{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YXCNUHIQ34GJC5Q3OB4WCAGPQQ","short_pith_number":"pith:YXCNUHIQ","canonical_record":{"source":{"id":"1602.01821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-04T20:34:31Z","cross_cats_sorted":[],"title_canon_sha256":"efae10fa9ba1f5627f01716acfc683f191bf4323f2a9ef5d5d69fd01ea67de92","abstract_canon_sha256":"95d1263255ba47e16367c9f7285b2c6271cfee2b79c8db6c956b10798b55115f"},"schema_version":"1.0"},"canonical_sha256":"c5c4da1d10df0c91761b70796100cf8427573e7cc4313a6587b48601a76969f1","source":{"kind":"arxiv","id":"1602.01821","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01821","created_at":"2026-05-18T01:21:16Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01821v1","created_at":"2026-05-18T01:21:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01821","created_at":"2026-05-18T01:21:16Z"},{"alias_kind":"pith_short_12","alias_value":"YXCNUHIQ34GJ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YXCNUHIQ34GJC5Q3","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YXCNUHIQ","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YXCNUHIQ34GJC5Q3OB4WCAGPQQ","target":"record","payload":{"canonical_record":{"source":{"id":"1602.01821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-04T20:34:31Z","cross_cats_sorted":[],"title_canon_sha256":"efae10fa9ba1f5627f01716acfc683f191bf4323f2a9ef5d5d69fd01ea67de92","abstract_canon_sha256":"95d1263255ba47e16367c9f7285b2c6271cfee2b79c8db6c956b10798b55115f"},"schema_version":"1.0"},"canonical_sha256":"c5c4da1d10df0c91761b70796100cf8427573e7cc4313a6587b48601a76969f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:16.612114Z","signature_b64":"9I6OUYoZ1ZAcvtkQPvCUNrqnvZKMKaCTJoJLTaPtdwpDE9bMXYAvbW51GKblfWHosVrsIXOWDViw47zK736/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5c4da1d10df0c91761b70796100cf8427573e7cc4313a6587b48601a76969f1","last_reissued_at":"2026-05-18T01:21:16.611598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:16.611598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.01821","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":"2026-05-18T01:21:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oac/acpMr7HqOnLlF5XysrJ22v4DxuJzpRwIi3+4M43c/AQjT3ITgPS+XOaCF4wl/yulEOUW9MdVoyzfTYn0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:26:06.954197Z"},"content_sha256":"f6b7225270f8009df6e6584f465122dfd3516566e5b4942a78f3408105355442","schema_version":"1.0","event_id":"sha256:f6b7225270f8009df6e6584f465122dfd3516566e5b4942a78f3408105355442"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YXCNUHIQ34GJC5Q3OB4WCAGPQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sampling in de Branges Spaces and Naimark Dilation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric S. Weber, Sa'ud al-Sa'di","submitted_at":"2016-02-04T20:34:31Z","abstract_excerpt":"We consider the problem of sampling in de Branges spaces and develop some necessary conditions and some sufficient conditions for sampling sequences, which generalize some well-known sampling results in the Paley-Wiener space. These conditions are obtained by identifying the main construction with Naimark dilation of frames--embedding the de Branges space into a larger de Branges space while embedding the kernel functions associated with a sampling sequence into a Riesz basis for the larger space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01821","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":"2026-05-18T01:21:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q4WgKneCyrE3eOe6eljaHcAyDDn6NJWucX8NJlWpufKl/4HNOJOHXlZdyyK/I29fx4d8AB48AnofMLlNQrzGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:26:06.954938Z"},"content_sha256":"54f242cbbc9f3a244ba0f3292115ec6894160621760ff33e9b63b984c8927a70","schema_version":"1.0","event_id":"sha256:54f242cbbc9f3a244ba0f3292115ec6894160621760ff33e9b63b984c8927a70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/bundle.json","state_url":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/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":"2026-06-06T04:26:06Z","links":{"resolver":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ","bundle":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/bundle.json","state":"https://pith.science/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXCNUHIQ34GJC5Q3OB4WCAGPQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YXCNUHIQ34GJC5Q3OB4WCAGPQQ","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":"95d1263255ba47e16367c9f7285b2c6271cfee2b79c8db6c956b10798b55115f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-04T20:34:31Z","title_canon_sha256":"efae10fa9ba1f5627f01716acfc683f191bf4323f2a9ef5d5d69fd01ea67de92"},"schema_version":"1.0","source":{"id":"1602.01821","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01821","created_at":"2026-05-18T01:21:16Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01821v1","created_at":"2026-05-18T01:21:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01821","created_at":"2026-05-18T01:21:16Z"},{"alias_kind":"pith_short_12","alias_value":"YXCNUHIQ34GJ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YXCNUHIQ34GJC5Q3","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YXCNUHIQ","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:54f242cbbc9f3a244ba0f3292115ec6894160621760ff33e9b63b984c8927a70","target":"graph","created_at":"2026-05-18T01:21:16Z","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 consider the problem of sampling in de Branges spaces and develop some necessary conditions and some sufficient conditions for sampling sequences, which generalize some well-known sampling results in the Paley-Wiener space. These conditions are obtained by identifying the main construction with Naimark dilation of frames--embedding the de Branges space into a larger de Branges space while embedding the kernel functions associated with a sampling sequence into a Riesz basis for the larger space.","authors_text":"Eric S. Weber, Sa'ud al-Sa'di","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-04T20:34:31Z","title":"Sampling in de Branges Spaces and Naimark Dilation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01821","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:f6b7225270f8009df6e6584f465122dfd3516566e5b4942a78f3408105355442","target":"record","created_at":"2026-05-18T01:21:16Z","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":"95d1263255ba47e16367c9f7285b2c6271cfee2b79c8db6c956b10798b55115f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-02-04T20:34:31Z","title_canon_sha256":"efae10fa9ba1f5627f01716acfc683f191bf4323f2a9ef5d5d69fd01ea67de92"},"schema_version":"1.0","source":{"id":"1602.01821","kind":"arxiv","version":1}},"canonical_sha256":"c5c4da1d10df0c91761b70796100cf8427573e7cc4313a6587b48601a76969f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5c4da1d10df0c91761b70796100cf8427573e7cc4313a6587b48601a76969f1","first_computed_at":"2026-05-18T01:21:16.611598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:16.611598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9I6OUYoZ1ZAcvtkQPvCUNrqnvZKMKaCTJoJLTaPtdwpDE9bMXYAvbW51GKblfWHosVrsIXOWDViw47zK736/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:16.612114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01821","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6b7225270f8009df6e6584f465122dfd3516566e5b4942a78f3408105355442","sha256:54f242cbbc9f3a244ba0f3292115ec6894160621760ff33e9b63b984c8927a70"],"state_sha256":"993d1666ac300b33e082d226b6178616c92024099a1c17fe7bc326affdd81759"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"09H/fLiVIa6EIAUpwB9kr8+zKpKTYuqbmzqVbjzNR4uuwQ+kgGmvsAKLoJOGdMO47NZgVcRVZ6iVojTQBpfoBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T04:26:06.959576Z","bundle_sha256":"f092f50a591a914f20fe5a1e9e8d35f2bf45f7e0f612ef796e2dc0b3ac6cb4e0"}}