{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OVVKA3CMGS4CQW2OJBYJ5T5EAP","short_pith_number":"pith:OVVKA3CM","canonical_record":{"source":{"id":"1607.05735","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-19T20:01:01Z","cross_cats_sorted":["cond-mat.stat-mech","math.ST","stat.TH"],"title_canon_sha256":"51d5cb521c932f3a21cc51d6299260aa741be7a460a227edbeb88b364972dd3e","abstract_canon_sha256":"54e88c6b1f50db2cdb600ae8382fb3854b534ed39c8f5b364e299d75050e670b"},"schema_version":"1.0"},"canonical_sha256":"756aa06c4c34b8285b4e48709ecfa403f4f71a4ff64876c6f8c24a75440c5dc7","source":{"kind":"arxiv","id":"1607.05735","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05735","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05735v2","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05735","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"pith_short_12","alias_value":"OVVKA3CMGS4C","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OVVKA3CMGS4CQW2O","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OVVKA3CM","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OVVKA3CMGS4CQW2OJBYJ5T5EAP","target":"record","payload":{"canonical_record":{"source":{"id":"1607.05735","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-19T20:01:01Z","cross_cats_sorted":["cond-mat.stat-mech","math.ST","stat.TH"],"title_canon_sha256":"51d5cb521c932f3a21cc51d6299260aa741be7a460a227edbeb88b364972dd3e","abstract_canon_sha256":"54e88c6b1f50db2cdb600ae8382fb3854b534ed39c8f5b364e299d75050e670b"},"schema_version":"1.0"},"canonical_sha256":"756aa06c4c34b8285b4e48709ecfa403f4f71a4ff64876c6f8c24a75440c5dc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:07.894361Z","signature_b64":"5O0UwG6xo9DIKvMFK340v5Zi6YBTxsaOJ6SXlXMCUGZLb0LxJLVRwRZ8S9DwGr9fAGsiRd7xbXjNv2/lILGxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"756aa06c4c34b8285b4e48709ecfa403f4f71a4ff64876c6f8c24a75440c5dc7","last_reissued_at":"2026-05-18T00:53:07.893862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:07.893862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.05735","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":"2026-05-18T00:53:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3pVPqOaU8XlMAz0uKP77yU2uAODRhOvIn5eV2QjZKmAEov+RJtIyf3+odTgu+efeRM4fykDCFKNT34y82PFhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:42:25.752127Z"},"content_sha256":"1e2b17a006bc5fe86ed8b79087380385cc0f31ae95a72731684c619ee196da37","schema_version":"1.0","event_id":"sha256:1e2b17a006bc5fe86ed8b79087380385cc0f31ae95a72731684c619ee196da37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OVVKA3CMGS4CQW2OJBYJ5T5EAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Relative Lorenz Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.ST","stat.TH"],"primary_cat":"quant-ph","authors_text":"Francesco Buscemi, Gilad Gour","submitted_at":"2016-07-19T20:01:01Z","abstract_excerpt":"The theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogues. In doing so, we define the family of Hilbert $\\alpha$-divergences and show how it relates with other divergences used in quantum information theory. We then apply these tools to the problem of deciding"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05735","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":"2026-05-18T00:53:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pcS0MwIK2Vqagfqum90Q3LGkwgvCPI/Q3RKq0O0vLniHKO0LL1E5uYYRKMt+fXcxYbEIWfTaSZXSzMMcrEwaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:42:25.752505Z"},"content_sha256":"2be995a582b3b00008b72234cced62e5372b60a20c09276d7880b26ee4678ed1","schema_version":"1.0","event_id":"sha256:2be995a582b3b00008b72234cced62e5372b60a20c09276d7880b26ee4678ed1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVVKA3CMGS4CQW2OJBYJ5T5EAP/bundle.json","state_url":"https://pith.science/pith/OVVKA3CMGS4CQW2OJBYJ5T5EAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVVKA3CMGS4CQW2OJBYJ5T5EAP/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":"2026-05-28T01:42:25Z","links":{"resolver":"https://pith.science/pith/OVVKA3CMGS4CQW2OJBYJ5T5EAP","bundle":"https://pith.science/pith/OVVKA3CMGS4CQW2OJBYJ5T5EAP/bundle.json","state":"https://pith.science/pith/OVVKA3CMGS4CQW2OJBYJ5T5EAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVVKA3CMGS4CQW2OJBYJ5T5EAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OVVKA3CMGS4CQW2OJBYJ5T5EAP","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":"54e88c6b1f50db2cdb600ae8382fb3854b534ed39c8f5b364e299d75050e670b","cross_cats_sorted":["cond-mat.stat-mech","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-19T20:01:01Z","title_canon_sha256":"51d5cb521c932f3a21cc51d6299260aa741be7a460a227edbeb88b364972dd3e"},"schema_version":"1.0","source":{"id":"1607.05735","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05735","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05735v2","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05735","created_at":"2026-05-18T00:53:07Z"},{"alias_kind":"pith_short_12","alias_value":"OVVKA3CMGS4C","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OVVKA3CMGS4CQW2O","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OVVKA3CM","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:2be995a582b3b00008b72234cced62e5372b60a20c09276d7880b26ee4678ed1","target":"graph","created_at":"2026-05-18T00:53:07Z","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 theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogues. In doing so, we define the family of Hilbert $\\alpha$-divergences and show how it relates with other divergences used in quantum information theory. We then apply these tools to the problem of deciding","authors_text":"Francesco Buscemi, Gilad Gour","cross_cats":["cond-mat.stat-mech","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-19T20:01:01Z","title":"Quantum Relative Lorenz Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05735","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":"sha256:1e2b17a006bc5fe86ed8b79087380385cc0f31ae95a72731684c619ee196da37","target":"record","created_at":"2026-05-18T00:53:07Z","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":"54e88c6b1f50db2cdb600ae8382fb3854b534ed39c8f5b364e299d75050e670b","cross_cats_sorted":["cond-mat.stat-mech","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-19T20:01:01Z","title_canon_sha256":"51d5cb521c932f3a21cc51d6299260aa741be7a460a227edbeb88b364972dd3e"},"schema_version":"1.0","source":{"id":"1607.05735","kind":"arxiv","version":2}},"canonical_sha256":"756aa06c4c34b8285b4e48709ecfa403f4f71a4ff64876c6f8c24a75440c5dc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"756aa06c4c34b8285b4e48709ecfa403f4f71a4ff64876c6f8c24a75440c5dc7","first_computed_at":"2026-05-18T00:53:07.893862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:07.893862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5O0UwG6xo9DIKvMFK340v5Zi6YBTxsaOJ6SXlXMCUGZLb0LxJLVRwRZ8S9DwGr9fAGsiRd7xbXjNv2/lILGxDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:07.894361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05735","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e2b17a006bc5fe86ed8b79087380385cc0f31ae95a72731684c619ee196da37","sha256:2be995a582b3b00008b72234cced62e5372b60a20c09276d7880b26ee4678ed1"],"state_sha256":"74f4a7a34013b523e5347fceada968a1fb69dd691ecce27c81412bc068691e89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pz5s2l8y86Sz9IV4E5feoqIo3jWWC1sLKGypV/yKgh+UiIvoFTSJJexRT8YarCUmMJbZq18LD9GyODp2qr9nAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:42:25.754474Z","bundle_sha256":"7d31aeaca65c599967f8d11525d8e0f1927bff9680db36cf2760af8dab81111c"}}