{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OBVO576XPRYVGUN6ULKX5MWS2P","short_pith_number":"pith:OBVO576X","canonical_record":{"source":{"id":"1410.3170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-13T00:42:38Z","cross_cats_sorted":[],"title_canon_sha256":"8de9bd3f03f4ca0f1fc35ef94e075ed4d1a6d4e15cc1e8057a3a8c7dd2dc473b","abstract_canon_sha256":"d8cde56ceaed9a9478bea0144354ff967b86173b1848babab4a853bacd1dfd4f"},"schema_version":"1.0"},"canonical_sha256":"706aeeffd77c715351bea2d57eb2d2d3ef1ff3152c8e05dd88e765e9d6188e7a","source":{"kind":"arxiv","id":"1410.3170","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3170","created_at":"2026-05-18T02:40:16Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3170v1","created_at":"2026-05-18T02:40:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3170","created_at":"2026-05-18T02:40:16Z"},{"alias_kind":"pith_short_12","alias_value":"OBVO576XPRYV","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OBVO576XPRYVGUN6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OBVO576X","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OBVO576XPRYVGUN6ULKX5MWS2P","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3170","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-13T00:42:38Z","cross_cats_sorted":[],"title_canon_sha256":"8de9bd3f03f4ca0f1fc35ef94e075ed4d1a6d4e15cc1e8057a3a8c7dd2dc473b","abstract_canon_sha256":"d8cde56ceaed9a9478bea0144354ff967b86173b1848babab4a853bacd1dfd4f"},"schema_version":"1.0"},"canonical_sha256":"706aeeffd77c715351bea2d57eb2d2d3ef1ff3152c8e05dd88e765e9d6188e7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:16.806973Z","signature_b64":"UupQ9raDNjvgTkhL3d6HpLMcDdYZhPnvc+y7ACI7497ltN3FhO+jGomCDsv+luKvy4zPJYc8R2G7EyU4qpoQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"706aeeffd77c715351bea2d57eb2d2d3ef1ff3152c8e05dd88e765e9d6188e7a","last_reissued_at":"2026-05-18T02:40:16.806300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:16.806300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3170","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":"2026-05-18T02:40:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6HS6E3k7VK3jMzA/+23LKzvfRhRYpOVrBW1+gEVSoCCxDkZOY34ICCwlF13vEXSEMrFQiZJyt4/SSMw7+VODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:59.058076Z"},"content_sha256":"7895cc09a550a8a97ffcfddef1fce2a465b7c554a10138766ffbcba5205604f9","schema_version":"1.0","event_id":"sha256:7895cc09a550a8a97ffcfddef1fce2a465b7c554a10138766ffbcba5205604f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OBVO576XPRYVGUN6ULKX5MWS2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential bases, Paley-Wiener spaces and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alex Iosevich, Azita Mayeli","submitted_at":"2014-10-13T00:42:38Z","abstract_excerpt":"We investigate the connection between translation bases for Paley-Wiener spaces and exponential Fourier bases for a domain. We apply these results to the characterization of vector-valued time-frequency translates of a Paley-Wiener \"window\" signal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3170","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":"2026-05-18T02:40:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gCs/7DXn+yglx3+w2OVj3crs/miCm9iIUeXJry8RvElJT38Ok7sYveW0orFzfuNE3P7rPtcD4MLw6e1ju+tTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:59.058421Z"},"content_sha256":"7ed93885071c00092c86805cc31d0b85a1dfcae2f8f22136dc7f6eb3856c4607","schema_version":"1.0","event_id":"sha256:7ed93885071c00092c86805cc31d0b85a1dfcae2f8f22136dc7f6eb3856c4607"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OBVO576XPRYVGUN6ULKX5MWS2P/bundle.json","state_url":"https://pith.science/pith/OBVO576XPRYVGUN6ULKX5MWS2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OBVO576XPRYVGUN6ULKX5MWS2P/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":"2026-06-03T18:37:59Z","links":{"resolver":"https://pith.science/pith/OBVO576XPRYVGUN6ULKX5MWS2P","bundle":"https://pith.science/pith/OBVO576XPRYVGUN6ULKX5MWS2P/bundle.json","state":"https://pith.science/pith/OBVO576XPRYVGUN6ULKX5MWS2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OBVO576XPRYVGUN6ULKX5MWS2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OBVO576XPRYVGUN6ULKX5MWS2P","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":"d8cde56ceaed9a9478bea0144354ff967b86173b1848babab4a853bacd1dfd4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-13T00:42:38Z","title_canon_sha256":"8de9bd3f03f4ca0f1fc35ef94e075ed4d1a6d4e15cc1e8057a3a8c7dd2dc473b"},"schema_version":"1.0","source":{"id":"1410.3170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3170","created_at":"2026-05-18T02:40:16Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3170v1","created_at":"2026-05-18T02:40:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3170","created_at":"2026-05-18T02:40:16Z"},{"alias_kind":"pith_short_12","alias_value":"OBVO576XPRYV","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OBVO576XPRYVGUN6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OBVO576X","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:7ed93885071c00092c86805cc31d0b85a1dfcae2f8f22136dc7f6eb3856c4607","target":"graph","created_at":"2026-05-18T02:40:16Z","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":"We investigate the connection between translation bases for Paley-Wiener spaces and exponential Fourier bases for a domain. We apply these results to the characterization of vector-valued time-frequency translates of a Paley-Wiener \"window\" signal.","authors_text":"Alex Iosevich, Azita Mayeli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-13T00:42:38Z","title":"Exponential bases, Paley-Wiener spaces and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3170","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":"sha256:7895cc09a550a8a97ffcfddef1fce2a465b7c554a10138766ffbcba5205604f9","target":"record","created_at":"2026-05-18T02:40:16Z","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":"d8cde56ceaed9a9478bea0144354ff967b86173b1848babab4a853bacd1dfd4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-13T00:42:38Z","title_canon_sha256":"8de9bd3f03f4ca0f1fc35ef94e075ed4d1a6d4e15cc1e8057a3a8c7dd2dc473b"},"schema_version":"1.0","source":{"id":"1410.3170","kind":"arxiv","version":1}},"canonical_sha256":"706aeeffd77c715351bea2d57eb2d2d3ef1ff3152c8e05dd88e765e9d6188e7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"706aeeffd77c715351bea2d57eb2d2d3ef1ff3152c8e05dd88e765e9d6188e7a","first_computed_at":"2026-05-18T02:40:16.806300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:16.806300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UupQ9raDNjvgTkhL3d6HpLMcDdYZhPnvc+y7ACI7497ltN3FhO+jGomCDsv+luKvy4zPJYc8R2G7EyU4qpoQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:16.806973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7895cc09a550a8a97ffcfddef1fce2a465b7c554a10138766ffbcba5205604f9","sha256:7ed93885071c00092c86805cc31d0b85a1dfcae2f8f22136dc7f6eb3856c4607"],"state_sha256":"c4c4006030826498fda83896b96bad5f3648936b27c00fa0bf6616f1991fa6eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yIy/QLqJm/r2ZhxqoUDGRRvfzxfFBenU6ekxt371nHzbJBeEPrVE035QcP0Aptks+v/vNiUtOVrD9lOlI0XUBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:37:59.060220Z","bundle_sha256":"c2ea6de45384e7d5b2cb3ebcf9498ff7f7443c2254d7c5385b719902d13cedf7"}}