{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:QWCQEZZKQGQ5WRVIEFPW5BJAIM","short_pith_number":"pith:QWCQEZZK","canonical_record":{"source":{"id":"0806.4373","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2008-06-26T18:21:18Z","cross_cats_sorted":["hep-th","math-ph","math.DG","math.GT","math.MP"],"title_canon_sha256":"2e5bc9abe0ca57bc7aea9ca3b76d95523ed08a5b867b476b61cfa3b06f415345","abstract_canon_sha256":"4393700eb85df9ef28381377081ad02ba66363528f2a7c5a6e68f1b9be0128bc"},"schema_version":"1.0"},"canonical_sha256":"858502672a81a1db46a8215f6e85204331487d59c99810f75b36f6ba21e36444","source":{"kind":"arxiv","id":"0806.4373","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4373","created_at":"2026-05-18T02:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4373v3","created_at":"2026-05-18T02:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4373","created_at":"2026-05-18T02:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"QWCQEZZKQGQ5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"QWCQEZZKQGQ5WRVI","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"QWCQEZZK","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:QWCQEZZKQGQ5WRVIEFPW5BJAIM","target":"record","payload":{"canonical_record":{"source":{"id":"0806.4373","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2008-06-26T18:21:18Z","cross_cats_sorted":["hep-th","math-ph","math.DG","math.GT","math.MP"],"title_canon_sha256":"2e5bc9abe0ca57bc7aea9ca3b76d95523ed08a5b867b476b61cfa3b06f415345","abstract_canon_sha256":"4393700eb85df9ef28381377081ad02ba66363528f2a7c5a6e68f1b9be0128bc"},"schema_version":"1.0"},"canonical_sha256":"858502672a81a1db46a8215f6e85204331487d59c99810f75b36f6ba21e36444","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:15.722326Z","signature_b64":"rJNFcubigrSvyrowQN7SxUZuVFqftKjglZGKnv9zfk+vlP98eFi0oeSSwNKK0JIo5PnDV+03hrV+8xbR/6nWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"858502672a81a1db46a8215f6e85204331487d59c99810f75b36f6ba21e36444","last_reissued_at":"2026-05-18T02:35:15.721903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:15.721903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0806.4373","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":"2026-05-18T02:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YqKD6Ni/794k423XZnLkA+nYzHzQwY8PSGAul46I3lfN98hweMy8QFI9hqWLsixkyluF37HHf4wccTEL6gYLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:54:22.922501Z"},"content_sha256":"f72aa25f18b73532c3233a72fee791444e5d8708d05483757b14fdc87048aa81","schema_version":"1.0","event_id":"sha256:f72aa25f18b73532c3233a72fee791444e5d8708d05483757b14fdc87048aa81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:QWCQEZZKQGQ5WRVIEFPW5BJAIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A simple proof of the recent generalisations of Hawking's black hole topology theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.DG","math.GT","math.MP"],"primary_cat":"gr-qc","authors_text":"Istv\\'an R\\'acz","submitted_at":"2008-06-26T18:21:18Z","abstract_excerpt":"A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an \"apparent horizon\", separating the black hole region from the rest of the spacetime, are topologically two-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4373","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":""},"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":"2026-05-18T02:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gY9F+yy3a/sehNxIxQSKQuBVRZQ8UImEPsKaY26L1xpgAPJRqi3JCckCvpbDtGfkMCMzCULdBgw79CbR9dbcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:54:22.923093Z"},"content_sha256":"a8a07a0755a92bf1c0040040cd8127d23c902461a616f15602be3a9549a9186e","schema_version":"1.0","event_id":"sha256:a8a07a0755a92bf1c0040040cd8127d23c902461a616f15602be3a9549a9186e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWCQEZZKQGQ5WRVIEFPW5BJAIM/bundle.json","state_url":"https://pith.science/pith/QWCQEZZKQGQ5WRVIEFPW5BJAIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWCQEZZKQGQ5WRVIEFPW5BJAIM/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":"2026-06-04T06:54:22Z","links":{"resolver":"https://pith.science/pith/QWCQEZZKQGQ5WRVIEFPW5BJAIM","bundle":"https://pith.science/pith/QWCQEZZKQGQ5WRVIEFPW5BJAIM/bundle.json","state":"https://pith.science/pith/QWCQEZZKQGQ5WRVIEFPW5BJAIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWCQEZZKQGQ5WRVIEFPW5BJAIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:QWCQEZZKQGQ5WRVIEFPW5BJAIM","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":"4393700eb85df9ef28381377081ad02ba66363528f2a7c5a6e68f1b9be0128bc","cross_cats_sorted":["hep-th","math-ph","math.DG","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2008-06-26T18:21:18Z","title_canon_sha256":"2e5bc9abe0ca57bc7aea9ca3b76d95523ed08a5b867b476b61cfa3b06f415345"},"schema_version":"1.0","source":{"id":"0806.4373","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.4373","created_at":"2026-05-18T02:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"0806.4373v3","created_at":"2026-05-18T02:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.4373","created_at":"2026-05-18T02:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"QWCQEZZKQGQ5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"QWCQEZZKQGQ5WRVI","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"QWCQEZZK","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a8a07a0755a92bf1c0040040cd8127d23c902461a616f15602be3a9549a9186e","target":"graph","created_at":"2026-05-18T02:35:15Z","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":"A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an \"apparent horizon\", separating the black hole region from the rest of the spacetime, are topologically two-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been g","authors_text":"Istv\\'an R\\'acz","cross_cats":["hep-th","math-ph","math.DG","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2008-06-26T18:21:18Z","title":"A simple proof of the recent generalisations of Hawking's black hole topology theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4373","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:f72aa25f18b73532c3233a72fee791444e5d8708d05483757b14fdc87048aa81","target":"record","created_at":"2026-05-18T02:35:15Z","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":"4393700eb85df9ef28381377081ad02ba66363528f2a7c5a6e68f1b9be0128bc","cross_cats_sorted":["hep-th","math-ph","math.DG","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2008-06-26T18:21:18Z","title_canon_sha256":"2e5bc9abe0ca57bc7aea9ca3b76d95523ed08a5b867b476b61cfa3b06f415345"},"schema_version":"1.0","source":{"id":"0806.4373","kind":"arxiv","version":3}},"canonical_sha256":"858502672a81a1db46a8215f6e85204331487d59c99810f75b36f6ba21e36444","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"858502672a81a1db46a8215f6e85204331487d59c99810f75b36f6ba21e36444","first_computed_at":"2026-05-18T02:35:15.721903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:15.721903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rJNFcubigrSvyrowQN7SxUZuVFqftKjglZGKnv9zfk+vlP98eFi0oeSSwNKK0JIo5PnDV+03hrV+8xbR/6nWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:15.722326Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.4373","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f72aa25f18b73532c3233a72fee791444e5d8708d05483757b14fdc87048aa81","sha256:a8a07a0755a92bf1c0040040cd8127d23c902461a616f15602be3a9549a9186e"],"state_sha256":"469c2b19a6604fc5dc3dab6a315f7ff4901af4e4252bca5c680308762e54bb85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wuPz79b40ceA/Qh2UUqLSmEMPc4/D15q8pgSnJTvOfs0FJ50/z6SA9yL8yflBaY2W/AJE+OHmmspwZJXLD8gDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:54:22.926546Z","bundle_sha256":"53441a3aaad2178bf8dff1390df5d59d2c99b75eefb1c78b89aab291b8fbc160"}}