{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:JYI7V6BTXKWOJCTVTBJTAOJID3","short_pith_number":"pith:JYI7V6BT","canonical_record":{"source":{"id":"quant-ph/0104058","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2001-04-11T12:59:42Z","cross_cats_sorted":[],"title_canon_sha256":"b213d10eb763e82f7c2f5c4a5a7b6b03fb6cd13f81da5e074680006427708a1e","abstract_canon_sha256":"26ac32aaf0bf9c13592bde5ec535b079c08f9a0a29db811ca0c53f6d7964f168"},"schema_version":"1.0"},"canonical_sha256":"4e11faf833baace48a7598533039281ee89308c28e3353ac7928d12aaa6c2078","source":{"kind":"arxiv","id":"quant-ph/0104058","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0104058","created_at":"2026-05-18T03:24:20Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0104058v1","created_at":"2026-05-18T03:24:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0104058","created_at":"2026-05-18T03:24:20Z"},{"alias_kind":"pith_short_12","alias_value":"JYI7V6BTXKWO","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"JYI7V6BTXKWOJCTV","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"JYI7V6BT","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:JYI7V6BTXKWOJCTVTBJTAOJID3","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0104058","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2001-04-11T12:59:42Z","cross_cats_sorted":[],"title_canon_sha256":"b213d10eb763e82f7c2f5c4a5a7b6b03fb6cd13f81da5e074680006427708a1e","abstract_canon_sha256":"26ac32aaf0bf9c13592bde5ec535b079c08f9a0a29db811ca0c53f6d7964f168"},"schema_version":"1.0"},"canonical_sha256":"4e11faf833baace48a7598533039281ee89308c28e3353ac7928d12aaa6c2078","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:20.545174Z","signature_b64":"8cAk78eYGMa1Skdie3hTx6HpF7lchUt++ZmJGnrXrHdWPJQqVMgQALK2+REEcVyOtUwJxfhOT/H+d3luWJvlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e11faf833baace48a7598533039281ee89308c28e3353ac7928d12aaa6c2078","last_reissued_at":"2026-05-18T03:24:20.544519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:20.544519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0104058","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":"2026-05-18T03:24:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMUCi7Gv4FYpum8d8YL0sUjExNctmUiYIiczoGL79zu58borLaARBcEZrs6TvU//TnpNGUvvRE/TMBV3DQcHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:23:35.282802Z"},"content_sha256":"2be665ae1d9b4f80e7869d6a118aba346dc0164da3e27f90143e525171785759","schema_version":"1.0","event_id":"sha256:2be665ae1d9b4f80e7869d6a118aba346dc0164da3e27f90143e525171785759"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:JYI7V6BTXKWOJCTVTBJTAOJID3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The trumping relation and the structure of the bipartite entangled states","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Matthew Klimesh, Sumit Daftuar","submitted_at":"2001-04-11T12:59:42Z","abstract_excerpt":"The majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some new re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0104058","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":"2026-05-18T03:24:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LC4/FGJ9ZAd3BkShJEhPzsyNARk5J4hMdSsmd++J0J/DDESLrlE8yrLHCwG/y668nc2D7wyifioWf/jICiq/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:23:35.283526Z"},"content_sha256":"985f2505989fd59739e597be249edfc2f6f203ab03b47e08ba279dc6e6230af0","schema_version":"1.0","event_id":"sha256:985f2505989fd59739e597be249edfc2f6f203ab03b47e08ba279dc6e6230af0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JYI7V6BTXKWOJCTVTBJTAOJID3/bundle.json","state_url":"https://pith.science/pith/JYI7V6BTXKWOJCTVTBJTAOJID3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JYI7V6BTXKWOJCTVTBJTAOJID3/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":"2026-06-11T23:23:35Z","links":{"resolver":"https://pith.science/pith/JYI7V6BTXKWOJCTVTBJTAOJID3","bundle":"https://pith.science/pith/JYI7V6BTXKWOJCTVTBJTAOJID3/bundle.json","state":"https://pith.science/pith/JYI7V6BTXKWOJCTVTBJTAOJID3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JYI7V6BTXKWOJCTVTBJTAOJID3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:JYI7V6BTXKWOJCTVTBJTAOJID3","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":"26ac32aaf0bf9c13592bde5ec535b079c08f9a0a29db811ca0c53f6d7964f168","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2001-04-11T12:59:42Z","title_canon_sha256":"b213d10eb763e82f7c2f5c4a5a7b6b03fb6cd13f81da5e074680006427708a1e"},"schema_version":"1.0","source":{"id":"quant-ph/0104058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0104058","created_at":"2026-05-18T03:24:20Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0104058v1","created_at":"2026-05-18T03:24:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0104058","created_at":"2026-05-18T03:24:20Z"},{"alias_kind":"pith_short_12","alias_value":"JYI7V6BTXKWO","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"JYI7V6BTXKWOJCTV","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"JYI7V6BT","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:985f2505989fd59739e597be249edfc2f6f203ab03b47e08ba279dc6e6230af0","target":"graph","created_at":"2026-05-18T03:24:20Z","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 majorization relation has been shown to be useful in classifying which transformations of jointly held quantum states are possible using local operations and classical communication. In some cases, a direct transformation between two states is not possible, but it becomes possible in the presence of another state (known as a catalyst); this situation is described mathematically by the trumping relation, an extension of majorization. The structure of the trumping relation is not nearly as well understood as that of majorization. We give an introduction to this subject and derive some new re","authors_text":"Matthew Klimesh, Sumit Daftuar","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2001-04-11T12:59:42Z","title":"The trumping relation and the structure of the bipartite entangled states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0104058","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":"sha256:2be665ae1d9b4f80e7869d6a118aba346dc0164da3e27f90143e525171785759","target":"record","created_at":"2026-05-18T03:24:20Z","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":"26ac32aaf0bf9c13592bde5ec535b079c08f9a0a29db811ca0c53f6d7964f168","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2001-04-11T12:59:42Z","title_canon_sha256":"b213d10eb763e82f7c2f5c4a5a7b6b03fb6cd13f81da5e074680006427708a1e"},"schema_version":"1.0","source":{"id":"quant-ph/0104058","kind":"arxiv","version":1}},"canonical_sha256":"4e11faf833baace48a7598533039281ee89308c28e3353ac7928d12aaa6c2078","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e11faf833baace48a7598533039281ee89308c28e3353ac7928d12aaa6c2078","first_computed_at":"2026-05-18T03:24:20.544519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:20.544519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8cAk78eYGMa1Skdie3hTx6HpF7lchUt++ZmJGnrXrHdWPJQqVMgQALK2+REEcVyOtUwJxfhOT/H+d3luWJvlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:20.545174Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0104058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2be665ae1d9b4f80e7869d6a118aba346dc0164da3e27f90143e525171785759","sha256:985f2505989fd59739e597be249edfc2f6f203ab03b47e08ba279dc6e6230af0"],"state_sha256":"4986290e3a5a1e0254bd6b9c681b1b46b1c69ce26c4b18d7968053bc010c3449"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4HOlDDAS2cE3NlZBF80xo5QJBewqjQTU8Zg0mC0VA9fO8aaglQrpf1cfjwyEHa9ub/95xzktzz41+Fmf8prgAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:23:35.287987Z","bundle_sha256":"f5648122c82e8ca89b621fea75368fdf58a69a7cb285e0f532f88748b8610ed3"}}