{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5INUJ56DNMOGEJ72AJQVF2XZWP","short_pith_number":"pith:5INUJ56D","canonical_record":{"source":{"id":"1212.5023","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-12-20T13:10:29Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.OA"],"title_canon_sha256":"57c09fb564bdeaa11b8184534cceb5b9e7f8c37280902adae7a1a0c73d76d10d","abstract_canon_sha256":"2bb7388411b5e62fc744d19d0aeb9a8e142ce2cdf934acf830ff21c65139d92c"},"schema_version":"1.0"},"canonical_sha256":"ea1b44f7c36b1c6227fa026152eaf9b3e7acfcf95524d64bf57e5ec806886e68","source":{"kind":"arxiv","id":"1212.5023","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5023","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5023v2","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5023","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"5INUJ56DNMOG","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5INUJ56DNMOGEJ72","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5INUJ56D","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5INUJ56DNMOGEJ72AJQVF2XZWP","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5023","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-12-20T13:10:29Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.OA"],"title_canon_sha256":"57c09fb564bdeaa11b8184534cceb5b9e7f8c37280902adae7a1a0c73d76d10d","abstract_canon_sha256":"2bb7388411b5e62fc744d19d0aeb9a8e142ce2cdf934acf830ff21c65139d92c"},"schema_version":"1.0"},"canonical_sha256":"ea1b44f7c36b1c6227fa026152eaf9b3e7acfcf95524d64bf57e5ec806886e68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:22.739903Z","signature_b64":"1zcVmMILlUKVmvgD4/y71pRJDeP2qKsO5hB+p3atiLMpp1Dn0jGAnSW3+6QC/ijBg0BiPAa7NaXNdM8pYFA/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea1b44f7c36b1c6227fa026152eaf9b3e7acfcf95524d64bf57e5ec806886e68","last_reissued_at":"2026-05-18T03:26:22.739224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:22.739224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5023","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3BEi2HvcshT6lGgAB2QGbVLwdVG2vHSVeFiTw8Bb8bwYJZnIcz8cL3QSDfjKuOJXPOZFnShx0UqBAZVvIh5ZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:36:13.754389Z"},"content_sha256":"d490248e63f171fd163553303c88b4767c3b30b42b22489ca85ad6973cfd83e7","schema_version":"1.0","event_id":"sha256:d490248e63f171fd163553303c88b4767c3b30b42b22489ca85ad6973cfd83e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5INUJ56DNMOGEJ72AJQVF2XZWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditional mutual information and self-commutator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Lin Zhang","submitted_at":"2012-12-20T13:10:29Z","abstract_excerpt":"A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach towards the approximate version of SSA. That is, it is conjectured that small conditional mutual information implies small perturbation of quantum Markov chain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5023","kind":"arxiv","version":2},"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":"2026-05-18T03:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QuTe+mQ74j6VTOBWis0fbJAZ6qe52l40LCw1VdnrIm2jxNhv1vJM2v9P6z+VBbXsAcuYkmuOdiHtuDDQfzx5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:36:13.754742Z"},"content_sha256":"b3f50aae0252fcb0e5b1ea8c833b6055bc581b1226bfa3ae28f6ec5aa9a00934","schema_version":"1.0","event_id":"sha256:b3f50aae0252fcb0e5b1ea8c833b6055bc581b1226bfa3ae28f6ec5aa9a00934"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5INUJ56DNMOGEJ72AJQVF2XZWP/bundle.json","state_url":"https://pith.science/pith/5INUJ56DNMOGEJ72AJQVF2XZWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5INUJ56DNMOGEJ72AJQVF2XZWP/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":"2026-05-27T00:36:13Z","links":{"resolver":"https://pith.science/pith/5INUJ56DNMOGEJ72AJQVF2XZWP","bundle":"https://pith.science/pith/5INUJ56DNMOGEJ72AJQVF2XZWP/bundle.json","state":"https://pith.science/pith/5INUJ56DNMOGEJ72AJQVF2XZWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5INUJ56DNMOGEJ72AJQVF2XZWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5INUJ56DNMOGEJ72AJQVF2XZWP","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":"2bb7388411b5e62fc744d19d0aeb9a8e142ce2cdf934acf830ff21c65139d92c","cross_cats_sorted":["math-ph","math.FA","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-12-20T13:10:29Z","title_canon_sha256":"57c09fb564bdeaa11b8184534cceb5b9e7f8c37280902adae7a1a0c73d76d10d"},"schema_version":"1.0","source":{"id":"1212.5023","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5023","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5023v2","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5023","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"5INUJ56DNMOG","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5INUJ56DNMOGEJ72","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5INUJ56D","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:b3f50aae0252fcb0e5b1ea8c833b6055bc581b1226bfa3ae28f6ec5aa9a00934","target":"graph","created_at":"2026-05-18T03:26:22Z","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":"A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach towards the approximate version of SSA. That is, it is conjectured that small conditional mutual information implies small perturbation of quantum Markov chain.","authors_text":"Lin Zhang","cross_cats":["math-ph","math.FA","math.MP","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-12-20T13:10:29Z","title":"Conditional mutual information and self-commutator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5023","kind":"arxiv","version":2},"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:d490248e63f171fd163553303c88b4767c3b30b42b22489ca85ad6973cfd83e7","target":"record","created_at":"2026-05-18T03:26:22Z","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":"2bb7388411b5e62fc744d19d0aeb9a8e142ce2cdf934acf830ff21c65139d92c","cross_cats_sorted":["math-ph","math.FA","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-12-20T13:10:29Z","title_canon_sha256":"57c09fb564bdeaa11b8184534cceb5b9e7f8c37280902adae7a1a0c73d76d10d"},"schema_version":"1.0","source":{"id":"1212.5023","kind":"arxiv","version":2}},"canonical_sha256":"ea1b44f7c36b1c6227fa026152eaf9b3e7acfcf95524d64bf57e5ec806886e68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea1b44f7c36b1c6227fa026152eaf9b3e7acfcf95524d64bf57e5ec806886e68","first_computed_at":"2026-05-18T03:26:22.739224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:22.739224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1zcVmMILlUKVmvgD4/y71pRJDeP2qKsO5hB+p3atiLMpp1Dn0jGAnSW3+6QC/ijBg0BiPAa7NaXNdM8pYFA/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:22.739903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5023","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d490248e63f171fd163553303c88b4767c3b30b42b22489ca85ad6973cfd83e7","sha256:b3f50aae0252fcb0e5b1ea8c833b6055bc581b1226bfa3ae28f6ec5aa9a00934"],"state_sha256":"62f41c29709cc72719e00b408591d7871f0e39ba362d6aede8aac85b716b5aad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eoOSMg/tTs5Ot2rPQc1akw8v+7YvR+8BK280IxhNle5KHtz7f9clz01rtMAr78JNS31NDo5zt06IAvjdHjTYAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:36:13.757887Z","bundle_sha256":"a164212cb7d2dc16daea6fe39f1725e557cdb788bc6f55c5cbb832be9a6d7701"}}