{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YB3BKIQL3L3BIAD5QRRJQISMQV","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":"885c6ee0b8e4e990de0032705bf0b974cb84305faab88fd9777f2cf89167cfaa","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-09-21T21:44:22Z","title_canon_sha256":"ab25616deea6666d4445196a181dbca5cc12fdb2cfc356f9620a1c7c6bbfde84"},"schema_version":"1.0","source":{"id":"1709.07522","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.07522","created_at":"2026-05-18T00:34:32Z"},{"alias_kind":"arxiv_version","alias_value":"1709.07522v1","created_at":"2026-05-18T00:34:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07522","created_at":"2026-05-18T00:34:32Z"},{"alias_kind":"pith_short_12","alias_value":"YB3BKIQL3L3B","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YB3BKIQL3L3BIAD5","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YB3BKIQL","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:e8b60490f7f910cc0c7cf5233eb9ed13250eafa12ebd5b7c72bef639e79f039d","target":"graph","created_at":"2026-05-18T00:34:32Z","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"},"paper":{"abstract_excerpt":"For a fixed singular Borel probability measure $\\mu$ on $\\mathbb{T}$, we give several characterizations of when an entire function is the Fourier transform of some $f \\in L^2(\\mu)$. The first characterization is given in terms of criteria for sampling functions of the form $\\hat{f}$ when $f \\in L^2(\\mu)$. The second characterization is given in terms of criteria for interpolation of bounded sequences on $\\mathbb{N}_{0}$ by $\\hat{f}$. Both characterizations use the construction of Fourier series for $f \\in L^2(\\mu)$ demonstrated in Herr and Weber via the Kaczmarz algorithm and classical results","authors_text":"Eric S. Weber","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-09-21T21:44:22Z","title":"A Paley-Wiener Type Theorem for Singular Measures on $\\mathbb{T}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07522","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:a614cbdaf0ae5463cee0e01e84ca3de942b9ea137cae0427bc0bd0d79ac9762b","target":"record","created_at":"2026-05-18T00:34:32Z","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":"885c6ee0b8e4e990de0032705bf0b974cb84305faab88fd9777f2cf89167cfaa","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-09-21T21:44:22Z","title_canon_sha256":"ab25616deea6666d4445196a181dbca5cc12fdb2cfc356f9620a1c7c6bbfde84"},"schema_version":"1.0","source":{"id":"1709.07522","kind":"arxiv","version":1}},"canonical_sha256":"c07615220bdaf614007d846298224c855534203ebb9233c66971d3de8fc2effb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c07615220bdaf614007d846298224c855534203ebb9233c66971d3de8fc2effb","first_computed_at":"2026-05-18T00:34:32.953242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:32.953242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HYT6dOpG37jg5PRRxMuWpUAcDpo87e1Y5e+s7Yt3PvyU+64Mv23suCoQc6s7O2/FQ0tWIyusr/EhBHokBdvIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:32.953659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.07522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a614cbdaf0ae5463cee0e01e84ca3de942b9ea137cae0427bc0bd0d79ac9762b","sha256:e8b60490f7f910cc0c7cf5233eb9ed13250eafa12ebd5b7c72bef639e79f039d"],"state_sha256":"a8ef2b64d7a57fecf16786b6d659901d8d32a89fb4ac9f16042e604919ce94b8"}