{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:M2BUP4J7EXFNZ7WWPW6L3DNE4X","short_pith_number":"pith:M2BUP4J7","canonical_record":{"source":{"id":"1104.0996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-06T02:58:31Z","cross_cats_sorted":[],"title_canon_sha256":"ecc9f35ce7c2ae17b6c377ff5cbedcdceae7299579231856cf01c9701b1cfd9d","abstract_canon_sha256":"3b5293edbfa83c255d303ba2a9e7fac4e9943bb7eaa2f27358e879e0c43ee9cf"},"schema_version":"1.0"},"canonical_sha256":"668347f13f25cadcfed67dbcbd8da4e5e068519b046471fc9d8c016c483b9624","source":{"kind":"arxiv","id":"1104.0996","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0996","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0996v1","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0996","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"M2BUP4J7EXFN","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M2BUP4J7EXFNZ7WW","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M2BUP4J7","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:M2BUP4J7EXFNZ7WWPW6L3DNE4X","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-06T02:58:31Z","cross_cats_sorted":[],"title_canon_sha256":"ecc9f35ce7c2ae17b6c377ff5cbedcdceae7299579231856cf01c9701b1cfd9d","abstract_canon_sha256":"3b5293edbfa83c255d303ba2a9e7fac4e9943bb7eaa2f27358e879e0c43ee9cf"},"schema_version":"1.0"},"canonical_sha256":"668347f13f25cadcfed67dbcbd8da4e5e068519b046471fc9d8c016c483b9624","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:53.828575Z","signature_b64":"9ezZMvTPumqgeWq8EWjLk8hnX2sj39QLJXLNKTXN8PMfu4WYI57K0ovZNooYW2hDfQRqwecjVy5kGdXnIqEpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"668347f13f25cadcfed67dbcbd8da4e5e068519b046471fc9d8c016c483b9624","last_reissued_at":"2026-05-18T04:24:53.827873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:53.827873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0996","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":"2026-05-18T04:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5OAR+7lHb0KJO6pha7pNsYnjlykiJAZjZmWr6KlGsvyJUmbypkXCPRtthY8zyMFmk3nToG5LzThWe35vFAAyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:10:15.602122Z"},"content_sha256":"4c0ce483355fe93b1c1ef8e093a087e4fcb9991e4d764f4dc0eb25cf34ecf010","schema_version":"1.0","event_id":"sha256:4c0ce483355fe93b1c1ef8e093a087e4fcb9991e4d764f4dc0eb25cf34ecf010"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:M2BUP4J7EXFNZ7WWPW6L3DNE4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Principal bundles on compact complex manifolds with trivial tangent bundle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Indranil Biswas","submitted_at":"2011-04-06T02:58:31Z","abstract_excerpt":"Let $G$ be a connected complex Lie group and $\\Gamma\\subset G$ a cocompact lattice. Let $H$ be a complex Lie group. We prove that a holomorphic principal $H$-bundle $E_H$ over $G/\\Gamma$ admits a holomorphic connection if and only if $E_H$ is invariant. If $G$ is simply connected, we show that a holomorphic principal $H$-bundle $E_H$ over $G/\\Gamma$ admits a flat holomorphic connection if and only if $E_H$ is homogeneous."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0996","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":"2026-05-18T04:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZoRvKMzuat05JSjCNSZMJbk+dNmJWJjkewXUA4gwbFgyuOr7X9b2aYYWAlHQVQi3CoUTskDEozTqtW8v7miBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:10:15.602473Z"},"content_sha256":"019cdcda4e0216b14b5eba2ed7cfdc4dcd534e04621ffac76226212900910c47","schema_version":"1.0","event_id":"sha256:019cdcda4e0216b14b5eba2ed7cfdc4dcd534e04621ffac76226212900910c47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2BUP4J7EXFNZ7WWPW6L3DNE4X/bundle.json","state_url":"https://pith.science/pith/M2BUP4J7EXFNZ7WWPW6L3DNE4