{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JDIAPJBZW7DZREIUEBAUFKKO7S","short_pith_number":"pith:JDIAPJBZ","canonical_record":{"source":{"id":"1203.3603","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2012-03-16T02:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"8b9b15001f0727ebc55c44d37e299689e1fc1a32ed9cf44d603795f972f04a04","abstract_canon_sha256":"ad0b507db0d6963fca0d89c6359ba1fd957a7aedc7fa8007bc8efa318d862196"},"schema_version":"1.0"},"canonical_sha256":"48d007a439b7c7989114204142a94efc993a30f5d9e0bf9446942d92ab1b7264","source":{"kind":"arxiv","id":"1203.3603","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3603","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3603v1","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3603","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"pith_short_12","alias_value":"JDIAPJBZW7DZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JDIAPJBZW7DZREIU","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JDIAPJBZ","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JDIAPJBZW7DZREIUEBAUFKKO7S","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3603","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2012-03-16T02:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"8b9b15001f0727ebc55c44d37e299689e1fc1a32ed9cf44d603795f972f04a04","abstract_canon_sha256":"ad0b507db0d6963fca0d89c6359ba1fd957a7aedc7fa8007bc8efa318d862196"},"schema_version":"1.0"},"canonical_sha256":"48d007a439b7c7989114204142a94efc993a30f5d9e0bf9446942d92ab1b7264","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:50.496344Z","signature_b64":"94hGHI5egrOv+gKZlr6TR+dsQsUp1sbOXh+rZALJg9X/nYfUjulj6c44SJ0hhfKt/bLcL2rg0FF0HU39bzQnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48d007a439b7c7989114204142a94efc993a30f5d9e0bf9446942d92ab1b7264","last_reissued_at":"2026-05-18T03:59:50.495564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:50.495564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3603","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":"2026-05-18T03:59:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a/oEBs3rrOqK89VYfUMbPSd/RR4aFUZSToPzpnVHLYLm4/SZY0HS3vr1sc3gYM2Mgt3rliAbnCmary5BdsALAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:11:42.101734Z"},"content_sha256":"90ccb9f0320d25544a5801a55f73d6fd1c9b1b418aa2c3ebcb492a289bca575d","schema_version":"1.0","event_id":"sha256:90ccb9f0320d25544a5801a55f73d6fd1c9b1b418aa2c3ebcb492a289bca575d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JDIAPJBZW7DZREIUEBAUFKKO7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schauder Bases and Operator Theory","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bingzhe Hou, Geng Tian, Yang Cao","submitted_at":"2012-03-16T02:27:38Z","abstract_excerpt":"In this paper, we firstly give a matrix approach to the bases of a separable Hilbert space and then correct a mistake appearing in both review and the English translation of the Olevskii's paper. After this, we show that even a diagonal compact operator may map an orthonormal basis into a conditional basis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3603","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":"2026-05-18T03:59:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XyFngdqkxrcfrCa5fr2K06m9ZMnWnHQkegvNQZhQTrrzvv856Fl0f0ASGwqJhHZN68cwwG32hw1gfVF5aBqsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:11:42.102086Z"},"content_sha256":"8c4ebcd736f8376e4b8ad0a3df8552fb7ac32b6362baec27cae183f583e74488","schema_version":"1.0","event_id":"sha256:8c4ebcd736f8376e4b8ad0a3df8552fb7ac32b6362baec27cae183f583e74488"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDIAPJBZW7DZREIUEBAUFKKO7S/bundle.json","state_url":"https://pith.science/pith/JDIAPJBZW7DZREIUEBAUFKKO7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDIAPJBZW7DZREIUEBAUFKKO7S/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":"2026-06-24T19:11:42Z","links":{"resolver":"https://pith.science/pith/JDIAPJBZW7DZREIUEBAUFKKO7S","bundle":"https://pith.science/pith/JDIAPJBZW7DZREIUEBAUFKKO7S/bundle.json","state":"https://pith.science/pith/JDIAPJBZW7DZREIUEBAUFKKO7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDIAPJBZW7DZREIUEBAUFKKO7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JDIAPJBZW7DZREIUEBAUFKKO7S","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":"ad0b507db0d6963fca0d89c6359ba1fd957a7aedc7fa8007bc8efa318d862196","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2012-03-16T02:27:38Z","title_canon_sha256":"8b9b15001f0727ebc55c44d37e299689e1fc1a32ed9cf44d603795f972f04a04"},"schema_version":"1.0","source":{"id":"1203.3603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3603","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3603v1","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3603","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"pith_short_12","alias_value":"JDIAPJBZW7DZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JDIAPJBZW7DZREIU","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JDIAPJBZ","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:8c4ebcd736f8376e4b8ad0a3df8552fb7ac32b6362baec27cae183f583e74488","target":"graph","created_at":"2026-05-18T03:59:50Z","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":"In this paper, we firstly give a matrix approach to the bases of a separable Hilbert space and then correct a mistake appearing in both review and the English translation of the Olevskii's paper. After this, we show that even a diagonal compact operator may map an orthonormal basis into a conditional basis.","authors_text":"Bingzhe Hou, Geng Tian, Yang Cao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2012-03-16T02:27:38Z","title":"Schauder Bases and Operator Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3603","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":"sha256:90ccb9f0320d25544a5801a55f73d6fd1c9b1b418aa2c3ebcb492a289bca575d","target":"record","created_at":"2026-05-18T03:59:50Z","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":"ad0b507db0d6963fca0d89c6359ba1fd957a7aedc7fa8007bc8efa318d862196","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2012-03-16T02:27:38Z","title_canon_sha256":"8b9b15001f0727ebc55c44d37e299689e1fc1a32ed9cf44d603795f972f04a04"},"schema_version":"1.0","source":{"id":"1203.3603","kind":"arxiv","version":1}},"canonical_sha256":"48d007a439b7c7989114204142a94efc993a30f5d9e0bf9446942d92ab1b7264","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48d007a439b7c7989114204142a94efc993a30f5d9e0bf9446942d92ab1b7264","first_computed_at":"2026-05-18T03:59:50.495564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:50.495564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"94hGHI5egrOv+gKZlr6TR+dsQsUp1sbOXh+rZALJg9X/nYfUjulj6c44SJ0hhfKt/bLcL2rg0FF0HU39bzQnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:50.496344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90ccb9f0320d25544a5801a55f73d6fd1c9b1b418aa2c3ebcb492a289bca575d","sha256:8c4ebcd736f8376e4b8ad0a3df8552fb7ac32b6362baec27cae183f583e74488"],"state_sha256":"81aa5db4ecdd2a3103b5ab3f68094c146b2d987d0b8113a4bd4cded804fc5109"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Utd4fIMNOTenh+qRB9RlrNrUMLHOqqoDsb/QoqnsJsnW8wl8Osk+KuK+Ta95lrFIY3nGmosXkLMZn226THCqAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:11:42.104113Z","bundle_sha256":"f72195a172003409fed695483c463c1d0b3a28b08a08c790057f36a3f17d0b54"}}