{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XWIBIPVC5QEZAKMLHFK4Z442NF","short_pith_number":"pith:XWIBIPVC","canonical_record":{"source":{"id":"1106.0576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-03T07:36:03Z","cross_cats_sorted":[],"title_canon_sha256":"96e5a2c8ac971e051b554cebdcab8cbd0cf2f69e34a37a7b75695b7724658808","abstract_canon_sha256":"d2eb7f1ee9422b8708a866e4d6df67de914f0a3484c9b8c3e57c0f35f56827f3"},"schema_version":"1.0"},"canonical_sha256":"bd90143ea2ec0990298b3955ccf39a6955f3acf0ad39a7f98a41837d1fd5bf4c","source":{"kind":"arxiv","id":"1106.0576","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0576","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0576v1","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0576","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"XWIBIPVC5QEZ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XWIBIPVC5QEZAKML","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XWIBIPVC","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XWIBIPVC5QEZAKMLHFK4Z442NF","target":"record","payload":{"canonical_record":{"source":{"id":"1106.0576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-03T07:36:03Z","cross_cats_sorted":[],"title_canon_sha256":"96e5a2c8ac971e051b554cebdcab8cbd0cf2f69e34a37a7b75695b7724658808","abstract_canon_sha256":"d2eb7f1ee9422b8708a866e4d6df67de914f0a3484c9b8c3e57c0f35f56827f3"},"schema_version":"1.0"},"canonical_sha256":"bd90143ea2ec0990298b3955ccf39a6955f3acf0ad39a7f98a41837d1fd5bf4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:49.149797Z","signature_b64":"02XG3pDieezYWqewJaCBq90LkkkbpVjvYcNUQVprLDgBnFqeNiQ/MsAhGlIv877gyqYZJybtpGKDnQTTeeIRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd90143ea2ec0990298b3955ccf39a6955f3acf0ad39a7f98a41837d1fd5bf4c","last_reissued_at":"2026-05-18T04:20:49.149210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:49.149210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.0576","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":"2026-05-18T04:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n1/nsBfCvteTnV7mMDuSvNPGRRn5z3PKgtWHqhAmqh9VFbpWvTpTck/GW/ETjtIXbX/jtmGsM715MG+tDn8VAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:46:07.512538Z"},"content_sha256":"4164baf49c02df944d2e34ca8dec4088b06c016d159e86d6f41d48c179529681","schema_version":"1.0","event_id":"sha256:4164baf49c02df944d2e34ca8dec4088b06c016d159e86d6f41d48c179529681"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XWIBIPVC5QEZAKMLHFK4Z442NF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Beurling's sampling theorem in $\\R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexander Olevskii, Alexander Ulanovskii","submitted_at":"2011-06-03T07:36:03Z","abstract_excerpt":"We present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0576","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":"2026-05-18T04:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"en827dfE7QyQDuiR4fvUJMZX40ROrQiVS8p96iD2Z8YfDPUpzNpLRG13lX5eDkSf0fTMaDTtldbF6eNFuEY0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:46:07.512879Z"},"content_sha256":"59f364ccf7a6d9503a080675dc9de721a244fda0e3be365c3dadbc0209c5162e","schema_version":"1.0","event_id":"sha256:59f364ccf7a6d9503a080675dc9de721a244fda0e3be365c3dadbc0209c5162e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWIBIPVC5QEZAKMLHFK4Z442NF/bundle.json","state_url":"https://pith.science/pith/XWIBIPVC5QEZAKMLHFK4Z442NF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWIBIPVC5QEZAKMLHFK4Z442NF/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":"2026-05-28T12:46:07Z","links":{"resolver":"https://pith.science/pith/XWIBIPVC5QEZAKMLHFK4Z442NF","bundle":"https://pith.science/pith/XWIBIPVC5QEZAKMLHFK4Z442NF/bundle.json","state":"https://pith.science/pith/XWIBIPVC5QEZAKMLHFK4Z442NF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWIBIPVC5QEZAKMLHFK4Z442NF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XWIBIPVC5QEZAKMLHFK4Z442NF","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":"d2eb7f1ee9422b8708a866e4d6df67de914f0a3484c9b8c3e57c0f35f56827f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-03T07:36:03Z","title_canon_sha256":"96e5a2c8ac971e051b554cebdcab8cbd0cf2f69e34a37a7b75695b7724658808"},"schema_version":"1.0","source":{"id":"1106.0576","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0576","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0576v1","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0576","created_at":"2026-05-18T04:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"XWIBIPVC5QEZ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XWIBIPVC5QEZAKML","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XWIBIPVC","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:59f364ccf7a6d9503a080675dc9de721a244fda0e3be365c3dadbc0209c5162e","target":"graph","created_at":"2026-05-18T04:20:49Z","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 present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions.","authors_text":"Alexander Olevskii, Alexander Ulanovskii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-03T07:36:03Z","title":"On Beurling's sampling theorem in $\\R^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0576","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":"sha256:4164baf49c02df944d2e34ca8dec4088b06c016d159e86d6f41d48c179529681","target":"record","created_at":"2026-05-18T04:20:49Z","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":"d2eb7f1ee9422b8708a866e4d6df67de914f0a3484c9b8c3e57c0f35f56827f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-03T07:36:03Z","title_canon_sha256":"96e5a2c8ac971e051b554cebdcab8cbd0cf2f69e34a37a7b75695b7724658808"},"schema_version":"1.0","source":{"id":"1106.0576","kind":"arxiv","version":1}},"canonical_sha256":"bd90143ea2ec0990298b3955ccf39a6955f3acf0ad39a7f98a41837d1fd5bf4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd90143ea2ec0990298b3955ccf39a6955f3acf0ad39a7f98a41837d1fd5bf4c","first_computed_at":"2026-05-18T04:20:49.149210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:49.149210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"02XG3pDieezYWqewJaCBq90LkkkbpVjvYcNUQVprLDgBnFqeNiQ/MsAhGlIv877gyqYZJybtpGKDnQTTeeIRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:49.149797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0576","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4164baf49c02df944d2e34ca8dec4088b06c016d159e86d6f41d48c179529681","sha256:59f364ccf7a6d9503a080675dc9de721a244fda0e3be365c3dadbc0209c5162e"],"state_sha256":"302c3bd3115d2717d0272ed13bfd63224ab1016b35edca5ec4a65f5e79553097"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P8zAaVYJuf6BY6wis65qwTC29iUUZijnLw8o697mrtgEUDjTKRbVGNGdE+KZCa5K5lh2Ea/K/KFWAaMvvjnACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:46:07.515371Z","bundle_sha256":"1483830e7d919fa60dec541c3880a07197a91ca9077b4221c0f992c4fc12bc41"}}