{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:EFWIUDVHN4NHQ2L3QJBVVU5ZPM","short_pith_number":"pith:EFWIUDVH","canonical_record":{"source":{"id":"quant-ph/0609227","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-09-29T10:16:41Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"e2d8902f8c09f2b0d29394aaa945d2e190d69c7610eb471068d26754618b5da4","abstract_canon_sha256":"b69ec3821e56088a05f16b29ec1a886cbee1279dfce51831ba07b07e4c342c04"},"schema_version":"1.0"},"canonical_sha256":"216c8a0ea76f1a78697b82435ad3b97b141dc191ebb6801a4952a1f2c00033aa","source":{"kind":"arxiv","id":"quant-ph/0609227","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0609227","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0609227v4","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0609227","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"EFWIUDVHN4NH","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"EFWIUDVHN4NHQ2L3","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"EFWIUDVH","created_at":"2026-07-04T15:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:EFWIUDVHN4NHQ2L3QJBVVU5ZPM","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0609227","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-09-29T10:16:41Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"e2d8902f8c09f2b0d29394aaa945d2e190d69c7610eb471068d26754618b5da4","abstract_canon_sha256":"b69ec3821e56088a05f16b29ec1a886cbee1279dfce51831ba07b07e4c342c04"},"schema_version":"1.0"},"canonical_sha256":"216c8a0ea76f1a78697b82435ad3b97b141dc191ebb6801a4952a1f2c00033aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:26:12.858761Z","signature_b64":"PZB+nK/1/9wTgXbSeVfOR83Zh5c3cUhwETqhmMUBn0UOb61IDC/FkdJWS1q2jjbCiTIUo06Dl3vQW7DrRSYmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"216c8a0ea76f1a78697b82435ad3b97b141dc191ebb6801a4952a1f2c00033aa","last_reissued_at":"2026-07-04T15:26:12.858342Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:26:12.858342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0609227","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/+FhEwpiL3J0xJqBc3LnIJj/8sb/yncfyKM7ZlPMhqw/Sw7hl1uiBPgBFawNlA/7tyrrEWshhg82j5pQkzeWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T17:13:13.351931Z"},"content_sha256":"1100c9b4fb4f00a5c66c0a3fb8495169f917426e07443c91a8de5e3e59b373ec","schema_version":"1.0","event_id":"sha256:1100c9b4fb4f00a5c66c0a3fb8495169f917426e07443c91a8de5e3e59b373ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:EFWIUDVHN4NHQ2L3QJBVVU5ZPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"E_7 and the tripartite entanglement of seven qubits","license":"","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"quant-ph","authors_text":"M. J. Duff, S. Ferrara","submitted_at":"2006-09-29T10:16:41Z","abstract_excerpt":"In quantum information theory, it is well known that the tripartite entanglement of three qubits is described by the group [SL(2,C)]^3 and that the entanglement measure is given by Cayley's hyperdeterminant. This has provided an analogy with certain N=2 supersymmetric black holes in string theory, whose entropy is also given by the hyperdeterminant. In this paper, we extend the analogy to N=8. We propose that a particular tripartite entanglement of seven qubits, encoded in the Fano plane, is described by the exceptional group E_7(C) and that the entanglement measure is given by Cartan's quarti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0609227","kind":"arxiv","version":4},"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/0609227/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":"2026-07-04T15:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzK8nmNA3RuDH0P+oo+LsgdGpi5dNXkKCM8aqIXJi6NGcPpOpUoi2flCcGgRy2rVIVmEzCneJoBJA/IIeCKQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T17:13:13.352531Z"},"content_sha256":"b4312d0c0fe322829ee43767553e58914ab336b1e3e658f5655e30de445aaa2d","schema_version":"1.0","event_id":"sha256:b4312d0c0fe322829ee43767553e58914ab336b1e3e658f5655e30de445aaa2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFWIUDVHN4NHQ2L3QJBVVU5ZPM/bundle.json","state_url":"https://pith.science/pith/EFWIUDVHN4NHQ2L3QJBVVU5ZPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFWIUDVHN4NHQ2L3QJBVVU5ZPM/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":"2026-08-07T17:13:13Z","links":{"resolver":"https://pith.science/pith/EFWIUDVHN4NHQ2L3QJBVVU5ZPM","bundle":"https://pith.science/pith/EFWIUDVHN4NHQ2L3QJBVVU5ZPM/bundle.json","state":"https://pith.science/pith/EFWIUDVHN4NHQ2L3QJBVVU5ZPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFWIUDVHN4NHQ2L3QJBVVU5ZPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:EFWIUDVHN4NHQ2L3QJBVVU5ZPM","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":"b69ec3821e56088a05f16b29ec1a886cbee1279dfce51831ba07b07e4c342c04","cross_cats_sorted":["gr-qc","hep-th"],"license":"","primary_cat":"quant-ph","submitted_at":"2006-09-29T10:16:41Z","title_canon_sha256":"e2d8902f8c09f2b0d29394aaa945d2e190d69c7610eb471068d26754618b5da4"},"schema_version":"1.0","source":{"id":"quant-ph/0609227","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0609227","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0609227v4","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0609227","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"EFWIUDVHN4NH","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"EFWIUDVHN4NHQ2L3","created_at":"2026-07-04T15:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"EFWIUDVH","created_at":"2026-07-04T15:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:b4312d0c0fe322829ee43767553e58914ab336b1e3e658f5655e30de445aaa2d","target":"graph","created_at":"2026-07-04T15:26:12Z","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/0609227/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In quantum information theory, it is well known that the tripartite entanglement of three qubits is described by the group [SL(2,C)]^3 and that the entanglement measure is given by Cayley's hyperdeterminant. This has provided an analogy with certain N=2 supersymmetric black holes in string theory, whose entropy is also given by the hyperdeterminant. In this paper, we extend the analogy to N=8. We propose that a particular tripartite entanglement of seven qubits, encoded in the Fano plane, is described by the exceptional group E_7(C) and that the entanglement measure is given by Cartan's quarti","authors_text":"M. J. Duff, S. Ferrara","cross_cats":["gr-qc","hep-th"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-09-29T10:16:41Z","title":"E_7 and the tripartite entanglement of seven qubits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0609227","kind":"arxiv","version":4},"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":"sha256:1100c9b4fb4f00a5c66c0a3fb8495169f917426e07443c91a8de5e3e59b373ec","target":"record","created_at":"2026-07-04T15:26:12Z","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":"b69ec3821e56088a05f16b29ec1a886cbee1279dfce51831ba07b07e4c342c04","cross_cats_sorted":["gr-qc","hep-th"],"license":"","primary_cat":"quant-ph","submitted_at":"2006-09-29T10:16:41Z","title_canon_sha256":"e2d8902f8c09f2b0d29394aaa945d2e190d69c7610eb471068d26754618b5da4"},"schema_version":"1.0","source":{"id":"quant-ph/0609227","kind":"arxiv","version":4}},"canonical_sha256":"216c8a0ea76f1a78697b82435ad3b97b141dc191ebb6801a4952a1f2c00033aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"216c8a0ea76f1a78697b82435ad3b97b141dc191ebb6801a4952a1f2c00033aa","first_computed_at":"2026-07-04T15:26:12.858342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:26:12.858342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZB+nK/1/9wTgXbSeVfOR83Zh5c3cUhwETqhmMUBn0UOb61IDC/FkdJWS1q2jjbCiTIUo06Dl3vQW7DrRSYmBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:26:12.858761Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0609227","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1100c9b4fb4f00a5c66c0a3fb8495169f917426e07443c91a8de5e3e59b373ec","sha256:b4312d0c0fe322829ee43767553e58914ab336b1e3e658f5655e30de445aaa2d"],"state_sha256":"51f2475b65d9ee1e525a4353a0d2c879b7acc49afe262e43d1b5676a3413a192"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yZq1ydi8yjOpmezPPsC9+VSAIMosxkbs+OyhmMh7oZoRUn22FXuKzeXJTE7dVpFA6MdS/Enq5axpysLiDYdYDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T17:13:13.357532Z","bundle_sha256":"4cdadc8715e4191ed195ed422d4be4cb2a545aba57c5aec65240e447a09b34ea"}}