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2BUP4J7EXFNZ7WWPW6L3DNE4X/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":"2026-06-02T03:10:15Z","links":{"resolver":"https://pith.science/pith/M2BUP4J7EXFNZ7WWPW6L3DNE4X","bundle":"https://pith.science/pith/M2BUP4J7EXFNZ7WWPW6L3DNE4X/bundle.json","state":"https://pith.science/pith/M2BUP4J7EXFNZ7WWPW6L3DNE4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2BUP4J7EXFNZ7WWPW6L3DNE4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:M2BUP4J7EXFNZ7WWPW6L3DNE4X","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":"3b5293edbfa83c255d303ba2a9e7fac4e9943bb7eaa2f27358e879e0c43ee9cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-06T02:58:31Z","title_canon_sha256":"ecc9f35ce7c2ae17b6c377ff5cbedcdceae7299579231856cf01c9701b1cfd9d"},"schema_version":"1.0","source":{"id":"1104.0996","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0996","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0996v1","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0996","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"M2BUP4J7EXFN","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M2BUP4J7EXFNZ7WW","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M2BUP4J7","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:019cdcda4e0216b14b5eba2ed7cfdc4dcd534e04621ffac76226212900910c47","target":"graph","created_at":"2026-05-18T04:24:53Z","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":"Let $G$ be a connected complex Lie group and $\\Gamma\\subset G$ a cocompact lattice. Let $H$ be a complex Lie group. We prove that a holomorphic principal $H$-bundle $E_H$ over $G/\\Gamma$ admits a holomorphic connection if and only if $E_H$ is invariant. If $G$ is simply connected, we show that a holomorphic principal $H$-bundle $E_H$ over $G/\\Gamma$ admits a flat holomorphic connection if and only if $E_H$ is homogeneous.","authors_text":"Indranil Biswas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-06T02:58:31Z","title":"Principal bundles on compact complex manifolds with trivial tangent bundle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0996","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":"sha256:4c0ce483355fe93b1c1ef8e093a087e4fcb9991e4d764f4dc0eb25cf34ecf010","target":"record","created_at":"2026-05-18T04:24:53Z","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":"3b5293edbfa83c255d303ba2a9e7fac4e9943bb7eaa2f27358e879e0c43ee9cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-06T02:58:31Z","title_canon_sha256":"ecc9f35ce7c2ae17b6c377ff5cbedcdceae7299579231856cf01c9701b1cfd9d"},"schema_version":"1.0","source":{"id":"1104.0996","kind":"arxiv","version":1}},"canonical_sha256":"668347f13f25cadcfed67dbcbd8da4e5e068519b046471fc9d8c016c483b9624","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"668347f13f25cadcfed67dbcbd8da4e5e068519b046471fc9d8c016c483b9624","first_computed_at":"2026-05-18T04:24:53.827873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:53.827873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ezZMvTPumqgeWq8EWjLk8hnX2sj39QLJXLNKTXN8PMfu4WYI57K0ovZNooYW2hDfQRqwecjVy5kGdXnIqEpDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:53.828575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0996","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c0ce483355fe93b1c1ef8e093a087e4fcb9991e4d764f4dc0eb25cf34ecf010","sha256:019cdcda4e0216b14b5eba2ed7cfdc4dcd534e04621ffac76226212900910c47"],"state_sha256":"27eed35ac489cb1378fa68b5eaaf41b5ce12fef7b2758355e41d42164056d4c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLQtFUeFC9oxSUVmhesfND6hzWt6kfPkn8v5fT8QMWZiz0pRjxnGKyP3gr5Ftjc77qjYnPtt4mmsCNkIMX13Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:10:15.604323Z","bundle_sha256":"415c92ef46382e2946ac78f50338a3490020fd54270f4bb35b604474ae4d4aa2"}}