{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:BFHAXJPVJ7VCBEALIHPTVPY2NO","short_pith_number":"pith:BFHAXJPV","canonical_record":{"source":{"id":"hep-th/0612036","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-12-05T12:23:47Z","cross_cats_sorted":["gr-qc","quant-ph"],"title_canon_sha256":"376a8c38e9c85a5ca161d78a5242b18ed2d6d6c57738c0b7f1dbe9330fa5fd60","abstract_canon_sha256":"1b91fc68017635335f36d126c91317b59a9f05610645295200492151e0d48522"},"schema_version":"1.0"},"canonical_sha256":"094e0ba5f54fea20900b41df3abf1a6ba00a5f4a9f2ed595f23564362769f8f0","source":{"kind":"arxiv","id":"hep-th/0612036","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0612036","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0612036v3","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0612036","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"BFHAXJPVJ7VC","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_16","alias_value":"BFHAXJPVJ7VCBEAL","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_8","alias_value":"BFHAXJPV","created_at":"2026-07-04T15:34:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:BFHAXJPVJ7VCBEALIHPTVPY2NO","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0612036","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-12-05T12:23:47Z","cross_cats_sorted":["gr-qc","quant-ph"],"title_canon_sha256":"376a8c38e9c85a5ca161d78a5242b18ed2d6d6c57738c0b7f1dbe9330fa5fd60","abstract_canon_sha256":"1b91fc68017635335f36d126c91317b59a9f05610645295200492151e0d48522"},"schema_version":"1.0"},"canonical_sha256":"094e0ba5f54fea20900b41df3abf1a6ba00a5f4a9f2ed595f23564362769f8f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:34:28.297121Z","signature_b64":"Pljz4+eTKWaIWQhSBhGcODM4l41vJqHwHkbIgBcAuyVGC4MckF1bey+Mx/oJYruUoNMi2JgcVw0BOYBkCcoeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"094e0ba5f54fea20900b41df3abf1a6ba00a5f4a9f2ed595f23564362769f8f0","last_reissued_at":"2026-07-04T15:34:28.296754Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:34:28.296754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0612036","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":"2026-07-04T15:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l66COEUA/usxvOamOQBl3vq/Fq6n47xfWZHN+yzX4rBHCHLrJ0JCIKObKS0ozlV/8oQFm0/SXgca9GGvp3HsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:05:14.216706Z"},"content_sha256":"f7fa594c717e4ceb1e0824c20be0e45cf3c4aef6ea3dc4a18b357a200663307b","schema_version":"1.0","event_id":"sha256:f7fa594c717e4ceb1e0824c20be0e45cf3c4aef6ea3dc4a18b357a200663307b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:BFHAXJPVJ7VCBEALIHPTVPY2NO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Black hole entropy and quantum information","license":"","headline":"","cross_cats":["gr-qc","quant-ph"],"primary_cat":"hep-th","authors_text":"M. J. Duff, S. Ferrara","submitted_at":"2006-12-05T12:23:47Z","abstract_excerpt":"We review some recently established connections between the mathematics of black hole entropy in string theory and that of multipartite entanglement in quantum information theory. In the case of N=2 black holes and the entanglement of three qubits, the quartic [SL(2)]^3 invariant, Cayley's hyperdeterminant, provides both the black hole entropy and the measure of tripartite entanglement. In the case of N=8 black holes and the entanglement of seven qubits, the quartic E_7 invariant of Cartan provides both the black hole entropy and the measure of a particular tripartite entanglement encoded in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0612036","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/hep-th/0612036/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":"2026-07-04T15:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8vtYjilJSHPxZFJ6PyKJpxA+PCqs6fd88gPyL0aNqz9xZ0ywSqkqDT6LsGIiNYnYYWc9SZtGK9cvBrpseCnWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:05:14.217223Z"},"content_sha256":"fee05367a0630fc7acecd5633c98717b5790b6b3a07dbdfda37123e25f95433c","schema_version":"1.0","event_id":"sha256:fee05367a0630fc7acecd5633c98717b5790b6b3a07dbdfda37123e25f95433c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFHAXJPVJ7VCBEALIHPTVPY2NO/bundle.json","state_url":"https://pith.science/pith/BFHAXJPVJ7VCBEALIHPTVPY2NO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFHAXJPVJ7VCBEALIHPTVPY2NO/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":"2026-08-07T18:05:14Z","links":{"resolver":"https://pith.science/pith/BFHAXJPVJ7VCBEALIHPTVPY2NO","bundle":"https://pith.science/pith/BFHAXJPVJ7VCBEALIHPTVPY2NO/bundle.json","state":"https://pith.science/pith/BFHAXJPVJ7VCBEALIHPTVPY2NO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFHAXJPVJ7VCBEALIHPTVPY2NO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:BFHAXJPVJ7VCBEALIHPTVPY2NO","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":"1b91fc68017635335f36d126c91317b59a9f05610645295200492151e0d48522","cross_cats_sorted":["gr-qc","quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2006-12-05T12:23:47Z","title_canon_sha256":"376a8c38e9c85a5ca161d78a5242b18ed2d6d6c57738c0b7f1dbe9330fa5fd60"},"schema_version":"1.0","source":{"id":"hep-th/0612036","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0612036","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0612036v3","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0612036","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"BFHAXJPVJ7VC","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_16","alias_value":"BFHAXJPVJ7VCBEAL","created_at":"2026-07-04T15:34:28Z"},{"alias_kind":"pith_short_8","alias_value":"BFHAXJPV","created_at":"2026-07-04T15:34:28Z"}],"graph_snapshots":[{"event_id":"sha256:fee05367a0630fc7acecd5633c98717b5790b6b3a07dbdfda37123e25f95433c","target":"graph","created_at":"2026-07-04T15:34:28Z","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/hep-th/0612036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We review some recently established connections between the mathematics of black hole entropy in string theory and that of multipartite entanglement in quantum information theory. In the case of N=2 black holes and the entanglement of three qubits, the quartic [SL(2)]^3 invariant, Cayley's hyperdeterminant, provides both the black hole entropy and the measure of tripartite entanglement. In the case of N=8 black holes and the entanglement of seven qubits, the quartic E_7 invariant of Cartan provides both the black hole entropy and the measure of a particular tripartite entanglement encoded in t","authors_text":"M. J. Duff, S. Ferrara","cross_cats":["gr-qc","quant-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2006-12-05T12:23:47Z","title":"Black hole entropy and quantum information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0612036","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:f7fa594c717e4ceb1e0824c20be0e45cf3c4aef6ea3dc4a18b357a200663307b","target":"record","created_at":"2026-07-04T15:34:28Z","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":"1b91fc68017635335f36d126c91317b59a9f05610645295200492151e0d48522","cross_cats_sorted":["gr-qc","quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2006-12-05T12:23:47Z","title_canon_sha256":"376a8c38e9c85a5ca161d78a5242b18ed2d6d6c57738c0b7f1dbe9330fa5fd60"},"schema_version":"1.0","source":{"id":"hep-th/0612036","kind":"arxiv","version":3}},"canonical_sha256":"094e0ba5f54fea20900b41df3abf1a6ba00a5f4a9f2ed595f23564362769f8f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"094e0ba5f54fea20900b41df3abf1a6ba00a5f4a9f2ed595f23564362769f8f0","first_computed_at":"2026-07-04T15:34:28.296754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:34:28.296754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pljz4+eTKWaIWQhSBhGcODM4l41vJqHwHkbIgBcAuyVGC4MckF1bey+Mx/oJYruUoNMi2JgcVw0BOYBkCcoeBg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:34:28.297121Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0612036","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7fa594c717e4ceb1e0824c20be0e45cf3c4aef6ea3dc4a18b357a200663307b","sha256:fee05367a0630fc7acecd5633c98717b5790b6b3a07dbdfda37123e25f95433c"],"state_sha256":"de01154c2424f0d85d6bc56a6815146c5069c162a8410eda1cbb1e137c6cd4f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NIfwg/F2f1gFg0DIxWHm2Dr0Xk4w/hsZX2dOuWNkR8+HDL4akCUILRwL+NbO993Q+X7aa4TvJZRn/xytrfcECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T18:05:14.222466Z","bundle_sha256":"bc83d1ac5c56d0a2b6572509c69a71284030e6428c9d6d559796af67483b348e"}}