{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5YNLPKALBATRXFKKIF4SSM7QNG","short_pith_number":"pith:5YNLPKAL","canonical_record":{"source":{"id":"1011.3883","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T04:23:42Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"38b76c3578ba990fa1cffbf0243a8e2dcf0aaaf43d8d9797352dc285f6a19edd","abstract_canon_sha256":"759c8e6e8f411e561b206d9b9a4c686171c6905e0ec0ebfa9b79a6effdddc9a2"},"schema_version":"1.0"},"canonical_sha256":"ee1ab7a80b08271b954a41792933f069baa52113ab78a42d0026b0bfa325422a","source":{"kind":"arxiv","id":"1011.3883","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3883","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3883v2","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3883","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"pith_short_12","alias_value":"5YNLPKALBATR","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5YNLPKALBATRXFKK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5YNLPKAL","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5YNLPKALBATRXFKKIF4SSM7QNG","target":"record","payload":{"canonical_record":{"source":{"id":"1011.3883","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T04:23:42Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"38b76c3578ba990fa1cffbf0243a8e2dcf0aaaf43d8d9797352dc285f6a19edd","abstract_canon_sha256":"759c8e6e8f411e561b206d9b9a4c686171c6905e0ec0ebfa9b79a6effdddc9a2"},"schema_version":"1.0"},"canonical_sha256":"ee1ab7a80b08271b954a41792933f069baa52113ab78a42d0026b0bfa325422a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:44.915388Z","signature_b64":"HhNU4tHB1evL6hflCWEXKOpQoaA2H1qJR/GG9I6zpbql7ZSxomRX+1ikE+LGMx4vBwmnhHX6It0e1mKqCPjLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee1ab7a80b08271b954a41792933f069baa52113ab78a42d0026b0bfa325422a","last_reissued_at":"2026-05-18T04:18:44.914686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:44.914686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.3883","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":"2026-05-18T04:18:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dbAtcho1WRSZILAHP6ZHtP/RrUJvK2y73r9/9men4U+22Ed96Ngr4Kp4qCNh80pxf+WHG2GS4Gm0YaGB0WHtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:40:56.980784Z"},"content_sha256":"4adb015054d3b32c5cb8b4d2c05efeb76a61dbdad4304f09c6f2b57034709065","schema_version":"1.0","event_id":"sha256:4adb015054d3b32c5cb8b4d2c05efeb76a61dbdad4304f09c6f2b57034709065"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5YNLPKALBATRXFKKIF4SSM7QNG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The BTZ spacetime as an algebraic embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Steven Willison","submitted_at":"2010-11-17T04:23:42Z","abstract_excerpt":"A simple algebraic global isometric embedding is presented for the nonrotating BTZ black hole and its counterpart of Euclidean signature. The image of the embedding, in Minkowski space of two extra dimensions, is the interection of two quadric hypersurfaces. Furthermore an embedding into $AdS_4$ or $H_4$ is also obtained, showing that the spacetime is of embedding class one with respect to maximally symmetric space of negative curvature. The rotating solution of Euclidean signature is also shown to admit a quadratic algebraic embedding, but seemingly requires more than two extra dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3883","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":"2026-05-18T04:18:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"525DJtcJDtOy/dIc8qW400yVF+0D0SPW9gxI8MeXaqPOFKEuj2b5ce6z3zT1Wd51idaQmUUWj/LEqVu/VesjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:40:56.981165Z"},"content_sha256":"a01e26d862a4e392a6c9d424c5cdaa38200b4bbb1e75985195c46d1ad27d837c","schema_version":"1.0","event_id":"sha256:a01e26d862a4e392a6c9d424c5cdaa38200b4bbb1e75985195c46d1ad27d837c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5YNLPKALBATRXFKKIF4SSM7QNG/bundle.json","state_url":"https://pith.science/pith/5YNLPKALBATRXFKKIF4SSM7QNG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5YNLPKALBATRXFKKIF4SSM7QNG/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":"2026-06-05T00:40:56Z","links":{"resolver":"https://pith.science/pith/5YNLPKALBATRXFKKIF4SSM7QNG","bundle":"https://pith.science/pith/5YNLPKALBATRXFKKIF4SSM7QNG/bundle.json","state":"https://pith.science/pith/5YNLPKALBATRXFKKIF4SSM7QNG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5YNLPKALBATRXFKKIF4SSM7QNG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5YNLPKALBATRXFKKIF4SSM7QNG","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":"759c8e6e8f411e561b206d9b9a4c686171c6905e0ec0ebfa9b79a6effdddc9a2","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T04:23:42Z","title_canon_sha256":"38b76c3578ba990fa1cffbf0243a8e2dcf0aaaf43d8d9797352dc285f6a19edd"},"schema_version":"1.0","source":{"id":"1011.3883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3883","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3883v2","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3883","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"pith_short_12","alias_value":"5YNLPKALBATR","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5YNLPKALBATRXFKK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5YNLPKAL","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:a01e26d862a4e392a6c9d424c5cdaa38200b4bbb1e75985195c46d1ad27d837c","target":"graph","created_at":"2026-05-18T04:18:44Z","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 simple algebraic global isometric embedding is presented for the nonrotating BTZ black hole and its counterpart of Euclidean signature. The image of the embedding, in Minkowski space of two extra dimensions, is the interection of two quadric hypersurfaces. Furthermore an embedding into $AdS_4$ or $H_4$ is also obtained, showing that the spacetime is of embedding class one with respect to maximally symmetric space of negative curvature. The rotating solution of Euclidean signature is also shown to admit a quadratic algebraic embedding, but seemingly requires more than two extra dimensions.","authors_text":"Steven Willison","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T04:23:42Z","title":"The BTZ spacetime as an algebraic embedding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3883","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":"sha256:4adb015054d3b32c5cb8b4d2c05efeb76a61dbdad4304f09c6f2b57034709065","target":"record","created_at":"2026-05-18T04:18:44Z","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":"759c8e6e8f411e561b206d9b9a4c686171c6905e0ec0ebfa9b79a6effdddc9a2","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-11-17T04:23:42Z","title_canon_sha256":"38b76c3578ba990fa1cffbf0243a8e2dcf0aaaf43d8d9797352dc285f6a19edd"},"schema_version":"1.0","source":{"id":"1011.3883","kind":"arxiv","version":2}},"canonical_sha256":"ee1ab7a80b08271b954a41792933f069baa52113ab78a42d0026b0bfa325422a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee1ab7a80b08271b954a41792933f069baa52113ab78a42d0026b0bfa325422a","first_computed_at":"2026-05-18T04:18:44.914686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:44.914686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HhNU4tHB1evL6hflCWEXKOpQoaA2H1qJR/GG9I6zpbql7ZSxomRX+1ikE+LGMx4vBwmnhHX6It0e1mKqCPjLDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:44.915388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4adb015054d3b32c5cb8b4d2c05efeb76a61dbdad4304f09c6f2b57034709065","sha256:a01e26d862a4e392a6c9d424c5cdaa38200b4bbb1e75985195c46d1ad27d837c"],"state_sha256":"b75193fd596f54a36b0225d72689c9ab0eabf40f687cf4000c36b531070f5e9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eNzwq6vzZY0DzRz50DHMmlsQney8bXc3s48BxQxjTVtuBUe+Bhz6WnRopoURsrEIV72lZISDu2JC5Og4QvlxBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:40:56.983199Z","bundle_sha256":"b42f57d88bdab27fab4ac3f1d5365728119948607f65c75d5840249abbf0ace3"}}