5","schema_version":"1.0","event_id":"sha256:4a8b6caddf218ea88fe20391eda3465f9711518a7f7a468dccba659aacfc61c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QTDLDIAH6JQV34GYPJNIBPUQCK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:58:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSFusskK3QrfMqMk9iiBO5RuMGHISOBKQQcNq+bCtGJusHEjVWRfqOE7/44hXEZ3Yh7SIY3JURk7Aj9fch73Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:36:43.760082Z"},"content_sha256":"92e6f373eb88114562fd56752f83a32bebc43bf0987dbacf0e1db8a42dad8576","schema_version":"1.0","event_id":"sha256:92e6f373eb88114562fd56752f83a32bebc43bf0987dbacf0e1db8a42dad8576"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/bundle.json","state_url":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-15T23:36:43Z","links":{"resolver":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK","bundle":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/bundle.json","state":"https://pith.science/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QTDLDIAH6JQV34GYPJNIBPUQCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QTDLDIAH6JQV34GYPJNIBPUQCK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"69801fd0ce38e7dd83fc08dc9bba716084aca7f07884f2dadaa7c229c3a81d88","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2025-08-25T12:06:14Z","title_canon_sha256":"e0ad074cde4fbac0dcbfad57192546b2c645e9c96cfa744ccee14ecac5f621f9"},"schema_version":"1.0","source":{"id":"2508.17938","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17938","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17938v1","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17938","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"pith_short_12","alias_value":"QTDLDIAH6JQV","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"pith_short_16","alias_value":"QTDLDIAH6JQV34GY","created_at":"2026-07-05T11:58:50Z"},{"alias_kind":"pith_short_8","alias_value":"QTDLDIAH","created_at":"2026-07-05T11:58:50Z"}],"graph_snapshots":[{"event_id":"sha256:92e6f373eb88114562fd56752f83a32bebc43bf0987dbacf0e1db8a42dad8576","target":"graph","created_at":"2026-07-05T11:58:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.17938/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Miquel Saucedo, Sergey Tikhonov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2025-08-25T12:06:14Z","title":"Extremizers of a Fourier uncertainty principle related to averaging"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17938","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4a8b6caddf218ea88fe20391eda3465f9711518a7f7a468dccba659aacfc61c5","target":"record","created_at":"2026-07-05T11:58:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"69801fd0ce38e7dd83fc08dc9bba716084aca7f07884f2dadaa7c229c3a81d88","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2025-08-25T12:06:14Z","title_canon_sha256":"e0ad074cde4fbac0dcbfad57192546b2c645e9c96cfa744ccee14ecac5f621f9"},"schema_version":"1.0","source":{"id":"2508.17938","kind":"arxiv","version":1}},"canonical_sha256":"84c6b1a007f2615df0d87a5a80be9012b46cd144367fa2400eb4ec0898f17ec5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84c6b1a007f2615df0d87a5a80be9012b46cd144367fa2400eb4ec0898f17ec5","first_computed_at":"2026-07-05T11:58:50.668175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:58:50.668175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8HQLH7OzjJfPDedqIklZho/0R0DHr++/0jSr7OmDbqDvLb7ssdhJiBisjADWLzb7GymQNjxygZIlFejyF72kAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:58:50.668703Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.17938","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a8b6caddf218ea88fe20391eda3465f9711518a7f7a468dccba659aacfc61c5","sha256:92e6f373eb88114562fd56752f83a32bebc43bf0987dbacf0e1db8a42dad8576"],"state_sha256":"3e8a9845b3b66d9be33a6067d86d886beafed0549e928e91f0344f0fe24e0fa2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bZ+HgGLNlmy0FwzISN8ucXTWUIwh4kbmie/aN+2QxOqPA0cCUTO+EC46FZpdmB6cxPJNhGN1txZQCnMh58aECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T23:36:43.765067Z","bundle_sha256":"f8fb9b14ba29a3f05b06c8ebdf87f99fe110b223fae37c5f5709e148ca507268"}}