{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2UIZISB2TCGVAFKCMEWDP4ZK7H","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":"ff1d07c1a3bafe71c7108e04dc80ef21f9ac2371b1b658b195afd958b5520f0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-01T13:08:51Z","title_canon_sha256":"19504814254b3ea18c7c1fd8b73dbf5862cf59914e0dd5471e80ae0ab3eeb0cb"},"schema_version":"1.0","source":{"id":"1706.00285","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00285","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00285v1","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00285","created_at":"2026-05-18T00:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"2UIZISB2TCGV","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2UIZISB2TCGVAFKC","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2UIZISB2","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:74abbaafa80db425d4ca7805f4352df232b5bce4d17cdefd8f9500cd16afba9f","target":"graph","created_at":"2026-05-18T00:43:14Z","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":"Here we give a new approach to the Paley--Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of \"polar-analytic function\" in the Mellin setting and Mellin--Bernstein spaces. A notion of Hardy spaces in the Mellin setting is also given along with applications to exponential sampling formulas of optical physics.","authors_text":"Carlo Bardaro, G. Schmeisser, Ilaria Mantellini, Paul L. Butzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-01T13:08:51Z","title":"A fresh approach to the Paley-Wiener theorem for Mellin transforms and the Mellin-Hardy spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00285","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":"sha256:0d9b58f90eca047e690ece8f2190d0d895efda7dc4d8c9d6419b714413e17eef","target":"record","created_at":"2026-05-18T00:43:14Z","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":"ff1d07c1a3bafe71c7108e04dc80ef21f9ac2371b1b658b195afd958b5520f0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-01T13:08:51Z","title_canon_sha256":"19504814254b3ea18c7c1fd8b73dbf5862cf59914e0dd5471e80ae0ab3eeb0cb"},"schema_version":"1.0","source":{"id":"1706.00285","kind":"arxiv","version":1}},"canonical_sha256":"d51194483a988d501542612c37f32af9c02a439ece1b5c62fccb46b667506fd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d51194483a988d501542612c37f32af9c02a439ece1b5c62fccb46b667506fd6","first_computed_at":"2026-05-18T00:43:14.459267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:14.459267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J+qGcc4sy54K+NZCEofP1Nvk5hDJc2nkpZtZeLkE5kbwMK2cDgBJYS4wD7OpNKynb2i1PR/M8WHGgWYUGki2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:14.459993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00285","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d9b58f90eca047e690ece8f2190d0d895efda7dc4d8c9d6419b714413e17eef","sha256:74abbaafa80db425d4ca7805f4352df232b5bce4d17cdefd8f9500cd16afba9f"],"state_sha256":"6f1d96945796a5d83adfefbde721384f3cae130f8be0ab9b9ce2c5a96d7303f9"}