{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2JLS7TOMTUNINQQAI7YMPRHA2Y","short_pith_number":"pith:2JLS7TOM","canonical_record":{"source":{"id":"1210.1380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-04T10:56:38Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"bbfeb9698ab488d2fe1bf298c8c4aeb7e635c491f9b714e97546162501f57490","abstract_canon_sha256":"0f7c647544b17e8a2cb7baeadd4cdd28727217c805c6dfe3eee6d4aac97b57d0"},"schema_version":"1.0"},"canonical_sha256":"d2572fcdcc9d1a86c20047f0c7c4e0d63f9d25a081a069ee38d245eb915d2118","source":{"kind":"arxiv","id":"1210.1380","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1380","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1380v1","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1380","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"2JLS7TOMTUNI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2JLS7TOMTUNINQQA","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2JLS7TOM","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2JLS7TOMTUNINQQAI7YMPRHA2Y","target":"record","payload":{"canonical_record":{"source":{"id":"1210.1380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-04T10:56:38Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"bbfeb9698ab488d2fe1bf298c8c4aeb7e635c491f9b714e97546162501f57490","abstract_canon_sha256":"0f7c647544b17e8a2cb7baeadd4cdd28727217c805c6dfe3eee6d4aac97b57d0"},"schema_version":"1.0"},"canonical_sha256":"d2572fcdcc9d1a86c20047f0c7c4e0d63f9d25a081a069ee38d245eb915d2118","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:42.470065Z","signature_b64":"jdasBOGGjl7VHlOjbQVm5jJNX5ncoNoXJ7AqgrJqQtlHlqAWdSuvoqgjDeisYcD3qhcj7h3h6vjpT2oLiVUBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2572fcdcc9d1a86c20047f0c7c4e0d63f9d25a081a069ee38d245eb915d2118","last_reissued_at":"2026-05-18T03:28:42.469459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:42.469459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.1380","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":"2026-05-18T03:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7FWoccd5Ok8H8MWNTGemW88ZJnxiIb7G/eX/BFi3FW0dzizrxPEY1cqWcesSq/sIM8ghnloxt918Blw1gjdcAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:18:03.721893Z"},"content_sha256":"ffa207bc7c472f7e883cc2aaa523c9aa06a59f2cdf4b65b3303e1629023b380a","schema_version":"1.0","event_id":"sha256:ffa207bc7c472f7e883cc2aaa523c9aa06a59f2cdf4b65b3303e1629023b380a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2JLS7TOMTUNINQQAI7YMPRHA2Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"F\\olner sequences and finite operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Dmitry V. Yakubovich, Fernando Lled\\'o","submitted_at":"2012-10-04T10:56:38Z","abstract_excerpt":"This article analyzes F\\olner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper F\\olner sequence (i.e. a F\\olner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper F\\olner sequence. Moreover, we show that an operator is finite if and only if it has a proper F\\olner sequence or if it has a non-trivial finite dimensional reducin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1380","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":"2026-05-18T03:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hBTweOfixu7zXczhTvX4Jh3MKNELU/A9ikyrNJRic+2OSF/Oh/Lp0KhVuHhCkp7si8HXmZ7MgHR4Cu/furd7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:18:03.722483Z"},"content_sha256":"8b501a3e477deb7e9f077d630fe6294dd5fd8937d0bb16a3f4da288e7fed19ea","schema_version":"1.0","event_id":"sha256:8b501a3e477deb7e9f077d630fe6294dd5fd8937d0bb16a3f4da288e7fed19ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JLS7TOMTUNINQQAI7YMPRHA2Y/bundle.json","state_url":"https://pith.science/pith/2JLS7TOMTUNINQQAI7YMPRHA2Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JLS7TOMTUNINQQAI7YMPRHA2Y/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":"2026-06-04T22:18:03Z","links":{"resolver":"https://pith.science/pith/2JLS7TOMTUNINQQAI7YMPRHA2Y","bundle":"https://pith.science/pith/2JLS7TOMTUNINQQAI7YMPRHA2Y/bundle.json","state":"https://pith.science/pith/2JLS7TOMTUNINQQAI7YMPRHA2Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JLS7TOMTUNINQQAI7YMPRHA2Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2JLS7TOMTUNINQQAI7YMPRHA2Y","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":"0f7c647544b17e8a2cb7baeadd4cdd28727217c805c6dfe3eee6d4aac97b57d0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-04T10:56:38Z","title_canon_sha256":"bbfeb9698ab488d2fe1bf298c8c4aeb7e635c491f9b714e97546162501f57490"},"schema_version":"1.0","source":{"id":"1210.1380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1380","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1380v1","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1380","created_at":"2026-05-18T03:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"2JLS7TOMTUNI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2JLS7TOMTUNINQQA","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2JLS7TOM","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:8b501a3e477deb7e9f077d630fe6294dd5fd8937d0bb16a3f4da288e7fed19ea","target":"graph","created_at":"2026-05-18T03:28:42Z","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":"This article analyzes F\\olner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper F\\olner sequence (i.e. a F\\olner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper F\\olner sequence. Moreover, we show that an operator is finite if and only if it has a proper F\\olner sequence or if it has a non-trivial finite dimensional reducin","authors_text":"Dmitry V. Yakubovich, Fernando Lled\\'o","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-04T10:56:38Z","title":"F\\olner sequences and finite operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1380","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:ffa207bc7c472f7e883cc2aaa523c9aa06a59f2cdf4b65b3303e1629023b380a","target":"record","created_at":"2026-05-18T03:28:42Z","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":"0f7c647544b17e8a2cb7baeadd4cdd28727217c805c6dfe3eee6d4aac97b57d0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-10-04T10:56:38Z","title_canon_sha256":"bbfeb9698ab488d2fe1bf298c8c4aeb7e635c491f9b714e97546162501f57490"},"schema_version":"1.0","source":{"id":"1210.1380","kind":"arxiv","version":1}},"canonical_sha256":"d2572fcdcc9d1a86c20047f0c7c4e0d63f9d25a081a069ee38d245eb915d2118","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2572fcdcc9d1a86c20047f0c7c4e0d63f9d25a081a069ee38d245eb915d2118","first_computed_at":"2026-05-18T03:28:42.469459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:42.469459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jdasBOGGjl7VHlOjbQVm5jJNX5ncoNoXJ7AqgrJqQtlHlqAWdSuvoqgjDeisYcD3qhcj7h3h6vjpT2oLiVUBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:42.470065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffa207bc7c472f7e883cc2aaa523c9aa06a59f2cdf4b65b3303e1629023b380a","sha256:8b501a3e477deb7e9f077d630fe6294dd5fd8937d0bb16a3f4da288e7fed19ea"],"state_sha256":"1c508a8484e10d4148d0947df0cdc11d7c8f9679a165ad61487f3617654e905d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ct6Jvd5Si51VFGHC9qDCaH9YlGwDhc5zeDaP+pCce7hmoV4/1uBS5u5EX/OABiuHR4nP2JAoKmQQzhfqMg65CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:18:03.725603Z","bundle_sha256":"53459d198ea6034dc1882b99ae3d8068ec13e132fbb15da31eeff243a48ca89f"}}