{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YZORLPNTUUEG3JW6LPRIHIFJYI","short_pith_number":"pith:YZORLPNT","canonical_record":{"source":{"id":"1404.1085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-04-03T20:03:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bff42c3bfcde0a2e47110f0f66a3b3a5ef6e1353fd1fe946dab6cb634c03b47f","abstract_canon_sha256":"c16188c6315ba3ff16eee5435da517007f066fba94ebd492be1c3d2a26b42e67"},"schema_version":"1.0"},"canonical_sha256":"c65d15bdb3a5086da6de5be283a0a9c21655288f2975c89a86517fbad1bc3265","source":{"kind":"arxiv","id":"1404.1085","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1085","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1085v1","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1085","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"YZORLPNTUUEG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZORLPNTUUEG3JW6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZORLPNT","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YZORLPNTUUEG3JW6LPRIHIFJYI","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-04-03T20:03:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bff42c3bfcde0a2e47110f0f66a3b3a5ef6e1353fd1fe946dab6cb634c03b47f","abstract_canon_sha256":"c16188c6315ba3ff16eee5435da517007f066fba94ebd492be1c3d2a26b42e67"},"schema_version":"1.0"},"canonical_sha256":"c65d15bdb3a5086da6de5be283a0a9c21655288f2975c89a86517fbad1bc3265","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:54.241617Z","signature_b64":"mbWbUuBLdRU8ZF6uIRTAuNwPVIo3D1XIsyatI6sfLceBnFBkJgSEkT+7OWmTGwZTV7uXIlXFY4pzbt+aLTGtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c65d15bdb3a5086da6de5be283a0a9c21655288f2975c89a86517fbad1bc3265","last_reissued_at":"2026-05-18T02:54:54.241168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:54.241168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1085","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":"2026-05-18T02:54:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FcTVtBK2Og7IeYfDWWTRXtIT8OXjKyRJegqdLrJmiMOV+gtuzr1jwszGH2iIYoAKmEDTqNlvxwL5SnJGj25PDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:25:14.228865Z"},"content_sha256":"efc36c6d47f733af5c52a2dbaf7a8d41a279032654f35e2f6234b6d0abf18487","schema_version":"1.0","event_id":"sha256:efc36c6d47f733af5c52a2dbaf7a8d41a279032654f35e2f6234b6d0abf18487"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YZORLPNTUUEG3JW6LPRIHIFJYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Quantum Marginal Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Christian Schilling","submitted_at":"2014-04-03T20:03:50Z","abstract_excerpt":"The question of whether given density operators for subsystems of a multipartite quantum system are compatible to one common total density operator is known as the quantum marginal problem. We briefly review the solution of a subclass of such problems found just recently. In particular, this provides the solution of the $1$-body $N$-representability problem. Its solution, the so-called generalized Pauli constraints, restrict the set of mathematically possible fermionic occupation numbers significantly, and strengthens Pauli's exclusion principle. Moreover, we review the study of a concrete phy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1085","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":"2026-05-18T02:54:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"clz/QC9MZLaDDCWKL1uy5ADJQ2TiWKzbwpD0At4Z0XrgteChz0w9tPPhGs0/NM9ffhEnWhT8HWcaNTJb7bKKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:25:14.229522Z"},"content_sha256":"c8530d4cbbff6a5bdd7b7e453865168667121f9a3d735607f0ee92976f0dee98","schema_version":"1.0","event_id":"sha256:c8530d4cbbff6a5bdd7b7e453865168667121f9a3d735607f0ee92976f0dee98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZORLPNTUUEG3JW6LPRIHIFJYI/bundle.json","state_url":"https://pith.science/pith/YZORLPNTUUEG3JW6LPRIHIFJYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZORLPNTUUEG3JW6LPRIHIFJYI/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":"2026-05-25T16:25:14Z","links":{"resolver":"https://pith.science/pith/YZORLPNTUUEG3JW6LPRIHIFJYI","bundle":"https://pith.science/pith/YZORLPNTUUEG3JW6LPRIHIFJYI/bundle.json","state":"https://pith.science/pith/YZORLPNTUUEG3JW6LPRIHIFJYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZORLPNTUUEG3JW6LPRIHIFJYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YZORLPNTUUEG3JW6LPRIHIFJYI","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":"c16188c6315ba3ff16eee5435da517007f066fba94ebd492be1c3d2a26b42e67","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-04-03T20:03:50Z","title_canon_sha256":"bff42c3bfcde0a2e47110f0f66a3b3a5ef6e1353fd1fe946dab6cb634c03b47f"},"schema_version":"1.0","source":{"id":"1404.1085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1085","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1085v1","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1085","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"YZORLPNTUUEG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZORLPNTUUEG3JW6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZORLPNT","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:c8530d4cbbff6a5bdd7b7e453865168667121f9a3d735607f0ee92976f0dee98","target":"graph","created_at":"2026-05-18T02:54:54Z","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 question of whether given density operators for subsystems of a multipartite quantum system are compatible to one common total density operator is known as the quantum marginal problem. We briefly review the solution of a subclass of such problems found just recently. In particular, this provides the solution of the $1$-body $N$-representability problem. Its solution, the so-called generalized Pauli constraints, restrict the set of mathematically possible fermionic occupation numbers significantly, and strengthens Pauli's exclusion principle. Moreover, we review the study of a concrete phy","authors_text":"Christian Schilling","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-04-03T20:03:50Z","title":"The Quantum Marginal Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1085","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:efc36c6d47f733af5c52a2dbaf7a8d41a279032654f35e2f6234b6d0abf18487","target":"record","created_at":"2026-05-18T02:54:54Z","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":"c16188c6315ba3ff16eee5435da517007f066fba94ebd492be1c3d2a26b42e67","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-04-03T20:03:50Z","title_canon_sha256":"bff42c3bfcde0a2e47110f0f66a3b3a5ef6e1353fd1fe946dab6cb634c03b47f"},"schema_version":"1.0","source":{"id":"1404.1085","kind":"arxiv","version":1}},"canonical_sha256":"c65d15bdb3a5086da6de5be283a0a9c21655288f2975c89a86517fbad1bc3265","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c65d15bdb3a5086da6de5be283a0a9c21655288f2975c89a86517fbad1bc3265","first_computed_at":"2026-05-18T02:54:54.241168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:54.241168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mbWbUuBLdRU8ZF6uIRTAuNwPVIo3D1XIsyatI6sfLceBnFBkJgSEkT+7OWmTGwZTV7uXIlXFY4pzbt+aLTGtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:54.241617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efc36c6d47f733af5c52a2dbaf7a8d41a279032654f35e2f6234b6d0abf18487","sha256:c8530d4cbbff6a5bdd7b7e453865168667121f9a3d735607f0ee92976f0dee98"],"state_sha256":"bfd49e991dffbda576a7c30302d69b4c81f4e6229ffd045547d17e540642447a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ScDiD46cTDqjvlvllbwZJAaMLLubgqrcqfN+O7qSBtnV3qmhWIXFFITfbA4d4w46NZ99mNFLeDR7T5HVM2oyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:25:14.233821Z","bundle_sha256":"325bdb643c6747c152c233c9e875dc5e17f6ca1da2a19b835e46ed045d191e3b"}}