{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:X47XE3UO5SOLLDMNB75ZH2NAV7","short_pith_number":"pith:X47XE3UO","canonical_record":{"source":{"id":"quant-ph/0409113","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-09-17T12:56:15Z","cross_cats_sorted":[],"title_canon_sha256":"3ea10517748759de44e4832c56a13e07724b3e74b223f2735285a39d762663b7","abstract_canon_sha256":"ff54572ab9fa315a667645b46410246fbe76ab94c79d8cb8dbde969e6daa6ce6"},"schema_version":"1.0"},"canonical_sha256":"bf3f726e8eec9cb58d8d0ffb93e9a0afc559adcdfa3807631866bf1ee436baac","source":{"kind":"arxiv","id":"quant-ph/0409113","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0409113","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0409113v1","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0409113","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"pith_short_12","alias_value":"X47XE3UO5SOL","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"pith_short_16","alias_value":"X47XE3UO5SOLLDMN","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"pith_short_8","alias_value":"X47XE3UO","created_at":"2026-07-04T14:46:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:X47XE3UO5SOLLDMNB75ZH2NAV7","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0409113","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-09-17T12:56:15Z","cross_cats_sorted":[],"title_canon_sha256":"3ea10517748759de44e4832c56a13e07724b3e74b223f2735285a39d762663b7","abstract_canon_sha256":"ff54572ab9fa315a667645b46410246fbe76ab94c79d8cb8dbde969e6daa6ce6"},"schema_version":"1.0"},"canonical_sha256":"bf3f726e8eec9cb58d8d0ffb93e9a0afc559adcdfa3807631866bf1ee436baac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:46:41.065839Z","signature_b64":"OOWaM+EMaGzURETUN+mZtHlIBSDU1Icg9ryagXPb8Q4O933yi8t8eo+1IIFbFKmBbMeTVwbcw1NTv6ohip44Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf3f726e8eec9cb58d8d0ffb93e9a0afc559adcdfa3807631866bf1ee436baac","last_reissued_at":"2026-07-04T14:46:41.065384Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:46:41.065384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0409113","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":"2026-07-04T14:46:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kjjrRMOmKrHJ8y8drxU1YF6K3BmBgECOVXogD5M5k+tlWGRjyKP7bsiYJdpuQAxJMSGlbOhJFnVoNEziN4dEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:27:30.244516Z"},"content_sha256":"822dde2f6b6f6d580490b2bc423de8eff1fd210312850c106fa4b0815b200fc5","schema_version":"1.0","event_id":"sha256:822dde2f6b6f6d580490b2bc423de8eff1fd210312850c106fa4b0815b200fc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:X47XE3UO5SOLLDMNB75ZH2NAV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum marginal problem and representations of the symmetric group","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander Klyachko","submitted_at":"2004-09-17T12:56:15Z","abstract_excerpt":"We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive tables of marginal inequalities, including arrays up to 4 qubits. In the second part of the paper we pursue another approach based on reduction of the problem to representation theory of the symmetric group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0409113","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0409113/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:46:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WAGiWst1mH5DNhSyAD5zzLKj9GA7YQfBvfR113NJiSle1GD+P75MgfKBc/KrcE8TFjfKu1RPQN6I5WbB2yyaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:27:30.245009Z"},"content_sha256":"8a784ee6bd8d83b4323b6a9997aee402d7467419ad97ce946e3c611940a06638","schema_version":"1.0","event_id":"sha256:8a784ee6bd8d83b4323b6a9997aee402d7467419ad97ce946e3c611940a06638"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X47XE3UO5SOLLDMNB75ZH2NAV7/bundle.json","state_url":"https://pith.science/pith/X47XE3UO5SOLLDMNB75ZH2NAV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X47XE3UO5SOLLDMNB75ZH2NAV7/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":"2026-08-06T11:27:30Z","links":{"resolver":"https://pith.science/pith/X47XE3UO5SOLLDMNB75ZH2NAV7","bundle":"https://pith.science/pith/X47XE3UO5SOLLDMNB75ZH2NAV7/bundle.json","state":"https://pith.science/pith/X47XE3UO5SOLLDMNB75ZH2NAV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X47XE3UO5SOLLDMNB75ZH2NAV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:X47XE3UO5SOLLDMNB75ZH2NAV7","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":"ff54572ab9fa315a667645b46410246fbe76ab94c79d8cb8dbde969e6daa6ce6","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-09-17T12:56:15Z","title_canon_sha256":"3ea10517748759de44e4832c56a13e07724b3e74b223f2735285a39d762663b7"},"schema_version":"1.0","source":{"id":"quant-ph/0409113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0409113","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0409113v1","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0409113","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"pith_short_12","alias_value":"X47XE3UO5SOL","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"pith_short_16","alias_value":"X47XE3UO5SOLLDMN","created_at":"2026-07-04T14:46:41Z"},{"alias_kind":"pith_short_8","alias_value":"X47XE3UO","created_at":"2026-07-04T14:46:41Z"}],"graph_snapshots":[{"event_id":"sha256:8a784ee6bd8d83b4323b6a9997aee402d7467419ad97ce946e3c611940a06638","target":"graph","created_at":"2026-07-04T14:46:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0409113/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive tables of marginal inequalities, including arrays up to 4 qubits. In the second part of the paper we pursue another approach based on reduction of the problem to representation theory of the symmetric group.","authors_text":"Alexander Klyachko","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-09-17T12:56:15Z","title":"Quantum marginal problem and representations of the symmetric group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0409113","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":"sha256:822dde2f6b6f6d580490b2bc423de8eff1fd210312850c106fa4b0815b200fc5","target":"record","created_at":"2026-07-04T14:46:41Z","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":"ff54572ab9fa315a667645b46410246fbe76ab94c79d8cb8dbde969e6daa6ce6","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-09-17T12:56:15Z","title_canon_sha256":"3ea10517748759de44e4832c56a13e07724b3e74b223f2735285a39d762663b7"},"schema_version":"1.0","source":{"id":"quant-ph/0409113","kind":"arxiv","version":1}},"canonical_sha256":"bf3f726e8eec9cb58d8d0ffb93e9a0afc559adcdfa3807631866bf1ee436baac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf3f726e8eec9cb58d8d0ffb93e9a0afc559adcdfa3807631866bf1ee436baac","first_computed_at":"2026-07-04T14:46:41.065384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:46:41.065384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OOWaM+EMaGzURETUN+mZtHlIBSDU1Icg9ryagXPb8Q4O933yi8t8eo+1IIFbFKmBbMeTVwbcw1NTv6ohip44Aw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:46:41.065839Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0409113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:822dde2f6b6f6d580490b2bc423de8eff1fd210312850c106fa4b0815b200fc5","sha256:8a784ee6bd8d83b4323b6a9997aee402d7467419ad97ce946e3c611940a06638"],"state_sha256":"5b05130057150fae6837e181e0caf8f28d87879d1b7dcef254e7e1ea90b5afd0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q0v9+SKyy3z7v06hs046Ma6r9lQ9Nga8OphUEC75S+X6ThPZQOZQSlvmmEm/g7PtT1t83lMpS97wVaxRcS5PBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T11:27:30.249933Z","bundle_sha256":"ce6a9bbbfde654c52bde544322844a8d4e5e4e6a80faef1a15e3903d99138eeb"}}