{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:HKVUBWFZ34TK27WUXTDIPCHWWN","short_pith_number":"pith:HKVUBWFZ","canonical_record":{"source":{"id":"math/0701927","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2007-01-31T15:14:51Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"40f80b76aafebb5b201c5022e61a9d5b3eefde70352d9ebf10017b3dc32d4703","abstract_canon_sha256":"8e998f0cba914841e0957b48cd9a438732724899d07a9f211d299d6a0bab592f"},"schema_version":"1.0"},"canonical_sha256":"3aab40d8b9df26ad7ed4bcc68788f6b371bff4104591e010aa62e6b970e224e2","source":{"kind":"arxiv","id":"math/0701927","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701927","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701927v1","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701927","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"HKVUBWFZ34TK","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"HKVUBWFZ34TK27WU","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"HKVUBWFZ","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:HKVUBWFZ34TK27WUXTDIPCHWWN","target":"record","payload":{"canonical_record":{"source":{"id":"math/0701927","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2007-01-31T15:14:51Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"40f80b76aafebb5b201c5022e61a9d5b3eefde70352d9ebf10017b3dc32d4703","abstract_canon_sha256":"8e998f0cba914841e0957b48cd9a438732724899d07a9f211d299d6a0bab592f"},"schema_version":"1.0"},"canonical_sha256":"3aab40d8b9df26ad7ed4bcc68788f6b371bff4104591e010aa62e6b970e224e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:49.661218Z","signature_b64":"NxSCu5udijf83Doc9QRxf8eERbNwTKhSeDzykZP+3buYWD6lVoe/rZk2WXmnA8jX2yr5QhIyD5ysDotE41fjCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3aab40d8b9df26ad7ed4bcc68788f6b371bff4104591e010aa62e6b970e224e2","last_reissued_at":"2026-05-18T01:30:49.660637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:49.660637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0701927","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":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pYshDoIkxO5GI48ga+4zjEZbMyPkCzus0IImtwMxuPiZ2oXEnWPb9KJNNNI7vY7+pmkt3sdQDxGWmEpMeJZ8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:14:49.080838Z"},"content_sha256":"4c5ce85de6ccfda3c1a116a27d7351527afdbb229366a6cba70dc29b2ec92e63","schema_version":"1.0","event_id":"sha256:4c5ce85de6ccfda3c1a116a27d7351527afdbb229366a6cba70dc29b2ec92e63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:HKVUBWFZ34TK27WUXTDIPCHWWN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two Remarks on Kaehler Homogeneous Manifolds","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Bruce Gilligan, Karl Oeljeklaus","submitted_at":"2007-01-31T15:14:51Z","abstract_excerpt":"We prove that every Kaehler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algebraic groups in the case where the isotropy has the property that its intersection with the radical is Zariski dense in the radical."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701927","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":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N3NWQ34NdKadPfDqwDeOf9EMyZFtOEq1f78tUBZg9vY1rDxc0R99c5isQIDe2dY9svlHtgbbqgvY421g6a8ABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:14:49.081184Z"},"content_sha256":"eee9e46a0203718ac94f8733dbc0be3a647d25df150d41989c0b6677c209434e","schema_version":"1.0","event_id":"sha256:eee9e46a0203718ac94f8733dbc0be3a647d25df150d41989c0b6677c209434e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKVUBWFZ34TK27WUXTDIPCHWWN/bundle.json","state_url":"https://pith.science/pith/HKVUBWFZ34TK27WUXTDIPCHWWN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKVUBWFZ34TK27WUXTDIPCHWWN/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":"2026-06-01T21:14:49Z","links":{"resolver":"https://pith.science/pith/HKVUBWFZ34TK27WUXTDIPCHWWN","bundle":"https://pith.science/pith/HKVUBWFZ34TK27WUXTDIPCHWWN/bundle.json","state":"https://pith.science/pith/HKVUBWFZ34TK27WUXTDIPCHWWN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKVUBWFZ34TK27WUXTDIPCHWWN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:HKVUBWFZ34TK27WUXTDIPCHWWN","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":"8e998f0cba914841e0957b48cd9a438732724899d07a9f211d299d6a0bab592f","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.CV","submitted_at":"2007-01-31T15:14:51Z","title_canon_sha256":"40f80b76aafebb5b201c5022e61a9d5b3eefde70352d9ebf10017b3dc32d4703"},"schema_version":"1.0","source":{"id":"math/0701927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701927","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701927v1","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701927","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"HKVUBWFZ34TK","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"HKVUBWFZ34TK27WU","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"HKVUBWFZ","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:eee9e46a0203718ac94f8733dbc0be3a647d25df150d41989c0b6677c209434e","target":"graph","created_at":"2026-05-18T01:30:49Z","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 prove that every Kaehler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algebraic groups in the case where the isotropy has the property that its intersection with the radical is Zariski dense in the radical.","authors_text":"Bruce Gilligan, Karl Oeljeklaus","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"2007-01-31T15:14:51Z","title":"Two Remarks on Kaehler Homogeneous Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701927","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":"sha256:4c5ce85de6ccfda3c1a116a27d7351527afdbb229366a6cba70dc29b2ec92e63","target":"record","created_at":"2026-05-18T01:30:49Z","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":"8e998f0cba914841e0957b48cd9a438732724899d07a9f211d299d6a0bab592f","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.CV","submitted_at":"2007-01-31T15:14:51Z","title_canon_sha256":"40f80b76aafebb5b201c5022e61a9d5b3eefde70352d9ebf10017b3dc32d4703"},"schema_version":"1.0","source":{"id":"math/0701927","kind":"arxiv","version":1}},"canonical_sha256":"3aab40d8b9df26ad7ed4bcc68788f6b371bff4104591e010aa62e6b970e224e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aab40d8b9df26ad7ed4bcc68788f6b371bff4104591e010aa62e6b970e224e2","first_computed_at":"2026-05-18T01:30:49.660637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:49.660637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NxSCu5udijf83Doc9QRxf8eERbNwTKhSeDzykZP+3buYWD6lVoe/rZk2WXmnA8jX2yr5QhIyD5ysDotE41fjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:49.661218Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c5ce85de6ccfda3c1a116a27d7351527afdbb229366a6cba70dc29b2ec92e63","sha256:eee9e46a0203718ac94f8733dbc0be3a647d25df150d41989c0b6677c209434e"],"state_sha256":"4419f04adef05910686746adf1dbb660e8092515c9a26a27f439faaecdedfc9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Pzy4POXNhcoUAey8/fAFb7NSdICewnc+F4CpGWldzAjwheV4XhwOAdHtdA42/NkFyTKpTvuo2rHlI1PWQ0KDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:14:49.083138Z","bundle_sha256":"ba3a26e38cea6f1aec6b1f0ba03d9d72cda86d0bad79cdc81e883d353873412b"}}