{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FOQOTYSPHSM5FUFTEFZPS5QGQL","short_pith_number":"pith:FOQOTYSP","canonical_record":{"source":{"id":"1403.0292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-03T02:40:01Z","cross_cats_sorted":[],"title_canon_sha256":"e6e45332121cea639b028651feacb4c0a40f29f6524aa789016b7c4d6d313e09","abstract_canon_sha256":"b5d7aee437ddb70b30cd99d6c956d33d9366713335f9d88c1b44209d364e9ed8"},"schema_version":"1.0"},"canonical_sha256":"2ba0e9e24f3c99d2d0b32172f9760682f0696ea61c8eb6dcba1f26e43d416ebd","source":{"kind":"arxiv","id":"1403.0292","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0292","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0292v1","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0292","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"FOQOTYSPHSM5","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FOQOTYSPHSM5FUFT","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FOQOTYSP","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FOQOTYSPHSM5FUFTEFZPS5QGQL","target":"record","payload":{"canonical_record":{"source":{"id":"1403.0292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-03T02:40:01Z","cross_cats_sorted":[],"title_canon_sha256":"e6e45332121cea639b028651feacb4c0a40f29f6524aa789016b7c4d6d313e09","abstract_canon_sha256":"b5d7aee437ddb70b30cd99d6c956d33d9366713335f9d88c1b44209d364e9ed8"},"schema_version":"1.0"},"canonical_sha256":"2ba0e9e24f3c99d2d0b32172f9760682f0696ea61c8eb6dcba1f26e43d416ebd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:18.860530Z","signature_b64":"G1v0fRHWjqoHqGB3jA6oMpy1RJYa23fOhjT4PdHc9B/mcVMgDUJ6j3bAzHGbPzDkGogQ7841Nwo4R3GqCdbuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ba0e9e24f3c99d2d0b32172f9760682f0696ea61c8eb6dcba1f26e43d416ebd","last_reissued_at":"2026-05-18T02:27:18.859710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:18.859710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.0292","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":"2026-05-18T02:27:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7yhXp4Qr3C+PXa8e5959QokxCZuN8bI09BMSUox6xV9OTxnDNPLEaN19Q8XgRKJyeIhpYUs95D9WNjKSyYbXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:00:51.270611Z"},"content_sha256":"4187ecf692918f810e37c7ba0239b80ef285da9bf75bca89e1672267be5b2d3b","schema_version":"1.0","event_id":"sha256:4187ecf692918f810e37c7ba0239b80ef285da9bf75bca89e1672267be5b2d3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FOQOTYSPHSM5FUFTEFZPS5QGQL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sampling formulas for one-parameter groups of operators in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Isaac Z. Pesenson","submitted_at":"2014-03-03T02:40:01Z","abstract_excerpt":"We extend some results about sampling of entire functions of exponential type to Banach spaces. By using generator $D$ of one-parameter group $e^{tD}$ of isometries of a Banach space $E$ we introduce Bernstein subspaces $\\mathbf{B}_{\\sigma}(D),\\>\\>\\sigma>0,$ of vectors $f$ in $E$ for which trajectories $e^{tD}f$ are abstract-valued functions of exponential type which are bounded on the real line. This property allows to reduce sampling problems for $e^{tD}f$ with $f\\in \\mathbf{B}_{\\sigma}(D)$ to known sampling results for regular functions of exponential type $\\sigma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0292","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":"2026-05-18T02:27:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fvDKjIEePI+TVKZKI33KiZsZvkuq/fLFqmufR2bJ2XoT4ezhv5gWwg+HQe3ErrjR/qvTHU/za/xwvwA8K1rEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:00:51.270967Z"},"content_sha256":"f8fa1f031c91975d00ae34af21601d8108c9697e516fc977fd0e13a20afe2b42","schema_version":"1.0","event_id":"sha256:f8fa1f031c91975d00ae34af21601d8108c9697e516fc977fd0e13a20afe2b42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FOQOTYSPHSM5FUFTEFZPS5QGQL/bundle.json","state