{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WZZ4OIEQKCJ5VQ562W5P247SGH","short_pith_number":"pith:WZZ4OIEQ","canonical_record":{"source":{"id":"1211.0812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T10:20:10Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"1762bbad1eb501ead7405d7f46457b418ba40131e516172d28b6067c703aee5e","abstract_canon_sha256":"a9c38071a2d96762c20c9fac2e1814d8b4969aeedb09293af6f68b307a3cee89"},"schema_version":"1.0"},"canonical_sha256":"b673c720905093dac3bed5bafd73f231fa0b0ffb22d4f3e277c1511a0e2f6c47","source":{"kind":"arxiv","id":"1211.0812","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0812","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0812v1","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0812","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"WZZ4OIEQKCJ5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WZZ4OIEQKCJ5VQ56","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WZZ4OIEQ","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WZZ4OIEQKCJ5VQ562W5P247SGH","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T10:20:10Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"1762bbad1eb501ead7405d7f46457b418ba40131e516172d28b6067c703aee5e","abstract_canon_sha256":"a9c38071a2d96762c20c9fac2e1814d8b4969aeedb09293af6f68b307a3cee89"},"schema_version":"1.0"},"canonical_sha256":"b673c720905093dac3bed5bafd73f231fa0b0ffb22d4f3e277c1511a0e2f6c47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:25.439905Z","signature_b64":"v3aulMwAYTLaQtMdOudefUJ9JCMNd15p0P/uqEE8/uG9X+YNlRezaE8yiExNj2nD1LRvAIBdSYOt1W57LmDTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b673c720905093dac3bed5bafd73f231fa0b0ffb22d4f3e277c1511a0e2f6c47","last_reissued_at":"2026-05-18T03:30:25.439113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:25.439113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0812","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":"2026-05-18T03:30:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o39nPfWXGd1vx+wLsFwFSc2f9jhYdmEwHpShSLBOVTWkN/w40UImHfcFQtyavq0fQdYqOSAj4ie49WG+rme3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:31:53.295636Z"},"content_sha256":"213f65166830a9e03d0cf507cb85c9c5549fcbd5abc3a7215dc9109e171132e1","schema_version":"1.0","event_id":"sha256:213f65166830a9e03d0cf507cb85c9c5549fcbd5abc3a7215dc9109e171132e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WZZ4OIEQKCJ5VQ562W5P247SGH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Once More on Positive Commutators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Roman Drnov\\v{s}ek","submitted_at":"2012-11-05T10:20:10Z","abstract_excerpt":"Let A and B be bounded operators on a Banach lattice E such that the commutator C=AB-BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ideals of E. This theorem answers an open question posed in a paper by Bra\\v{c}i\\v{c}, Drnov\\v{s}ek, Farforovskaya, Rabkin and Zem\\'{a}nek."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0812","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":"2026-05-18T03:30:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqVN5wGUzKo4VHVtFZPxEWGi/czftikPcqWuViIS2DYXGdnv+NYQKyUr6LcGZ8VogXg6/lZ7gDBazxY8W6xZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:31:53.295978Z"},"content_sha256":"2181e989d41f9974ce3b792f445adb712877d8680b4d393ad5986bea6aaa4ef9","schema_version":"1.0","event_id":"sha256:2181e989d41f9974ce3b792f445adb712877d8680b4d393ad5986bea6aaa4ef9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WZZ4OIEQKCJ5VQ562W5P247SGH/bundle.json","state_url":"https://pith.science/pith/WZZ4OIEQKCJ5VQ562W5P247SGH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WZZ4OIEQKCJ5VQ562W5P247SGH/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":"2026-06-04T10:31:53Z","links":{"resolver":"https://pith.science/pith/WZZ4OIEQKCJ5VQ562W5P247SGH","bundle":"https://pith.science/pith/WZZ4OIEQKCJ5VQ562W5P247SGH/bundle.json","state":"https://pith.science/pith/WZZ4OIEQKCJ5VQ562W5P247SGH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WZZ4OIEQKCJ5VQ562W5P247SGH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WZZ4OIEQKCJ5VQ562W5P247SGH","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":"a9c38071a2d96762c20c9fac2e1814d8b4969aeedb09293af6f68b307a3cee89","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T10:20:10Z","title_canon_sha256":"1762bbad1eb501ead7405d7f46457b418ba40131e516172d28b6067c703aee5e"},"schema_version":"1.0","source":{"id":"1211.0812","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0812","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0812v1","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0812","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"WZZ4OIEQKCJ5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WZZ4OIEQKCJ5VQ56","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WZZ4OIEQ","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:2181e989d41f9974ce3b792f445adb712877d8680b4d393ad5986bea6aaa4ef9","target":"graph","created_at":"2026-05-18T03:30:25Z","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":"Let A and B be bounded operators on a Banach lattice E such that the commutator C=AB-BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ideals of E. This theorem answers an open question posed in a paper by Bra\\v{c}i\\v{c}, Drnov\\v{s}ek, Farforovskaya, Rabkin and Zem\\'{a}nek.","authors_text":"Roman Drnov\\v{s}ek","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T10:20:10Z","title":"Once More on Positive Commutators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0812","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":"sha256:213f65166830a9e03d0cf507cb85c9c5549fcbd5abc3a7215dc9109e171132e1","target":"record","created_at":"2026-05-18T03:30:25Z","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":"a9c38071a2d96762c20c9fac2e1814d8b4969aeedb09293af6f68b307a3cee89","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-05T10:20:10Z","title_canon_sha256":"1762bbad1eb501ead7405d7f46457b418ba40131e516172d28b6067c703aee5e"},"schema_version":"1.0","source":{"id":"1211.0812","kind":"arxiv","version":1}},"canonical_sha256":"b673c720905093dac3bed5bafd73f231fa0b0ffb22d4f3e277c1511a0e2f6c47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b673c720905093dac3bed5bafd73f231fa0b0ffb22d4f3e277c1511a0e2f6c47","first_computed_at":"2026-05-18T03:30:25.439113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:25.439113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v3aulMwAYTLaQtMdOudefUJ9JCMNd15p0P/uqEE8/uG9X+YNlRezaE8yiExNj2nD1LRvAIBdSYOt1W57LmDTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:25.439905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0812","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:213f65166830a9e03d0cf507cb85c9c5549fcbd5abc3a7215dc9109e171132e1","sha256:2181e989d41f9974ce3b792f445adb712877d8680b4d393ad5986bea6aaa4ef9"],"state_sha256":"42c2732d9e55a45a1f34ea8e904777d98c7facabbf41a9a3bd052d741fbd1959"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PSdX63apiAN3B4DJyCcBwHH4ylDcJ+vQSWMIFa+5sQ310i9926bfgHyc+Ia+kCOXlrMPHwq7m/0gzLB7RlE/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:31:53.297884Z","bundle_sha256":"535b5ffe14342bec3be1d5cb5a5e4b722ea66c4e69a3763b707d73e7d5834e19"}}