{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:S67KE6YE6T4NFS54ZLYZH4E4RW","short_pith_number":"pith:S67KE6YE","canonical_record":{"source":{"id":"1502.05121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-18T05:26:21Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"f4dd405f93c1874d1c8ddc9fc39387ae2c421ed4c7e2c96938af9d581a6380aa","abstract_canon_sha256":"3228edebe86850f5806c3604438d0624cde89d1823ed7b334431ca3acf95c8c3"},"schema_version":"1.0"},"canonical_sha256":"97bea27b04f4f8d2cbbccaf193f09c8da6e7365ceb74c88a2f2a5303e1151722","source":{"kind":"arxiv","id":"1502.05121","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05121","created_at":"2026-05-18T02:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05121v1","created_at":"2026-05-18T02:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05121","created_at":"2026-05-18T02:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"S67KE6YE6T4N","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S67KE6YE6T4NFS54","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S67KE6YE","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:S67KE6YE6T4NFS54ZLYZH4E4RW","target":"record","payload":{"canonical_record":{"source":{"id":"1502.05121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-18T05:26:21Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"f4dd405f93c1874d1c8ddc9fc39387ae2c421ed4c7e2c96938af9d581a6380aa","abstract_canon_sha256":"3228edebe86850f5806c3604438d0624cde89d1823ed7b334431ca3acf95c8c3"},"schema_version":"1.0"},"canonical_sha256":"97bea27b04f4f8d2cbbccaf193f09c8da6e7365ceb74c88a2f2a5303e1151722","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:52.342623Z","signature_b64":"5ZFDkgJM/0z0g/Fd9U+lHp0mxZnKReWiuyFWuhnOSvyMoi+IG0G2892Am2/WVaOnRh/x7+m2Irnnn52ojhbpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97bea27b04f4f8d2cbbccaf193f09c8da6e7365ceb74c88a2f2a5303e1151722","last_reissued_at":"2026-05-18T02:26:52.342229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:52.342229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.05121","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":"2026-05-18T02:26:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NyP0VB4s9OHAZ/IBXoOVgzzNjyg1gw6vV86r8pV3Yl5LIHpX0QyrdD8jDoiU7pu1annUkZw9EfyQZeeaD52oDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:48:49.497305Z"},"content_sha256":"037f0ef5472f29ed062e0d2d0f97f61171297c1f32e10ad71d12fbf3d04d7457","schema_version":"1.0","event_id":"sha256:037f0ef5472f29ed062e0d2d0f97f61171297c1f32e10ad71d12fbf3d04d7457"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:S67KE6YE6T4NFS54ZLYZH4E4RW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semidirect products and invariant connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Indranil Biswas","submitted_at":"2015-02-18T05:26:21Z","abstract_excerpt":"Let $S$ be a complex reductive group acting holomorphically on a complex Lie group $N$ via holomorphic automorphisms. Let $K(S)\\subset S$ be a maximal compact subgroup. The semidirect product $G := N\\rtimes K(S)$ acts on $N$ via biholomorphisms. We give an explicit description of the isomorphism classes of $G$-equivariant almost holomorphic hermitian principal bundles on $N$. Under the assumption that there is a central subgroup $Z= \\text{U}(1)$ of $K(S)$ that acts on $\\text{Lie}(N)$ as multiplication through a single nontrivial character, we give an explicit description of the isomorphism cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05121","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":"2026-05-18T02:26:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8x0uds57e4TAVeekNYuGoN1Ji7bRw+esDBRsxNQZlp6tgQHrUOqHzAJUYdSBUv2kYI8DOTcpQslPjfE3pzq/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:48:49.498043Z"},"content_sha256":"1f9357af647dea37b02379b3b30ccd36b11268a6a9e27b2aeb8f421168f5239c","schema_version":"1.0","event_id":"sha256:1f9357af647dea37b02379b3b30ccd36b11268a6a9e27b2aeb8f421168f5239c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S67KE6YE6T4NFS54ZLYZH4E4RW/bundle.json","