_url":"https://pith.science/pith/FOQOTYSPHSM5FUFTEFZPS5QGQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FOQOTYSPHSM5FUFTEFZPS5QGQL/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":"2026-05-26T11:00:51Z","links":{"resolver":"https://pith.science/pith/FOQOTYSPHSM5FUFTEFZPS5QGQL","bundle":"https://pith.science/pith/FOQOTYSPHSM5FUFTEFZPS5QGQL/bundle.json","state":"https://pith.science/pith/FOQOTYSPHSM5FUFTEFZPS5QGQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FOQOTYSPHSM5FUFTEFZPS5QGQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FOQOTYSPHSM5FUFTEFZPS5QGQL","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":"b5d7aee437ddb70b30cd99d6c956d33d9366713335f9d88c1b44209d364e9ed8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-03T02:40:01Z","title_canon_sha256":"e6e45332121cea639b028651feacb4c0a40f29f6524aa789016b7c4d6d313e09"},"schema_version":"1.0","source":{"id":"1403.0292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0292","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0292v1","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0292","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"FOQOTYSPHSM5","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FOQOTYSPHSM5FUFT","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FOQOTYSP","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:f8fa1f031c91975d00ae34af21601d8108c9697e516fc977fd0e13a20afe2b42","target":"graph","created_at":"2026-05-18T02:27:18Z","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 extend some results about sampling of entire functions of exponential type to Banach spaces. By using generator $D$ of one-parameter group $e^{tD}$ of isometries of a Banach space $E$ we introduce Bernstein subspaces $\\mathbf{B}_{\\sigma}(D),\\>\\>\\sigma>0,$ of vectors $f$ in $E$ for which trajectories $e^{tD}f$ are abstract-valued functions of exponential type which are bounded on the real line. This property allows to reduce sampling problems for $e^{tD}f$ with $f\\in \\mathbf{B}_{\\sigma}(D)$ to known sampling results for regular functions of exponential type $\\sigma$.","authors_text":"Isaac Z. Pesenson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-03T02:40:01Z","title":"Sampling formulas for one-parameter groups of operators in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0292","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":"sha256:4187ecf692918f810e37c7ba0239b80ef285da9bf75bca89e1672267be5b2d3b","target":"record","created_at":"2026-05-18T02:27:18Z","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":"b5d7aee437ddb70b30cd99d6c956d33d9366713335f9d88c1b44209d364e9ed8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-03T02:40:01Z","title_canon_sha256":"e6e45332121cea639b028651feacb4c0a40f29f6524aa789016b7c4d6d313e09"},"schema_version":"1.0","source":{"id":"1403.0292","kind":"arxiv","version":1}},"canonical_sha256":"2ba0e9e24f3c99d2d0b32172f9760682f0696ea61c8eb6dcba1f26e43d416ebd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ba0e9e24f3c99d2d0b32172f9760682f0696ea61c8eb6dcba1f26e43d416ebd","first_computed_at":"2026-05-18T02:27:18.859710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:18.859710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G1v0fRHWjqoHqGB3jA6oMpy1RJYa23fOhjT4PdHc9B/mcVMgDUJ6j3bAzHGbPzDkGogQ7841Nwo4R3GqCdbuDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:18.860530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4187ecf692918f810e37c7ba0239b80ef285da9bf75bca89e1672267be5b2d3b","sha256:f8fa1f031c91975d00ae34af21601d8108c9697e516fc977fd0e13a20afe2b42"],"state_sha256":"fa8f893ab0986daaf40f315c4f072e61dd91a0651593e584a11d11b4dff7019f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DR6vZXxCEI37LgBcCIs/TsuEUNG4i8rPbq+Hj7Xe/tLnmLSZ2x/vGl2krHwgiNMdfnebijSceyTZoJqRGwCaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:00:51.273505Z","bundle_sha256":"a5f61e9337df2aee52d4e4977980a963c7855814d46e5a685b9d5c5fd917a649"}}