{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XPWXISRHSEGZ4BLW2KTBTHWHHG","short_pith_number":"pith:XPWXISRH","canonical_record":{"source":{"id":"1211.0783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T08:05:58Z","cross_cats_sorted":[],"title_canon_sha256":"6375ab7a604cea46e27f1e43f5247a12268d4456a758c0e6d9b9b205c2bbcf6e","abstract_canon_sha256":"35e9168a86d6ae0570beeb6be37158000e497859435b27821a5d242000851280"},"schema_version":"1.0"},"canonical_sha256":"bbed744a27910d9e0576d2a6199ec739a3cc29e1349a1c760dede9fc431c4362","source":{"kind":"arxiv","id":"1211.0783","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0783","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0783v1","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0783","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"XPWXISRHSEGZ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XPWXISRHSEGZ4BLW","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XPWXISRH","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XPWXISRHSEGZ4BLW2KTBTHWHHG","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T08:05:58Z","cross_cats_sorted":[],"title_canon_sha256":"6375ab7a604cea46e27f1e43f5247a12268d4456a758c0e6d9b9b205c2bbcf6e","abstract_canon_sha256":"35e9168a86d6ae0570beeb6be37158000e497859435b27821a5d242000851280"},"schema_version":"1.0"},"canonical_sha256":"bbed744a27910d9e0576d2a6199ec739a3cc29e1349a1c760dede9fc431c4362","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:31.588086Z","signature_b64":"IrdjnEgoO68OIjZ3ek219VGcQi7kazKVwT8Lbb6P/nJ8+3qMLMzkJY6j7a/a2Ul9Y+UHp1PQ6AhhV5ZpQPl5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbed744a27910d9e0576d2a6199ec739a3cc29e1349a1c760dede9fc431c4362","last_reissued_at":"2026-05-18T03:41:31.587268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:31.587268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0783","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":"2026-05-18T03:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKjw/OAh7ewfNSu9DUYkPzYjho45NSG5S7ucsyrWBD9mkUreAsE8qhM5SeHBo6RskEp/5W8FfZZCPe0xI+H+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:59:55.447940Z"},"content_sha256":"993e5339a3225312aa115d8189844ac3230e0016f17f66dd6526b83f5260b78b","schema_version":"1.0","event_id":"sha256:993e5339a3225312aa115d8189844ac3230e0016f17f66dd6526b83f5260b78b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XPWXISRHSEGZ4BLW2KTBTHWHHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simultaneous generic approximation by the iterates of the Cesaro operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Theodosios Douvropoulos","submitted_at":"2012-11-05T08:05:58Z","abstract_excerpt":"We show that for the generic sequence (a) of elements in a subset A of a separable locally convex metrisable space V, the sequences [T^k(a)]_n, n=1,2,... are dense in the convex hull convA of A for all k=1,2,...; where T is the Cesaro operator. Further, if convA is dense in V, then for every sequence x_k of elements of V, k=1,2,... there exists a sequence of indices l_n, n=1,2,..., such that, we have the simultaneous approximation that [T^k(a)]_(l_n) converges to x_k as n tends to infinity for all k=1,2,... These phenomena are topologically generic and in the case where A is a vector space the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0783","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":"2026-05-18T03:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ss4eBrYWhXQ24qOsEGdDymQDCL7nuGEtqsCGPTGUze8SGzpSYngVRc0jwAUACFuumU/1PE57qdmKiYmUYhKhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:59:55.448280Z"},"content_sha256":"7b2702389cd6586cebb74b506ed71f7e58f3525fb461de4442c9a76e3804a0be","schema_version":"1.0","event_id":"sha256:7b2702389cd6586cebb74b506ed71f7e58f3525fb461de4442c9a76e3804a0be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XPWXISRHSEGZ4BLW2KTBTHWHHG/bundle.json","state_url":"https://pith.science/pith/XPWXISRHSEGZ4BLW2KTBTHWHHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XPWXISRHSEGZ4BLW2KTBTHWHHG/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":"2026-06-29T10:59:55Z","links":{"resolver":"https://pith.science/pith/XPWXISRHSEGZ4BLW2KTBTHWHHG","bundle":"https://pith.science/pith/XPWXISRHSEGZ4BLW2KTBTHWHHG/bundle.json","state":"https://pith.science/pith/XPWXISRHSEGZ4BLW2KTBTHWHHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XPWXISRHSEGZ4BLW2KTBTHWHHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XPWXISRHSEGZ4BLW2KTBTHWHHG","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":"35e9168a86d6ae0570beeb6be37158000e497859435b27821a5d242000851280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T08:05:58Z","title_canon_sha256":"6375ab7a604cea46e27f1e43f5247a12268d4456a758c0e6d9b9b205c2bbcf6e"},"schema_version":"1.0","source":{"id":"1211.0783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0783","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0783v1","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0783","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"XPWXISRHSEGZ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XPWXISRHSEGZ4BLW","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XPWXISRH","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:7b2702389cd6586cebb74b506ed71f7e58f3525fb461de4442c9a76e3804a0be","target":"graph","created_at":"2026-05-18T03:41:31Z","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 show that for the generic sequence (a) of elements in a subset A of a separable locally convex metrisable space V, the sequences [T^k(a)]_n, n=1,2,... are dense in the convex hull convA of A for all k=1,2,...; where T is the Cesaro operator. Further, if convA is dense in V, then for every sequence x_k of elements of V, k=1,2,... there exists a sequence of indices l_n, n=1,2,..., such that, we have the simultaneous approximation that [T^k(a)]_(l_n) converges to x_k as n tends to infinity for all k=1,2,... These phenomena are topologically generic and in the case where A is a vector space the","authors_text":"Theodosios Douvropoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T08:05:58Z","title":"Simultaneous generic approximation by the iterates of the Cesaro operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0783","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":"sha256:993e5339a3225312aa115d8189844ac3230e0016f17f66dd6526b83f5260b78b","target":"record","created_at":"2026-05-18T03:41:31Z","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":"35e9168a86d6ae0570beeb6be37158000e497859435b27821a5d242000851280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T08:05:58Z","title_canon_sha256":"6375ab7a604cea46e27f1e43f5247a12268d4456a758c0e6d9b9b205c2bbcf6e"},"schema_version":"1.0","source":{"id":"1211.0783","kind":"arxiv","version":1}},"canonical_sha256":"bbed744a27910d9e0576d2a6199ec739a3cc29e1349a1c760dede9fc431c4362","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbed744a27910d9e0576d2a6199ec739a3cc29e1349a1c760dede9fc431c4362","first_computed_at":"2026-05-18T03:41:31.587268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:31.587268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IrdjnEgoO68OIjZ3ek219VGcQi7kazKVwT8Lbb6P/nJ8+3qMLMzkJY6j7a/a2Ul9Y+UHp1PQ6AhhV5ZpQPl5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:31.588086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:993e5339a3225312aa115d8189844ac3230e0016f17f66dd6526b83f5260b78b","sha256:7b2702389cd6586cebb74b506ed71f7e58f3525fb461de4442c9a76e3804a0be"],"state_sha256":"d39a8385dc274a50f690e33aa87f90abe57709ab804a9bff46bdadc76c67384e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fIZ1PQm52Z9RyCy9I3Mv32IH5c5pOk13TzAFVALEtzeZN8Ztz1lWNvBsBX6O8t72oGZ99a4lht93Br8w3WYoAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T10:59:55.450127Z","bundle_sha256":"24ca7b3214c4a3e1e1d669484f9da95684304430eb7759d10a2ff1579fc7043b"}}