state_url":"https://pith.science/pith/S67KE6YE6T4NFS54ZLYZH4E4RW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S67KE6YE6T4NFS54ZLYZH4E4RW/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":"2026-06-08T18:48:49Z","links":{"resolver":"https://pith.science/pith/S67KE6YE6T4NFS54ZLYZH4E4RW","bundle":"https://pith.science/pith/S67KE6YE6T4NFS54ZLYZH4E4RW/bundle.json","state":"https://pith.science/pith/S67KE6YE6T4NFS54ZLYZH4E4RW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S67KE6YE6T4NFS54ZLYZH4E4RW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S67KE6YE6T4NFS54ZLYZH4E4RW","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":"3228edebe86850f5806c3604438d0624cde89d1823ed7b334431ca3acf95c8c3","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-18T05:26:21Z","title_canon_sha256":"f4dd405f93c1874d1c8ddc9fc39387ae2c421ed4c7e2c96938af9d581a6380aa"},"schema_version":"1.0","source":{"id":"1502.05121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05121","created_at":"2026-05-18T02:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05121v1","created_at":"2026-05-18T02:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05121","created_at":"2026-05-18T02:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"S67KE6YE6T4N","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S67KE6YE6T4NFS54","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S67KE6YE","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:1f9357af647dea37b02379b3b30ccd36b11268a6a9e27b2aeb8f421168f5239c","target":"graph","created_at":"2026-05-18T02:26:52Z","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 $S$ be a complex reductive group acting holomorphically on a complex Lie group $N$ via holomorphic automorphisms. Let $K(S)\\subset S$ be a maximal compact subgroup. The semidirect product $G := N\\rtimes K(S)$ acts on $N$ via biholomorphisms. We give an explicit description of the isomorphism classes of $G$-equivariant almost holomorphic hermitian principal bundles on $N$. Under the assumption that there is a central subgroup $Z= \\text{U}(1)$ of $K(S)$ that acts on $\\text{Lie}(N)$ as multiplication through a single nontrivial character, we give an explicit description of the isomorphism cla","authors_text":"Indranil Biswas","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-18T05:26:21Z","title":"Semidirect products and invariant connections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05121","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":"sha256:037f0ef5472f29ed062e0d2d0f97f61171297c1f32e10ad71d12fbf3d04d7457","target":"record","created_at":"2026-05-18T02:26:52Z","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":"3228edebe86850f5806c3604438d0624cde89d1823ed7b334431ca3acf95c8c3","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-18T05:26:21Z","title_canon_sha256":"f4dd405f93c1874d1c8ddc9fc39387ae2c421ed4c7e2c96938af9d581a6380aa"},"schema_version":"1.0","source":{"id":"1502.05121","kind":"arxiv","version":1}},"canonical_sha256":"97bea27b04f4f8d2cbbccaf193f09c8da6e7365ceb74c88a2f2a5303e1151722","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97bea27b04f4f8d2cbbccaf193f09c8da6e7365ceb74c88a2f2a5303e1151722","first_computed_at":"2026-05-18T02:26:52.342229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:52.342229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ZFDkgJM/0z0g/Fd9U+lHp0mxZnKReWiuyFWuhnOSvyMoi+IG0G2892Am2/WVaOnRh/x7+m2Irnnn52ojhbpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:52.342623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:037f0ef5472f29ed062e0d2d0f97f61171297c1f32e10ad71d12fbf3d04d7457","sha256:1f9357af647dea37b02379b3b30ccd36b11268a6a9e27b2aeb8f421168f5239c"],"state_sha256":"aeb713288d4d8c0fec4cfaf42c4192f88f0bf195f4aff3252038090018ef628e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fI47RDWL33HNo9FXkJWer14/CVfFku9ZIywe1WPHeQVB7wdrIbp7cdDBZSBknbxbHi6hRrc33jSpW1Fo0xX/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:48:49.501968Z","bundle_sha256":"86e625aa4cc62d6dc77f30702ddccd7cc4a473fe8ac7ccd2977be948a9e7ba84"}}