{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:B3B4XZDFHIYTX4WGOVE43K2PW5","short_pith_number":"pith:B3B4XZDF","canonical_record":{"source":{"id":"1106.3592","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-17T23:07:32Z","cross_cats_sorted":[],"title_canon_sha256":"e943a1a94e2db467b5d7435dd78f82688a562436c54b4b3e651a8a34cdcc2880","abstract_canon_sha256":"76efd7063c42e1b9af89c5ba6988a11aaa55212f2c46e0439985e52337500928"},"schema_version":"1.0"},"canonical_sha256":"0ec3cbe4653a313bf2c67549cdab4fb769e7143d481a20ebe1a4a9afb63e9bde","source":{"kind":"arxiv","id":"1106.3592","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3592","created_at":"2026-05-18T02:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3592v2","created_at":"2026-05-18T02:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3592","created_at":"2026-05-18T02:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"B3B4XZDFHIYT","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"B3B4XZDFHIYTX4WG","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"B3B4XZDF","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:B3B4XZDFHIYTX4WGOVE43K2PW5","target":"record","payload":{"canonical_record":{"source":{"id":"1106.3592","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-17T23:07:32Z","cross_cats_sorted":[],"title_canon_sha256":"e943a1a94e2db467b5d7435dd78f82688a562436c54b4b3e651a8a34cdcc2880","abstract_canon_sha256":"76efd7063c42e1b9af89c5ba6988a11aaa55212f2c46e0439985e52337500928"},"schema_version":"1.0"},"canonical_sha256":"0ec3cbe4653a313bf2c67549cdab4fb769e7143d481a20ebe1a4a9afb63e9bde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:35.388466Z","signature_b64":"mhrCwOIC7qtZXUfYDJLeh/AnSHBVAE6ejLID1KUlR6oZ74bbYoCwdPykpbEY00QfUpdzLE3JaKi9+ICCJyVzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ec3cbe4653a313bf2c67549cdab4fb769e7143d481a20ebe1a4a9afb63e9bde","last_reissued_at":"2026-05-18T02:01:35.387725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:35.387725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.3592","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":"2026-05-18T02:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lpfer0sCXOW1JklyTOkYyEPiWUFaU0oElnJa3Qa5acObKUEjWbPL8XPCP2YSzgpypovvothTPBCSTi0sCzo6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:18:53.405947Z"},"content_sha256":"c4bfc4d9319b5157f0389557a57892e0ce6246b9341a60f7d99734c01e60748a","schema_version":"1.0","event_id":"sha256:c4bfc4d9319b5157f0389557a57892e0ce6246b9341a60f7d99734c01e60748a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:B3B4XZDFHIYTX4WGOVE43K2PW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SLOCC determinant invariants of order 2^{n/2} for even n qubits","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dafa Li, Xiangrong Li","submitted_at":"2011-06-17T23:07:32Z","abstract_excerpt":"In this paper, we study SLOCC determinant invariants of order 2^{n/2} for any even n qubits which satisfy the SLOCC determinant equations. The determinant invariants can be constructed by a simple method and the set of all these determinant invariants is complete with respect to permutations of qubits. SLOCC entanglement classification can be achieved via the vanishing or not of the determinant invariants. We exemplify the method for several even number of qubits, with an emphasis on six qubits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3592","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":"2026-05-18T02:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7FH56dQzRhbHwwhWtgRa3BpWEdl0r8qhrkpv0N0x+DiaVSNd9icx8ACS9ianlVH6tNwi1zVEipATzYdQRLEtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:18:53.406298Z"},"content_sha256":"6af5438c26b96d3cc21262b118a863d85110a01886f45b2872e9d63953dd1662","schema_version":"1.0","event_id":"sha256:6af5438c26b96d3cc21262b118a863d85110a01886f45b2872e9d63953dd1662"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3B4XZDFHIYTX4WGOVE43K2PW5/bundle.json","state_url":"https://pith.science/pith/B3B4XZDFHIYTX4WGOVE43K2PW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3B4XZDFHIYTX4WGOVE43K2PW5/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":"2026-06-27T18:18:53Z","links":{"resolver":"https://pith.science/pith/B3B4XZDFHIYTX4WGOVE43K2PW5","bundle":"https://pith.science/pith/B3B4XZDFHIYTX4WGOVE43K2PW5/bundle.json","state":"https://pith.science/pith/B3B4XZDFHIYTX4WGOVE43K2PW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3B4XZDFHIYTX4WGOVE43K2PW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:B3B4XZDFHIYTX4WGOVE43K2PW5","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":"76efd7063c42e1b9af89c5ba6988a11aaa55212f2c46e0439985e52337500928","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-17T23:07:32Z","title_canon_sha256":"e943a1a94e2db467b5d7435dd78f82688a562436c54b4b3e651a8a34cdcc2880"},"schema_version":"1.0","source":{"id":"1106.3592","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3592","created_at":"2026-05-18T02:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3592v2","created_at":"2026-05-18T02:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3592","created_at":"2026-05-18T02:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"B3B4XZDFHIYT","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"B3B4XZDFHIYTX4WG","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"B3B4XZDF","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:6af5438c26b96d3cc21262b118a863d85110a01886f45b2872e9d63953dd1662","target":"graph","created_at":"2026-05-18T02:01:35Z","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":"In this paper, we study SLOCC determinant invariants of order 2^{n/2} for any even n qubits which satisfy the SLOCC determinant equations. The determinant invariants can be constructed by a simple method and the set of all these determinant invariants is complete with respect to permutations of qubits. SLOCC entanglement classification can be achieved via the vanishing or not of the determinant invariants. We exemplify the method for several even number of qubits, with an emphasis on six qubits.","authors_text":"Dafa Li, Xiangrong Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-17T23:07:32Z","title":"SLOCC determinant invariants of order 2^{n/2} for even n qubits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3592","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:c4bfc4d9319b5157f0389557a57892e0ce6246b9341a60f7d99734c01e60748a","target":"record","created_at":"2026-05-18T02:01:35Z","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":"76efd7063c42e1b9af89c5ba6988a11aaa55212f2c46e0439985e52337500928","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2011-06-17T23:07:32Z","title_canon_sha256":"e943a1a94e2db467b5d7435dd78f82688a562436c54b4b3e651a8a34cdcc2880"},"schema_version":"1.0","source":{"id":"1106.3592","kind":"arxiv","version":2}},"canonical_sha256":"0ec3cbe4653a313bf2c67549cdab4fb769e7143d481a20ebe1a4a9afb63e9bde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ec3cbe4653a313bf2c67549cdab4fb769e7143d481a20ebe1a4a9afb63e9bde","first_computed_at":"2026-05-18T02:01:35.387725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:35.387725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mhrCwOIC7qtZXUfYDJLeh/AnSHBVAE6ejLID1KUlR6oZ74bbYoCwdPykpbEY00QfUpdzLE3JaKi9+ICCJyVzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:35.388466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3592","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4bfc4d9319b5157f0389557a57892e0ce6246b9341a60f7d99734c01e60748a","sha256:6af5438c26b96d3cc21262b118a863d85110a01886f45b2872e9d63953dd1662"],"state_sha256":"b40f0054f0a57fbd82f6d924623393d82609362c0a4e49ab0872a270c076faba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItjHnsaqfgo8bZ6GCILFMs+0x+Q+63eKsOFy6g8HDHRezWQGB32rPgMdx95Cr87DoWHvQKN6uGldLWnWzqsKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T18:18:53.408307Z","bundle_sha256":"e9dd0018a88723e6c4a3ddef4d32c236ca14207d1c297f174bb041388c4da786"}}