{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ODPMOEZCWEQ6JWCNVJKSZRPTJJ","short_pith_number":"pith:ODPMOEZC","canonical_record":{"source":{"id":"1101.3093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-16T21:15:48Z","cross_cats_sorted":[],"title_canon_sha256":"c20699cbaad82a07b3aba4e42f05ba94c36f7afe467e236239dc49da06e6f81f","abstract_canon_sha256":"531c8edcd49864ecbceb6119badcd19e2929e3fbfb26cf3dc00787b092fe715f"},"schema_version":"1.0"},"canonical_sha256":"70dec71322b121e4d84daa552cc5f34a5aded1230f66934f55bd7f69cbc9dde3","source":{"kind":"arxiv","id":"1101.3093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3093","created_at":"2026-05-18T02:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3093v1","created_at":"2026-05-18T02:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3093","created_at":"2026-05-18T02:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"ODPMOEZCWEQ6","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"ODPMOEZCWEQ6JWCN","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"ODPMOEZC","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ODPMOEZCWEQ6JWCNVJKSZRPTJJ","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-16T21:15:48Z","cross_cats_sorted":[],"title_canon_sha256":"c20699cbaad82a07b3aba4e42f05ba94c36f7afe467e236239dc49da06e6f81f","abstract_canon_sha256":"531c8edcd49864ecbceb6119badcd19e2929e3fbfb26cf3dc00787b092fe715f"},"schema_version":"1.0"},"canonical_sha256":"70dec71322b121e4d84daa552cc5f34a5aded1230f66934f55bd7f69cbc9dde3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:39.462615Z","signature_b64":"c87+VOuh3MOnfUPPz27X7iyY0MPZnZeEZuYU0dBBsa9uKFi1s5oQFzikJd1KmGZ1f1rZnoMB0yIrGhKRDuzeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70dec71322b121e4d84daa552cc5f34a5aded1230f66934f55bd7f69cbc9dde3","last_reissued_at":"2026-05-18T02:03:39.462213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:39.462213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3093","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":"2026-05-18T02:03:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YRCxkdwm/csJaPaDwpa38HDtvFY1WFoU55PE229xaNyiDUVBAZLBT7nEFNjLGFpV+T1gh5Wqz0eEjdxbJqd9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:46:26.491626Z"},"content_sha256":"958d6e9f374a9e4a5227c49aa93978d017911d9928c532517886aa41c2912b63","schema_version":"1.0","event_id":"sha256:958d6e9f374a9e4a5227c49aa93978d017911d9928c532517886aa41c2912b63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ODPMOEZCWEQ6JWCNVJKSZRPTJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogeneous Lorentzian manifolds of a semisimple group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"D.V. Alekseevsky","submitted_at":"2011-01-16T21:15:48Z","abstract_excerpt":"We describe the structure of $d$-dimensional homogeneous Lorentzian $G$-manifolds $M=G/H$ of a semisimple Lie group $G$. Due to a result by N. Kowalsky, it is sufficient to consider the case when the group $G$ acts properly, that is the stabilizer $H$ is compact. Then any homogeneous space $G/\\bar H$ with a smaller group $\\bar H \\subset H$ admits an invariant Lorentzian metric. A homogeneous manifold $G/H$ with a connected compact stabilizer $H$ is called a minimal admissible manifold if it admits an invariant Lorentzian metric, but no homogeneous $G$-manifold $G/\\tilde H$ with a larger connec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3093","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":"2026-05-18T02:03:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QfYCVQFgV6gTMLZav/N8UyaIwwNA/44dnoJ4M2wfEFL6YK0ku33+ouZib3lH8c82JBmwRx8/l2Oqpjs4knByDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:46:26.491977Z"},"content_sha256":"5a70b6326edc5dad34f2cb51af1493ff84c77c9efa2d2f390e6026cdf6e4c203","schema_version":"1.0","event_id":"sha256:5a70b6326edc5dad34f2cb51af1493ff84c77c9efa2d2f390e6026cdf6e4c203"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ODPMOEZCWEQ6JWCNVJKSZRPTJJ/bundle.json","state_url":"https://pith.science/pith/ODPMOEZCWEQ6JWCNVJKSZRPTJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ODPMOEZCWEQ6JWCNVJKSZRPTJJ/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":"2026-06-24T10:46:26Z","links":{"resolver":"https://pith.science/pith/ODPMOEZCWEQ6JWCNVJKSZRPTJJ","bundle":"https://pith.science/pith/ODPMOEZCWEQ6JWCNVJKSZRPTJJ/bundle.json","state":"https://pith.science/pith/ODPMOEZCWEQ6JWCNVJKSZRPTJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ODPMOEZCWEQ6JWCNVJKSZRPTJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ODPMOEZCWEQ6JWCNVJKSZRPTJJ","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":"531c8edcd49864ecbceb6119badcd19e2929e3fbfb26cf3dc00787b092fe715f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-16T21:15:48Z","title_canon_sha256":"c20699cbaad82a07b3aba4e42f05ba94c36f7afe467e236239dc49da06e6f81f"},"schema_version":"1.0","source":{"id":"1101.3093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3093","created_at":"2026-05-18T02:03:39Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3093v1","created_at":"2026-05-18T02:03:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3093","created_at":"2026-05-18T02:03:39Z"},{"alias_kind":"pith_short_12","alias_value":"ODPMOEZCWEQ6","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"ODPMOEZCWEQ6JWCN","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"ODPMOEZC","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:5a70b6326edc5dad34f2cb51af1493ff84c77c9efa2d2f390e6026cdf6e4c203","target":"graph","created_at":"2026-05-18T02:03:39Z","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 describe the structure of $d$-dimensional homogeneous Lorentzian $G$-manifolds $M=G/H$ of a semisimple Lie group $G$. Due to a result by N. Kowalsky, it is sufficient to consider the case when the group $G$ acts properly, that is the stabilizer $H$ is compact. Then any homogeneous space $G/\\bar H$ with a smaller group $\\bar H \\subset H$ admits an invariant Lorentzian metric. A homogeneous manifold $G/H$ with a connected compact stabilizer $H$ is called a minimal admissible manifold if it admits an invariant Lorentzian metric, but no homogeneous $G$-manifold $G/\\tilde H$ with a larger connec","authors_text":"D.V. Alekseevsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-16T21:15:48Z","title":"Homogeneous Lorentzian manifolds of a semisimple group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3093","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":"sha256:958d6e9f374a9e4a5227c49aa93978d017911d9928c532517886aa41c2912b63","target":"record","created_at":"2026-05-18T02:03:39Z","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":"531c8edcd49864ecbceb6119badcd19e2929e3fbfb26cf3dc00787b092fe715f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-16T21:15:48Z","title_canon_sha256":"c20699cbaad82a07b3aba4e42f05ba94c36f7afe467e236239dc49da06e6f81f"},"schema_version":"1.0","source":{"id":"1101.3093","kind":"arxiv","version":1}},"canonical_sha256":"70dec71322b121e4d84daa552cc5f34a5aded1230f66934f55bd7f69cbc9dde3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70dec71322b121e4d84daa552cc5f34a5aded1230f66934f55bd7f69cbc9dde3","first_computed_at":"2026-05-18T02:03:39.462213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:39.462213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c87+VOuh3MOnfUPPz27X7iyY0MPZnZeEZuYU0dBBsa9uKFi1s5oQFzikJd1KmGZ1f1rZnoMB0yIrGhKRDuzeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:39.462615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:958d6e9f374a9e4a5227c49aa93978d017911d9928c532517886aa41c2912b63","sha256:5a70b6326edc5dad34f2cb51af1493ff84c77c9efa2d2f390e6026cdf6e4c203"],"state_sha256":"86830a584bedfbb23afd5fff295053522539bee9510da0c12949e2f703d7f0a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPDJuXkarJZUxmUQ6Zveudy71fe8fbHMm0VpUtBgQR4g1ZhxrgN8hAylZYvn/Rxm7qwvhTFlmzea7ZbFR+mHBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:46:26.493974Z","bundle_sha256":"c9706081850b9fd65162afee93ada62115ff274b58d8ebb87d90213973394beb"}}