{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:I7GW5ZUDZB3QE7J4MDUMLWVFR2","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":"99cb90e1900a7685182938f9defa8af2bbadda8609ef46e98c894b0b3e65b394","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-03-19T22:56:49Z","title_canon_sha256":"71f53754f158f03aad50585053dfc8298f4300f9a830605c699f7b47adc461ee"},"schema_version":"1.0","source":{"id":"2503.15733","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.15733","created_at":"2026-07-05T10:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"2503.15733v1","created_at":"2026-07-05T10:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.15733","created_at":"2026-07-05T10:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"I7GW5ZUDZB3Q","created_at":"2026-07-05T10:35:57Z"},{"alias_kind":"pith_short_16","alias_value":"I7GW5ZUDZB3QE7J4","created_at":"2026-07-05T10:35:57Z"},{"alias_kind":"pith_short_8","alias_value":"I7GW5ZUD","created_at":"2026-07-05T10:35:57Z"}],"graph_snapshots":[{"event_id":"sha256:3e691f132e305816090fb4766ead3f4e74f0f13241076f551ddf8dcfd1d80683","target":"graph","created_at":"2026-07-05T10:35:57Z","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/2503.15733/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By applying new functional analysis tools in the framework of Fourier interpolation formulas, such as sc-Fredholm operators and Schauder frames, we are able to improve and refine several properties of these aforementioned formulas on the real line.\n  As two examples of our main contributions, we highlight: (i) that we may upgrade perturbed interpolation bases all the way to the Schwartz space, which shows that even the perturbed interpolation formulas are as regular as the Radchenko-Viazovska case; (ii) that a certain subset of the interpolation formulae considered by Kulikov-Nazarov-Sodin may","authors_text":"Gabriele Cassese, Jo\\~ao P. G. Ramos","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-03-19T22:56:49Z","title":"On the regularity of Fourier interpolation formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.15733","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":"sha256:99789147ccfa7255348cbfdcd81e6f9f5d4e16a56fd600244a1ae58e2773f254","target":"record","created_at":"2026-07-05T10:35:57Z","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":"99cb90e1900a7685182938f9defa8af2bbadda8609ef46e98c894b0b3e65b394","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-03-19T22:56:49Z","title_canon_sha256":"71f53754f158f03aad50585053dfc8298f4300f9a830605c699f7b47adc461ee"},"schema_version":"1.0","source":{"id":"2503.15733","kind":"arxiv","version":1}},"canonical_sha256":"47cd6ee683c877027d3c60e8c5daa58ea0c556e11c601f9d4b8b16dd428f267d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47cd6ee683c877027d3c60e8c5daa58ea0c556e11c601f9d4b8b16dd428f267d","first_computed_at":"2026-07-05T10:35:57.551584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:35:57.551584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nm+fUHQyuzNppbyJpYHYtkvYkJryhINdrupJCVf6UbD/eZwa7Ud70TmuVeXPcnI8HsbBsu8acBwhEsdXM+SaBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:35:57.552348Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.15733","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99789147ccfa7255348cbfdcd81e6f9f5d4e16a56fd600244a1ae58e2773f254","sha256:3e691f132e305816090fb4766ead3f4e74f0f13241076f551ddf8dcfd1d80683"],"state_sha256":"c6989cb63fa474bad86aac268a55bf01a81849db06139ba0df069240af055835"}