{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U2FWSE44AHSFZPTAARCM2BN6HF","short_pith_number":"pith:U2FWSE44","canonical_record":{"source":{"id":"1304.5721","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-21T11:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"f44d4fa7c60676629a9bbca4bcba6d961f49819726177a28c183615a700d8eae","abstract_canon_sha256":"5309bea4ac2c2e99dc928f89902ca772db8a76c5e1f67d320ad22ce355745e6b"},"schema_version":"1.0"},"canonical_sha256":"a68b69139c01e45cbe600444cd05be3948673b31711b739232be961fb470f50f","source":{"kind":"arxiv","id":"1304.5721","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5721","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5721v1","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5721","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"U2FWSE44AHSF","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U2FWSE44AHSFZPTA","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U2FWSE44","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U2FWSE44AHSFZPTAARCM2BN6HF","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5721","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-21T11:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"f44d4fa7c60676629a9bbca4bcba6d961f49819726177a28c183615a700d8eae","abstract_canon_sha256":"5309bea4ac2c2e99dc928f89902ca772db8a76c5e1f67d320ad22ce355745e6b"},"schema_version":"1.0"},"canonical_sha256":"a68b69139c01e45cbe600444cd05be3948673b31711b739232be961fb470f50f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:32.886999Z","signature_b64":"uREZppg7FlyExCmjB1aa1xHK6pq5iyCMjo4a492U1+9c2F4KZFpTB21yoQGhu8fFsSNe2zslXyRnjEdfH/+GBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a68b69139c01e45cbe600444cd05be3948673b31711b739232be961fb470f50f","last_reissued_at":"2026-05-18T01:09:32.886580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:32.886580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5721","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":"2026-05-18T01:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"014slAh6LYY5DUwZw2st0bDP9BPu4m2liSf3qPuwNM4pDlHlP9Q5CeTSTjH3vx1Lu9sVztbHjfuwqPwWSDTaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:16:38.920196Z"},"content_sha256":"86f4f8afbae89b34ef2110b190253f2e3eb82474863c0b92352798e188c5ec0e","schema_version":"1.0","event_id":"sha256:86f4f8afbae89b34ef2110b190253f2e3eb82474863c0b92352798e188c5ec0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U2FWSE44AHSFZPTAARCM2BN6HF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric series of positive linear operators and inverse Voronovskaya theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mircea Ivan, Radu P\\u{a}lt\\u{a}nea, Ulrich Abel","submitted_at":"2013-04-21T11:31:22Z","abstract_excerpt":"We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators, the Bernstein-Durrmeyer-type operators, and the symmetrical version of Meyer-K\\\"onig and Zeller operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5721","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":"2026-05-18T01:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fVUfBQxmQaqhUGOswvmWU8G2j9ymZAepSjC8doG44xRX1TrwVuo3AD9AnI8yPYLHSc3mwHSjkPnHZxCHgSDZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:16:38.920877Z"},"content_sha256":"10811d5b6c13b91c7225c8a71dce4e860ebd09eef3ea09886c73cad8f22a7448","schema_version":"1.0","event_id":"sha256:10811d5b6c13b91c7225c8a71dce4e860ebd09eef3ea09886c73cad8f22a7448"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2FWSE44AHSFZPTAARCM2BN6HF/bundle.json","state_url":"https://pith.science/pith/U2FWSE44AHSFZPTAARCM2BN6HF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2FWSE44AHSFZPTAARCM2BN6HF/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":"2026-06-07T18:16:38Z","links":{"resolver":"https://pith.science/pith/U2FWSE44AHSFZPTAARCM2BN6HF","bundle":"https://pith.science/pith/U2FWSE44AHSFZPTAARCM2BN6HF/bundle.json","state":"https://pith.science/pith/U2FWSE44AHSFZPTAARCM2BN6HF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2FWSE44AHSFZPTAARCM2BN6HF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U2FWSE44AHSFZPTAARCM2BN6HF","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":"5309bea4ac2c2e99dc928f89902ca772db8a76c5e1f67d320ad22ce355745e6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-21T11:31:22Z","title_canon_sha256":"f44d4fa7c60676629a9bbca4bcba6d961f49819726177a28c183615a700d8eae"},"schema_version":"1.0","source":{"id":"1304.5721","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5721","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5721v1","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5721","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"U2FWSE44AHSF","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U2FWSE44AHSFZPTA","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U2FWSE44","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:10811d5b6c13b91c7225c8a71dce4e860ebd09eef3ea09886c73cad8f22a7448","target":"graph","created_at":"2026-05-18T01:09:32Z","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 define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators, the Bernstein-Durrmeyer-type operators, and the symmetrical version of Meyer-K\\\"onig and Zeller operators.","authors_text":"Mircea Ivan, Radu P\\u{a}lt\\u{a}nea, Ulrich Abel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-21T11:31:22Z","title":"Geometric series of positive linear operators and inverse Voronovskaya theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5721","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":"sha256:86f4f8afbae89b34ef2110b190253f2e3eb82474863c0b92352798e188c5ec0e","target":"record","created_at":"2026-05-18T01:09:32Z","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":"5309bea4ac2c2e99dc928f89902ca772db8a76c5e1f67d320ad22ce355745e6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-21T11:31:22Z","title_canon_sha256":"f44d4fa7c60676629a9bbca4bcba6d961f49819726177a28c183615a700d8eae"},"schema_version":"1.0","source":{"id":"1304.5721","kind":"arxiv","version":1}},"canonical_sha256":"a68b69139c01e45cbe600444cd05be3948673b31711b739232be961fb470f50f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a68b69139c01e45cbe600444cd05be3948673b31711b739232be961fb470f50f","first_computed_at":"2026-05-18T01:09:32.886580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:32.886580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uREZppg7FlyExCmjB1aa1xHK6pq5iyCMjo4a492U1+9c2F4KZFpTB21yoQGhu8fFsSNe2zslXyRnjEdfH/+GBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:32.886999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5721","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86f4f8afbae89b34ef2110b190253f2e3eb82474863c0b92352798e188c5ec0e","sha256:10811d5b6c13b91c7225c8a71dce4e860ebd09eef3ea09886c73cad8f22a7448"],"state_sha256":"c6c172c2288aa02a39b0fe8a8f08b628b53c9ab91cb5680e267564440d5b2a3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F/iVmXlwzXBIWE88Ckl4pD3PvJFvdSf1vhOVQEAJPST/qZMAxA0WLAV6Gws4BwopEvC3nNtb1ZlKsME/ZzxuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:16:38.925128Z","bundle_sha256":"6e78aaefd9640236bc13d30e6ccf07abcce0916617c432023b56fe318524e8f0"}}