{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YXIBQY3XKEXARN4N5I65JKQ5DA","short_pith_number":"pith:YXIBQY3X","schema_version":"1.0","canonical_sha256":"c5d0186377512e08b78dea3dd4aa1d180cc1b7c3491925a54c6082bead356d02","source":{"kind":"arxiv","id":"1109.5808","version":1},"attestation_state":"computed","paper":{"title":"Hermitian-Einstein connections on principal bundles over flat affine manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Indranil Biswas, John Loftin","submitted_at":"2011-09-27T09:06:37Z","abstract_excerpt":"Let $M$ be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric $g$ and a covariant constant volume form. Let $G$ be either a connected reductive complex linear algebraic group or the real locus of a split real form of a complex reductive group. We prove that a flat principal $G$-bundle $E_G$ over $M$ admits a Hermitian-Einstein structure if and only if $E_G$ is polystable. A polystable flat principal $G$--bundle over $M$ admits a unique Hermitian-Einstein connection. We also prove the existence and uniqueness of a Harder-Narasimhan filtration for "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1109.5808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-27T09:06:37Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6f753bd8eb0a69a8ddca5d4a3f4aee4028ae72d415fe7fac8a7d3e0d614ca66b","abstract_canon_sha256":"f131394f0d94215597f1737fb45d29d39138b14ae2de42c8a3039b7770617b7d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:11.153213Z","signature_b64":"SyNgOSA7+vDdYUyf44LJyqKwEDc7xCPar42wYTKFzOXSqvciOfndwIj/yQgCqgFmT3a5Yr3WAUKHwwA1lWI5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5d0186377512e08b78dea3dd4aa1d180cc1b7c3491925a54c6082bead356d02","last_reissued_at":"2026-05-18T04:12:11.152761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:11.152761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hermitian-Einstein connections on principal bundles over flat affine manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Indranil Biswas, John Loftin","submitted_at":"2011-09-27T09:06:37Z","abstract_excerpt":"Let $M$ be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric $g$ and a covariant constant volume form. Let $G$ be either a connected reductive complex linear algebraic group or the real locus of a split real form of a complex reductive group. We prove that a flat principal $G$-bundle $E_G$ over $M$ admits a Hermitian-Einstein structure if and only if $E_G$ is polystable. A polystable flat principal $G$--bundle over $M$ admits a unique Hermitian-Einstein connection. We also prove the existence and uniqueness of a Harder-Narasimhan filtration for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5808","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.5808","created_at":"2026-05-18T04:12:11.152843+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5808v1","created_at":"2026-05-18T04:12:11.152843+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5808","created_at":"2026-05-18T04:12:11.152843+00:00"},{"alias_kind":"pith_short_12","alias_value":"YXIBQY3XKEXA","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YXIBQY3XKEXARN4N","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YXIBQY3X","created_at":"2026-05-18T12:26:47.523578+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YXIBQY3XKEXARN4N5I65JKQ5DA","json":"https://pith.science/pith/YXIBQY3XKEXARN4N5I65JKQ5DA.json","graph_json":"https://pith.science/api/pith-number/YXIBQY3XKEXARN4N5I65JKQ5DA/graph.json","events_json":"https://pith.science/api/pith-number/YXIBQY3XKEXARN4N5I65JKQ5DA/events.json","paper":"https://pith.science/paper/YXIBQY3X"},"agent_actions":{"view_html":"https://pith.science/pith/YXIBQY3XKEXARN4N5I65JKQ5DA","download_json":"https://pith.science/pith/YXIBQY3XKEXARN4N5I65JKQ5DA.json","view_paper":"https://pith.science/paper/YXIBQY3X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5808&json=true","fetch_graph":"https://pith.science/api/pith-number/YXIBQY3XKEXARN4N5I65JKQ5DA/graph.json","fetch_events":"https://pith.science/api/pith-number/YXIBQY3XKEXARN4N5I65JKQ5DA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YXIBQY3XKEXARN4N5I65JKQ5DA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YXIBQY3XKEXARN4N5I65JKQ5DA/action/storage_attestation","attest_author":"https://pith.science/pith/YXIBQY3XKEXARN4N5I65JKQ5DA/action/author_attestation","sign_citation":"https://pith.science/pith/YXIBQY3XKEXARN4N5I65JKQ5DA/action/citation_signature","submit_replication":"https://pith.science/pith/YXIBQY3XKEXARN4N5I65JKQ5DA/action/replication_record"}},"created_at":"2026-05-18T04:12:11.152843+00:00","updated_at":"2026-05-18T04:12:11.152843+00:00"}