{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:YMGXJLQACPEYKUIKYXTES3WKLY","short_pith_number":"pith:YMGXJLQA","schema_version":"1.0","canonical_sha256":"c30d74ae0013c985510ac5e6496eca5e2ddd79329e597cb589f3eafdaaec9d12","source":{"kind":"arxiv","id":"math/0611714","version":3},"attestation_state":"computed","paper":{"title":"Stable bundles on hypercomplex surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Misha Verbitsky, Ruxandra Moraru","submitted_at":"2006-11-23T02:31:27Z","abstract_excerpt":"A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsion. In the language of Hitchin's and Gualtieri's generalized complex geometry, (4,4)-ma"},"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":"math/0611714","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-11-23T02:31:27Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"edce5fb0d050a7d6d88bf1c912199f122ff9a312250de03afbefd0dce3fa5b73","abstract_canon_sha256":"96ba4e694c70ed867e546059dcc07db7dce7eaa43e19e1d2d678dba67cd5b867"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:43.397074Z","signature_b64":"pTYTBN1OCwUjQhehvf5tGJD7NhP16IkwPhUDCPve0CDhJPM9ssM0qST7V6+cAe6ZIi6AwqxWm4J9F9luLcBaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c30d74ae0013c985510ac5e6496eca5e2ddd79329e597cb589f3eafdaaec9d12","last_reissued_at":"2026-05-18T04:42:43.396664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:43.396664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable bundles on hypercomplex surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Misha Verbitsky, Ruxandra Moraru","submitted_at":"2006-11-23T02:31:27Z","abstract_excerpt":"A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsion. In the language of Hitchin's and Gualtieri's generalized complex geometry, (4,4)-ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611714","kind":"arxiv","version":3},"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":"math/0611714","created_at":"2026-05-18T04:42:43.396719+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0611714v3","created_at":"2026-05-18T04:42:43.396719+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611714","created_at":"2026-05-18T04:42:43.396719+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMGXJLQACPEY","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMGXJLQACPEYKUIK","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMGXJLQA","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2511.20568","citing_title":"On the rigidity of special and exceptional geometries with torsion a closed $3$-form","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YMGXJLQACPEYKUIKYXTES3WKLY","json":"https://pith.science/pith/YMGXJLQACPEYKUIKYXTES3WKLY.json","graph_json":"https://pith.science/api/pith-number/YMGXJLQACPEYKUIKYXTES3WKLY/graph.json","events_json":"https://pith.science/api/pith-number/YMGXJLQACPEYKUIKYXTES3WKLY/events.json","paper":"https://pith.science/paper/YMGXJLQA"},"agent_actions":{"view_html":"https://pith.science/pith/YMGXJLQACPEYKUIKYXTES3WKLY","download_json":"https://pith.science/pith/YMGXJLQACPEYKUIKYXTES3WKLY.json","view_paper":"https://pith.science/paper/YMGXJLQA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0611714&json=true","fetch_graph":"https://pith.science/api/pith-number/YMGXJLQACPEYKUIKYXTES3WKLY/graph.json","fetch_events":"https://pith.science/api/pith-number/YMGXJLQACPEYKUIKYXTES3WKLY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMGXJLQACPEYKUIKYXTES3WKLY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMGXJLQACPEYKUIKYXTES3WKLY/action/storage_attestation","attest_author":"https://pith.science/pith/YMGXJLQACPEYKUIKYXTES3WKLY/action/author_attestation","sign_citation":"https://pith.science/pith/YMGXJLQACPEYKUIKYXTES3WKLY/action/citation_signature","submit_replication":"https://pith.science/pith/YMGXJLQACPEYKUIKYXTES3WKLY/action/replication_record"}},"created_at":"2026-05-18T04:42:43.396719+00:00","updated_at":"2026-05-18T04:42:43.396719+00:00"}