{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:244XH2N4TA5KLJPLEFDYMVJ52U","short_pith_number":"pith:244XH2N4","canonical_record":{"source":{"id":"quant-ph/0604166","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-21T20:05:52Z","cross_cats_sorted":[],"title_canon_sha256":"cfa1f063c213c67aa075a732701288dcdda4e152e9a052f0576f50f2050d8f23","abstract_canon_sha256":"8b0046ccb4123245f1bda8d6c1948776bc6710363e5801ae5f0973f22d63325c"},"schema_version":"1.0"},"canonical_sha256":"d73973e9bc983aa5a5eb214786553dd51f974599eb6c7580cdd28db10d2a37a7","source":{"kind":"arxiv","id":"quant-ph/0604166","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0604166","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0604166v3","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0604166","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"244XH2N4TA5K","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"244XH2N4TA5KLJPL","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"244XH2N4","created_at":"2026-07-04T15:06:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:244XH2N4TA5KLJPLEFDYMVJ52U","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0604166","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-21T20:05:52Z","cross_cats_sorted":[],"title_canon_sha256":"cfa1f063c213c67aa075a732701288dcdda4e152e9a052f0576f50f2050d8f23","abstract_canon_sha256":"8b0046ccb4123245f1bda8d6c1948776bc6710363e5801ae5f0973f22d63325c"},"schema_version":"1.0"},"canonical_sha256":"d73973e9bc983aa5a5eb214786553dd51f974599eb6c7580cdd28db10d2a37a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:06:08.303417Z","signature_b64":"BltrP0t7tor/x8iIsnwfs9Aa4c9BIo6v+YteAJz1IqmA4jQ4xFdThlzfwnBiHbXCYnUcb+8BE4YtPDpbeZ/qBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d73973e9bc983aa5a5eb214786553dd51f974599eb6c7580cdd28db10d2a37a7","last_reissued_at":"2026-07-04T15:06:08.303016Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:06:08.303016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0604166","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/RmUVVjb4bV/YSohmqEuY7K77VUGfP5iLDdnKunL3OyEA0V9dYf8CbM9Ppl/DwzOwerEx/xm9iZ05LEnNLMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:50:28.737974Z"},"content_sha256":"bba8f29c0810f54197a271c9ffb37608ed4195fc7d817be2e7bc8810331d1e44","schema_version":"1.0","event_id":"sha256:bba8f29c0810f54197a271c9ffb37608ed4195fc7d817be2e7bc8810331d1e44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:244XH2N4TA5KLJPLEFDYMVJ52U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Consistency of Local Density Matrices is QMA-complete","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Yi-Kai Liu","submitted_at":"2006-04-21T20:05:52Z","abstract_excerpt":"Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes a subset C_i of the qubits. We say that the rho_i are ``consistent'' if there exists some global state sigma (on all n qubits) that matches each of the rho_i on the subsets C_i. This generalizes the classical notion of the consistency of marginal probability distributions.\n  We show that deciding the consistency of local density matrices is QMA-complete (where QMA is the quantum analogue of NP). This gives an interesting example of a hard problem in QMA. Our pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0604166","kind":"arxiv","version":3},"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/0604166/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":"2026-07-04T15:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hMDoN7vqZXDwsupw8+W+/CifEQ5dr3C5+eb5TJzklhEtOVkYWAx0im4Xxv7fMOLxW67j1NYQf5iiThYFD5PcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:50:28.738963Z"},"content_sha256":"5ea2002fea424b43ce50f328d6fece919917fec9735d7a490a56090cbbb5111d","schema_version":"1.0","event_id":"sha256:5ea2002fea424b43ce50f328d6fece919917fec9735d7a490a56090cbbb5111d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/244XH2N4TA5KLJPLEFDYMVJ52U/bundle.json","state_url":"https://pith.science/pith/244XH2N4TA5KLJPLEFDYMVJ52U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/244XH2N4TA5KLJPLEFDYMVJ52U/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":"2026-08-16T14:50:28Z","links":{"resolver":"https://pith.science/pith/244XH2N4TA5KLJPLEFDYMVJ52U","bundle":"https://pith.science/pith/244XH2N4TA5KLJPLEFDYMVJ52U/bundle.json","state":"https://pith.science/pith/244XH2N4TA5KLJPLEFDYMVJ52U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/244XH2N4TA5KLJPLEFDYMVJ52U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:244XH2N4TA5KLJPLEFDYMVJ52U","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":"8b0046ccb4123245f1bda8d6c1948776bc6710363e5801ae5f0973f22d63325c","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-21T20:05:52Z","title_canon_sha256":"cfa1f063c213c67aa075a732701288dcdda4e152e9a052f0576f50f2050d8f23"},"schema_version":"1.0","source":{"id":"quant-ph/0604166","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0604166","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0604166v3","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0604166","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"244XH2N4TA5K","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"244XH2N4TA5KLJPL","created_at":"2026-07-04T15:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"244XH2N4","created_at":"2026-07-04T15:06:08Z"}],"graph_snapshots":[{"event_id":"sha256:5ea2002fea424b43ce50f328d6fece919917fec9735d7a490a56090cbbb5111d","target":"graph","created_at":"2026-07-04T15:06:08Z","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/0604166/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes a subset C_i of the qubits. We say that the rho_i are ``consistent'' if there exists some global state sigma (on all n qubits) that matches each of the rho_i on the subsets C_i. This generalizes the classical notion of the consistency of marginal probability distributions.\n  We show that deciding the consistency of local density matrices is QMA-complete (where QMA is the quantum analogue of NP). This gives an interesting example of a hard problem in QMA. Our pr","authors_text":"Yi-Kai Liu","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-04-21T20:05:52Z","title":"Consistency of Local Density Matrices is QMA-complete"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0604166","kind":"arxiv","version":3},"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:bba8f29c0810f54197a271c9ffb37608ed4195fc7d817be2e7bc8810331d1e44","target":"record","created_at":"2026-07-04T15:06:08Z","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":"8b0046ccb4123245f1bda8d6c1948776bc6710363e5801ae5f0973f22d63325c","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-21T20:05:52Z","title_canon_sha256":"cfa1f063c213c67aa075a732701288dcdda4e152e9a052f0576f50f2050d8f23"},"schema_version":"1.0","source":{"id":"quant-ph/0604166","kind":"arxiv","version":3}},"canonical_sha256":"d73973e9bc983aa5a5eb214786553dd51f974599eb6c7580cdd28db10d2a37a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d73973e9bc983aa5a5eb214786553dd51f974599eb6c7580cdd28db10d2a37a7","first_computed_at":"2026-07-04T15:06:08.303016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:06:08.303016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BltrP0t7tor/x8iIsnwfs9Aa4c9BIo6v+YteAJz1IqmA4jQ4xFdThlzfwnBiHbXCYnUcb+8BE4YtPDpbeZ/qBw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:06:08.303417Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0604166","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bba8f29c0810f54197a271c9ffb37608ed4195fc7d817be2e7bc8810331d1e44","sha256:5ea2002fea424b43ce50f328d6fece919917fec9735d7a490a56090cbbb5111d"],"state_sha256":"4e802a1761ab2abfee45167f3eb06b694561b7c29b4e1ce1e66c7b723a4270b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zQp/uPWmnUncoXnGxMZrEjNz6G8VdX3OUgNNyfylA5gEKdJHr02RQXQac5VijKOmAK4f9GrdyyCOVLkChOdvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T14:50:28.745404Z","bundle_sha256":"61a77cde151b05efc78c75d9ce936e6a44d5d8806429ab27505ec0c9a75fc189"}}