{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KVY4B4TURSNXSJ4KOBCLKVVOH6","short_pith_number":"pith:KVY4B4TU","canonical_record":{"source":{"id":"1303.5959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-24T15:20:27Z","cross_cats_sorted":[],"title_canon_sha256":"e41040511d2552ac7e9546c845cbb17e3d05edecb9ff705f91c2bdacf3517cd4","abstract_canon_sha256":"20fda8a9c5811d066d23e89d95b98e543420de0b5a1c084a87e2c632aa46cf18"},"schema_version":"1.0"},"canonical_sha256":"5571c0f2748c9b79278a7044b556ae3f8368785e69063448ec194b77b7c8009f","source":{"kind":"arxiv","id":"1303.5959","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5959","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5959v1","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5959","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"pith_short_12","alias_value":"KVY4B4TURSNX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KVY4B4TURSNXSJ4K","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KVY4B4TU","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KVY4B4TURSNXSJ4KOBCLKVVOH6","target":"record","payload":{"canonical_record":{"source":{"id":"1303.5959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-24T15:20:27Z","cross_cats_sorted":[],"title_canon_sha256":"e41040511d2552ac7e9546c845cbb17e3d05edecb9ff705f91c2bdacf3517cd4","abstract_canon_sha256":"20fda8a9c5811d066d23e89d95b98e543420de0b5a1c084a87e2c632aa46cf18"},"schema_version":"1.0"},"canonical_sha256":"5571c0f2748c9b79278a7044b556ae3f8368785e69063448ec194b77b7c8009f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:45.494531Z","signature_b64":"vLvOA7cSIICNi9epXStwLlBtnISmM8GqETVyPhB2r1bbGdiPUdOs65L2o0JfDA+MzYrMM6/vftmecFnYh3exDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5571c0f2748c9b79278a7044b556ae3f8368785e69063448ec194b77b7c8009f","last_reissued_at":"2026-05-18T03:19:45.493860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:45.493860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.5959","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":"2026-05-18T03:19:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4yF/CERu4Hug6tJDXGVYyRutRTSvYxTQ3e/DuqnvIAB4CNHCBwz0Ue3pL1M/9hTJpOkV3+0sRSdUSvQx8IpsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:21:35.152179Z"},"content_sha256":"a6f78f77cd99bd6d949c6c96fe920869c2aed310f656faf6b0f0e05edeb8c483","schema_version":"1.0","event_id":"sha256:a6f78f77cd99bd6d949c6c96fe920869c2aed310f656faf6b0f0e05edeb8c483"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KVY4B4TURSNXSJ4KOBCLKVVOH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recovery of Paley-Wiener functions using scattered translates of regular interpolators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jeff Ledford","submitted_at":"2013-03-24T15:20:27Z","abstract_excerpt":"It has been shown that Paley-Wiener functions may be recovered from their values on a complete interpolating sequence. This paper explores the same phenomenon, and gives a sufficient condition on a function $\\phi(x)$, called an interpolator, so that scattered translates of this function may be used to interpolate and recover any given Paley-Wiener function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5959","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":""},"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":"2026-05-18T03:19:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KumgZ1880f6iynBHsqgZhUrWkydcTe7ow/T61mgEPJ5QeA8YFAVa/bcJ42YtEVDLG5FFgo7ESEEQeTmci+ibDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:21:35.152539Z"},"content_sha256":"960ebeb0e5114020d924e0daba38d35117c4978ad497bbe95da3707ac6091499","schema_version":"1.0","event_id":"sha256:960ebeb0e5114020d924e0daba38d35117c4978ad497bbe95da3707ac6091499"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KVY4B4TURSNXSJ4KOBCLKVVOH6/bundle.json","state_url":"https://pith.science/pith/KVY4B4TURSNXSJ4KOBCLKVVOH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KVY4B4TURSNXSJ4KOBCLKVVOH6/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":"2026-06-26T01:21:35Z","links":{"resolver":"https://pith.science/pith/KVY4B4TURSNXSJ4KOBCLKVVOH6","bundle":"https://pith.science/pith/KVY4B4TURSNXSJ4KOBCLKVVOH6/bundle.json","state":"https://pith.science/pith/KVY4B4TURSNXSJ4KOBCLKVVOH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KVY4B4TURSNXSJ4KOBCLKVVOH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KVY4B4TURSNXSJ4KOBCLKVVOH6","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":"20fda8a9c5811d066d23e89d95b98e543420de0b5a1c084a87e2c632aa46cf18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-24T15:20:27Z","title_canon_sha256":"e41040511d2552ac7e9546c845cbb17e3d05edecb9ff705f91c2bdacf3517cd4"},"schema_version":"1.0","source":{"id":"1303.5959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5959","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5959v1","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5959","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"pith_short_12","alias_value":"KVY4B4TURSNX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KVY4B4TURSNXSJ4K","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KVY4B4TU","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:960ebeb0e5114020d924e0daba38d35117c4978ad497bbe95da3707ac6091499","target":"graph","created_at":"2026-05-18T03:19:45Z","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":"It has been shown that Paley-Wiener functions may be recovered from their values on a complete interpolating sequence. This paper explores the same phenomenon, and gives a sufficient condition on a function $\\phi(x)$, called an interpolator, so that scattered translates of this function may be used to interpolate and recover any given Paley-Wiener function.","authors_text":"Jeff Ledford","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-24T15:20:27Z","title":"Recovery of Paley-Wiener functions using scattered translates of regular interpolators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5959","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:a6f78f77cd99bd6d949c6c96fe920869c2aed310f656faf6b0f0e05edeb8c483","target":"record","created_at":"2026-05-18T03:19:45Z","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":"20fda8a9c5811d066d23e89d95b98e543420de0b5a1c084a87e2c632aa46cf18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-24T15:20:27Z","title_canon_sha256":"e41040511d2552ac7e9546c845cbb17e3d05edecb9ff705f91c2bdacf3517cd4"},"schema_version":"1.0","source":{"id":"1303.5959","kind":"arxiv","version":1}},"canonical_sha256":"5571c0f2748c9b79278a7044b556ae3f8368785e69063448ec194b77b7c8009f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5571c0f2748c9b79278a7044b556ae3f8368785e69063448ec194b77b7c8009f","first_computed_at":"2026-05-18T03:19:45.493860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:45.493860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vLvOA7cSIICNi9epXStwLlBtnISmM8GqETVyPhB2r1bbGdiPUdOs65L2o0JfDA+MzYrMM6/vftmecFnYh3exDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:45.494531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.5959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6f78f77cd99bd6d949c6c96fe920869c2aed310f656faf6b0f0e05edeb8c483","sha256:960ebeb0e5114020d924e0daba38d35117c4978ad497bbe95da3707ac6091499"],"state_sha256":"891b8c0b2eebdafd080d04d6c4b7d850591fb79e7b54776fc429ba3aaddc0fe5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dzVL9x5XaY62w2OZcjZPJ9HEyQphEHso+um4KHVqD8AYzY8Y+RW5kgQz6SxUOr1bQGcshTS6rnnS3NuIkU5UCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:21:35.154576Z","bundle_sha256":"d5baa8b084ff177064afd0d28287ef168d5dbb7f2fb930838f730854fca9e8d5"}}