{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:F73HKD36C4SC4NFASHW63L7DEU","short_pith_number":"pith:F73HKD36","canonical_record":{"source":{"id":"1202.1045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-02-06T04:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"a5b48118ff19505543a3d76508c4f10a0b729c5a7a6cce42ff15baf8cf7483f4","abstract_canon_sha256":"cb0e581cb0bd803b83c56cf29ba52e753d48d12442190a51e622884c8d5b3592"},"schema_version":"1.0"},"canonical_sha256":"2ff6750f7e17242e34a091ededafe3251c232b8067c3d52eafae6e50a5f4f1ba","source":{"kind":"arxiv","id":"1202.1045","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1045","created_at":"2026-05-18T01:58:33Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1045v1","created_at":"2026-05-18T01:58:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1045","created_at":"2026-05-18T01:58:33Z"},{"alias_kind":"pith_short_12","alias_value":"F73HKD36C4SC","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"F73HKD36C4SC4NFA","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"F73HKD36","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:F73HKD36C4SC4NFASHW63L7DEU","target":"record","payload":{"canonical_record":{"source":{"id":"1202.1045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-02-06T04:12:57Z","cross_cats_sorted":[],"title_canon_sha256":"a5b48118ff19505543a3d76508c4f10a0b729c5a7a6cce42ff15baf8cf7483f4","abstract_canon_sha256":"cb0e581cb0bd803b83c56cf29ba52e753d48d12442190a51e622884c8d5b3592"},"schema_version":"1.0"},"canonical_sha256":"2ff6750f7e17242e34a091ededafe3251c232b8067c3d52eafae6e50a5f4f1ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:33.661661Z","signature_b64":"t7sfIY2+X25/2Pz0HFYO9zN7ORAtmU77IhNzKa4dP34bY7Qedfs6lJkPVF7J/9081HyZWnfCBtCHMaBrt2JRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ff6750f7e17242e34a091ededafe3251c232b8067c3d52eafae6e50a5f4f1ba","last_reissued_at":"2026-05-18T01:58:33.661144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:33.661144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.1045","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:58:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ihvT8Oe/PVkIYl49Xyyf6WROy7jMngPdv+Powe2ti2MDJkvFNSK5b5lIcBjLi1zR/9XtFBzLDO6GxJ2oEQX1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:25:03.012083Z"},"content_sha256":"97f5a5e884a96ce3669cca33a259458cedf0fa84dbb6a778336d041c52079590","schema_version":"1.0","event_id":"sha256:97f5a5e884a96ce3669cca33a259458cedf0fa84dbb6a778336d041c52079590"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:F73HKD36C4SC4NFASHW63L7DEU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Apparent Horizons with Nontrivial Topology and the Hyperhoop Conjecture in Six-Dimensional Space-Times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Hirotaka Nakayama, Takahiro Okamoto, Tomohiro Kurata","submitted_at":"2012-02-06T04:12:57Z","abstract_excerpt":"We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static, conformally flat initial data sets each describing a gravitational field of uniform massive k-sphere sources, for k=1,2, on the five-dimensional Cauchy surface. The numerical result shows the validity of the hyperhoop conjecture for a wide range of model parameters. We also confirm for the first time the existence of an apparent horizon homeomorphism to S**2 x S**2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1045","kind":"arxiv","version":1},"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":"2026-05-18T01:58:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xOrBq82R0hsPWfdmqNgpLRrp3tpwrKOzOfEZskawAnqCCngZpDlHMnwC1ZQhOyvgnEhsiDejqninbPIIlOf8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:25:03.012444Z"},"content_sha256":"58f3d5daa583f4e9ba658f84fbeb00f2bfc4dad18cdd17f67007a6efbc22f5d8","schema_version":"1.0","event_id":"sha256:58f3d5daa583f4e9ba658f84fbeb00f2bfc4dad18cdd17f67007a6efbc22f5d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F73HKD36C4SC4NFASHW63L7DEU/bundle.json","state_url":"https://pith.science/pith/F73HKD36C4SC4NFASHW63L7DEU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F73HKD36C4SC4NFASHW63L7DEU/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":"2026-06-24T22:25:03Z","links":{"resolver":"https://pith.science/pith/F73HKD36C4SC4NFASHW63L7DEU","bundle":"https://pith.science/pith/F73HKD36C4SC4NFASHW63L7DEU/bundle.json","state":"https://pith.science/pith/F73HKD36C4SC4NFASHW63L7DEU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F73HKD36C4SC4NFASHW63L7DEU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:F73HKD36C4SC4NFASHW63L7DEU","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":"cb0e581cb0bd803b83c56cf29ba52e753d48d12442190a51e622884c8d5b3592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-02-06T04:12:57Z","title_canon_sha256":"a5b48118ff19505543a3d76508c4f10a0b729c5a7a6cce42ff15baf8cf7483f4"},"schema_version":"1.0","source":{"id":"1202.1045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.1045","created_at":"2026-05-18T01:58:33Z"},{"alias_kind":"arxiv_version","alias_value":"1202.1045v1","created_at":"2026-05-18T01:58:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1045","created_at":"2026-05-18T01:58:33Z"},{"alias_kind":"pith_short_12","alias_value":"F73HKD36C4SC","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"F73HKD36C4SC4NFA","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"F73HKD36","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:58f3d5daa583f4e9ba658f84fbeb00f2bfc4dad18cdd17f67007a6efbc22f5d8","target":"graph","created_at":"2026-05-18T01:58:33Z","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 investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static, conformally flat initial data sets each describing a gravitational field of uniform massive k-sphere sources, for k=1,2, on the five-dimensional Cauchy surface. The numerical result shows the validity of the hyperhoop conjecture for a wide range of model parameters. We also confirm for the first time the existence of an apparent horizon homeomorphism to S**2 x S**2","authors_text":"Hirotaka Nakayama, Takahiro Okamoto, Tomohiro Kurata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-02-06T04:12:57Z","title":"Apparent Horizons with Nontrivial Topology and the Hyperhoop Conjecture in Six-Dimensional Space-Times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1045","kind":"arxiv","version":1},"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":"sha256:97f5a5e884a96ce3669cca33a259458cedf0fa84dbb6a778336d041c52079590","target":"record","created_at":"2026-05-18T01:58:33Z","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":"cb0e581cb0bd803b83c56cf29ba52e753d48d12442190a51e622884c8d5b3592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-02-06T04:12:57Z","title_canon_sha256":"a5b48118ff19505543a3d76508c4f10a0b729c5a7a6cce42ff15baf8cf7483f4"},"schema_version":"1.0","source":{"id":"1202.1045","kind":"arxiv","version":1}},"canonical_sha256":"2ff6750f7e17242e34a091ededafe3251c232b8067c3d52eafae6e50a5f4f1ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ff6750f7e17242e34a091ededafe3251c232b8067c3d52eafae6e50a5f4f1ba","first_computed_at":"2026-05-18T01:58:33.661144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:33.661144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t7sfIY2+X25/2Pz0HFYO9zN7ORAtmU77IhNzKa4dP34bY7Qedfs6lJkPVF7J/9081HyZWnfCBtCHMaBrt2JRBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:33.661661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.1045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97f5a5e884a96ce3669cca33a259458cedf0fa84dbb6a778336d041c52079590","sha256:58f3d5daa583f4e9ba658f84fbeb00f2bfc4dad18cdd17f67007a6efbc22f5d8"],"state_sha256":"b40882feaf0e026c445e8c07d10848d1ed002fd994c9041a2d464054b5067e0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6sqAymdlp2Zw/UG9X5PaA/iqVycfJR6VoNO6efJWsRX1g5NTdH5GTFmGhftyS2vQpjIZZ4rc+8ITFWtrU1Q2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:25:03.014303Z","bundle_sha256":"21ce2fce545fb9fc957c23a9d87cad9a2f598288144c5edfe96d262a2966522b"}}