{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6GFLF3DLTQ6GTZ76EF4PDOIDCS","short_pith_number":"pith:6GFLF3DL","canonical_record":{"source":{"id":"1012.1111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-06T09:59:35Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"e94493736f2a1b2d5e87f95b93eba6e3dfa0d6f00e3ecdb6f93c2abea86747fa","abstract_canon_sha256":"f370ac3c48d8c9fd713667ea9d12254cdc4a82a186d32f6e1911b7d13198eaf0"},"schema_version":"1.0"},"canonical_sha256":"f18ab2ec6b9c3c69e7fe2178f1b90314ae58135233df04ee47f2a32380ac88ab","source":{"kind":"arxiv","id":"1012.1111","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1111","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1111v1","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1111","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"pith_short_12","alias_value":"6GFLF3DLTQ6G","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6GFLF3DLTQ6GTZ76","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6GFLF3DL","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6GFLF3DLTQ6GTZ76EF4PDOIDCS","target":"record","payload":{"canonical_record":{"source":{"id":"1012.1111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-06T09:59:35Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"e94493736f2a1b2d5e87f95b93eba6e3dfa0d6f00e3ecdb6f93c2abea86747fa","abstract_canon_sha256":"f370ac3c48d8c9fd713667ea9d12254cdc4a82a186d32f6e1911b7d13198eaf0"},"schema_version":"1.0"},"canonical_sha256":"f18ab2ec6b9c3c69e7fe2178f1b90314ae58135233df04ee47f2a32380ac88ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:00.746012Z","signature_b64":"DNrnIDCOZzZyhM6mPfrGVMRKbcseNRKBNbbKcYhspTZ9cl1o2Em94iqhdAuQ1pe0mifyN1kEIqv/Ahog5KjXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f18ab2ec6b9c3c69e7fe2178f1b90314ae58135233df04ee47f2a32380ac88ab","last_reissued_at":"2026-05-18T02:20:00.745441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:00.745441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.1111","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":"2026-05-18T02:20:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"846mMHXn2n0kFnI8xmIX23dITn2Of0A09ilMy2KjEbrQCLM6KBbsdIkc3LpNNSvEadEe8Ypyc/eaZPbAyikODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:11:35.152618Z"},"content_sha256":"5b25d4c922122d482a4f196ccae7c5cdda27da48e9198dc364776723344b8965","schema_version":"1.0","event_id":"sha256:5b25d4c922122d482a4f196ccae7c5cdda27da48e9198dc364776723344b8965"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6GFLF3DLTQ6GTZ76EF4PDOIDCS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the BCH formula of Rezek and Kosloff","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Jan Naudts, Winny O'Kelly de Galway","submitted_at":"2010-12-06T09:59:35Z","abstract_excerpt":"The BCH formula of Rezek and Kosloff is a convenient tool to handle a family of density matrices, which occurs in the study of quantum heat engines. We prove the formula using a known argument from Lie theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1111","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":"2026-05-18T02:20:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"liNlbgwqpaQB9ZHfQ/3PKBPQ2bTXrxx5BwdBaYf/mkxOGwkA5TeCojBG/ZaG6lKAErPQBESB+sXwZLglPET6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:11:35.152958Z"},"content_sha256":"b81cd0bfc4f981960df991be3918041e0ff2f11110055da9d84cffecaea02ca3","schema_version":"1.0","event_id":"sha256:b81cd0bfc4f981960df991be3918041e0ff2f11110055da9d84cffecaea02ca3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GFLF3DLTQ6GTZ76EF4PDOIDCS/bundle.json","state_url":"https://pith.science/pith/6GFLF3DLTQ6GTZ76EF4PDOIDCS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GFLF3DLTQ6GTZ76EF4PDOIDCS/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":"2026-06-08T23:11:35Z","links":{"resolver":"https://pith.science/pith/6GFLF3DLTQ6GTZ76EF4PDOIDCS","bundle":"https://pith.science/pith/6GFLF3DLTQ6GTZ76EF4PDOIDCS/bundle.json","state":"https://pith.science/pith/6GFLF3DLTQ6GTZ76EF4PDOIDCS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GFLF3DLTQ6GTZ76EF4PDOIDCS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6GFLF3DLTQ6GTZ76EF4PDOIDCS","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":"f370ac3c48d8c9fd713667ea9d12254cdc4a82a186d32f6e1911b7d13198eaf0","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-06T09:59:35Z","title_canon_sha256":"e94493736f2a1b2d5e87f95b93eba6e3dfa0d6f00e3ecdb6f93c2abea86747fa"},"schema_version":"1.0","source":{"id":"1012.1111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1111","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1111v1","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1111","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"pith_short_12","alias_value":"6GFLF3DLTQ6G","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6GFLF3DLTQ6GTZ76","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6GFLF3DL","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:b81cd0bfc4f981960df991be3918041e0ff2f11110055da9d84cffecaea02ca3","target":"graph","created_at":"2026-05-18T02:20:00Z","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":"The BCH formula of Rezek and Kosloff is a convenient tool to handle a family of density matrices, which occurs in the study of quantum heat engines. We prove the formula using a known argument from Lie theory.","authors_text":"Jan Naudts, Winny O'Kelly de Galway","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-06T09:59:35Z","title":"On the BCH formula of Rezek and Kosloff"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1111","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":"sha256:5b25d4c922122d482a4f196ccae7c5cdda27da48e9198dc364776723344b8965","target":"record","created_at":"2026-05-18T02:20:00Z","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":"f370ac3c48d8c9fd713667ea9d12254cdc4a82a186d32f6e1911b7d13198eaf0","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-06T09:59:35Z","title_canon_sha256":"e94493736f2a1b2d5e87f95b93eba6e3dfa0d6f00e3ecdb6f93c2abea86747fa"},"schema_version":"1.0","source":{"id":"1012.1111","kind":"arxiv","version":1}},"canonical_sha256":"f18ab2ec6b9c3c69e7fe2178f1b90314ae58135233df04ee47f2a32380ac88ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f18ab2ec6b9c3c69e7fe2178f1b90314ae58135233df04ee47f2a32380ac88ab","first_computed_at":"2026-05-18T02:20:00.745441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:00.745441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DNrnIDCOZzZyhM6mPfrGVMRKbcseNRKBNbbKcYhspTZ9cl1o2Em94iqhdAuQ1pe0mifyN1kEIqv/Ahog5KjXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:00.746012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b25d4c922122d482a4f196ccae7c5cdda27da48e9198dc364776723344b8965","sha256:b81cd0bfc4f981960df991be3918041e0ff2f11110055da9d84cffecaea02ca3"],"state_sha256":"dac91cf8a11cbcf8464acff73e2dc1ee457db8678612b6fd287d1432b2974795"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8srRVKNB/EOFpD/baNqXU2gVXxfYSD0+5iUD9v0RvqE6Nby7Gr1maqowxeG+r/CCmhB5b2JDoWuf40rZMoHfCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:11:35.154803Z","bundle_sha256":"d4868e5c377618ad373acf079c9dc81fff178fd5873a8ddc37c36fcee392c30e"}}