{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YLRVAWDEGLG52P2KNGKYJ2LAPI","short_pith_number":"pith:YLRVAWDE","canonical_record":{"source":{"id":"1106.6105","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-30T02:14:25Z","cross_cats_sorted":[],"title_canon_sha256":"128dbf786c2ca1dbaa60e97a2597101a45339149c8f9579eb89d11d8e0f033dd","abstract_canon_sha256":"b96ad388124aeb8d2851830f6350f66f5f6cb223736fe2dfa957969b58d17d25"},"schema_version":"1.0"},"canonical_sha256":"c2e350586432cddd3f4a699584e9607a075cf6f9ad63bdf40d99d126003e26fd","source":{"kind":"arxiv","id":"1106.6105","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.6105","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"arxiv_version","alias_value":"1106.6105v2","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6105","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"pith_short_12","alias_value":"YLRVAWDEGLG5","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YLRVAWDEGLG52P2K","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YLRVAWDE","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YLRVAWDEGLG52P2KNGKYJ2LAPI","target":"record","payload":{"canonical_record":{"source":{"id":"1106.6105","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-30T02:14:25Z","cross_cats_sorted":[],"title_canon_sha256":"128dbf786c2ca1dbaa60e97a2597101a45339149c8f9579eb89d11d8e0f033dd","abstract_canon_sha256":"b96ad388124aeb8d2851830f6350f66f5f6cb223736fe2dfa957969b58d17d25"},"schema_version":"1.0"},"canonical_sha256":"c2e350586432cddd3f4a699584e9607a075cf6f9ad63bdf40d99d126003e26fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:24.240522Z","signature_b64":"TyYRWpP61RD7nUquzT4bNWkPTNmLryRS5BF8dp3t+pJhg2PB6daMahyCpua4NhIm3r8A/T+5V7n+mfQH36B0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2e350586432cddd3f4a699584e9607a075cf6f9ad63bdf40d99d126003e26fd","last_reissued_at":"2026-05-18T03:56:24.239900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:24.239900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.6105","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":"2026-05-18T03:56:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JrKhKv4BGFEjvvDOth8ySgDd5y3VYVC/dLDN6GFnZx+dmXg5GH5KffdC4n5GdtluKVkfRZr9+qa+6/PwCoWODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:47:07.035821Z"},"content_sha256":"6dbd7840ded23ca30738da19f25ce8fe905fbfbec8e793854fa200566e62ff80","schema_version":"1.0","event_id":"sha256:6dbd7840ded23ca30738da19f25ce8fe905fbfbec8e793854fa200566e62ff80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YLRVAWDEGLG52P2KNGKYJ2LAPI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dafa Li, Xiangrong Li","submitted_at":"2011-06-30T02:14:25Z","abstract_excerpt":"We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient matrices associated with the states. The rank of the coefficient matrix is preserved under SLOCC and gives rise to a simple way of partitioning all the pure states of n qubits into different families of entanglement classes, as exemplified here. When applied to the symmetric states, this approach reveals that all the Dicke states |l,n> "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6105","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":"2026-05-18T03:56:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6BzAMZ3c/dz8ncd6ek3R78f3H95Dipq1azvpBvNe430QBJVhsSDmghhGrAvJJ0cWu3g+gLpWcvJ/d/gMO7dfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:47:07.036164Z"},"content_sha256":"9e715e3f06cd74766392fcbdebdd1a8e05f49b08117a287f2fe6f25cbf6dbed3","schema_version":"1.0","event_id":"sha256:9e715e3f06cd74766392fcbdebdd1a8e05f49b08117a287f2fe6f25cbf6dbed3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLRVAWDEGLG52P2KNGKYJ2LAPI/bundle.json","state_url":"https://pith.science/pith/YLRVAWDEGLG52P2KNGKYJ2LAPI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLRVAWDEGLG52P2KNGKYJ2LAPI/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":"2026-06-27T05:47:07Z","links":{"resolver":"https://pith.science/pith/YLRVAWDEGLG52P2KNGKYJ2LAPI","bundle":"https://pith.science/pith/YLRVAWDEGLG52P2KNGKYJ2LAPI/bundle.json","state":"https://pith.science/pith/YLRVAWDEGLG52P2KNGKYJ2LAPI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLRVAWDEGLG52P2KNGKYJ2LAPI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YLRVAWDEGLG52P2KNGKYJ2LAPI","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":"b96ad388124aeb8d2851830f6350f66f5f6cb223736fe2dfa957969b58d17d25","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-30T02:14:25Z","title_canon_sha256":"128dbf786c2ca1dbaa60e97a2597101a45339149c8f9579eb89d11d8e0f033dd"},"schema_version":"1.0","source":{"id":"1106.6105","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.6105","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"arxiv_version","alias_value":"1106.6105v2","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6105","created_at":"2026-05-18T03:56:24Z"},{"alias_kind":"pith_short_12","alias_value":"YLRVAWDEGLG5","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YLRVAWDEGLG52P2K","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YLRVAWDE","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:9e715e3f06cd74766392fcbdebdd1a8e05f49b08117a287f2fe6f25cbf6dbed3","target":"graph","created_at":"2026-05-18T03:56:24Z","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":"We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient matrices associated with the states. The rank of the coefficient matrix is preserved under SLOCC and gives rise to a simple way of partitioning all the pure states of n qubits into different families of entanglement classes, as exemplified here. When applied to the symmetric states, this approach reveals that all the Dicke states |l,n> ","authors_text":"Dafa Li, Xiangrong Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-30T02:14:25Z","title":"Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6105","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":"sha256:6dbd7840ded23ca30738da19f25ce8fe905fbfbec8e793854fa200566e62ff80","target":"record","created_at":"2026-05-18T03:56:24Z","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":"b96ad388124aeb8d2851830f6350f66f5f6cb223736fe2dfa957969b58d17d25","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-30T02:14:25Z","title_canon_sha256":"128dbf786c2ca1dbaa60e97a2597101a45339149c8f9579eb89d11d8e0f033dd"},"schema_version":"1.0","source":{"id":"1106.6105","kind":"arxiv","version":2}},"canonical_sha256":"c2e350586432cddd3f4a699584e9607a075cf6f9ad63bdf40d99d126003e26fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2e350586432cddd3f4a699584e9607a075cf6f9ad63bdf40d99d126003e26fd","first_computed_at":"2026-05-18T03:56:24.239900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:24.239900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TyYRWpP61RD7nUquzT4bNWkPTNmLryRS5BF8dp3t+pJhg2PB6daMahyCpua4NhIm3r8A/T+5V7n+mfQH36B0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:24.240522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.6105","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dbd7840ded23ca30738da19f25ce8fe905fbfbec8e793854fa200566e62ff80","sha256:9e715e3f06cd74766392fcbdebdd1a8e05f49b08117a287f2fe6f25cbf6dbed3"],"state_sha256":"9a8b442e214901d4cd98b40764595ce84c96d0973e3a5848db5f62b64fff87a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FXMuDtjbcH37t/O0e9P5UYN5G9KfPEIspdQRvGQXtGt4Qohl++zmZ7smkvzMserVW8Ete8UsKd2JdBHc/XBpCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T05:47:07.037974Z","bundle_sha256":"07dae18b960fd5df5335ab6284fcab2e1f56b177760e58f19a0d671e34ffe421"}}