{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:F3XSHRKALEFYRXA6JQM5CMLVDO","short_pith_number":"pith:F3XSHRKA","canonical_record":{"source":{"id":"math/0107182","kind":"arxiv","version":11},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2001-07-24T23:38:06Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"800b32c6c3598ca5ffdf11aba2c897ba87415608fc9d85377982232e1c0f48d6","abstract_canon_sha256":"93450da4b7a3169ee8d384e96b043d9444de11c6ccb57673ae876a83ebc622cf"},"schema_version":"1.0"},"canonical_sha256":"2eef23c540590b88dc1e4c19d131751baa8ecbebea7b7cff8411671843ce74c5","source":{"kind":"arxiv","id":"math/0107182","version":11},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107182","created_at":"2026-05-18T04:27:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107182v11","created_at":"2026-05-18T04:27:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107182","created_at":"2026-05-18T04:27:02Z"},{"alias_kind":"pith_short_12","alias_value":"F3XSHRKALEFY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"F3XSHRKALEFYRXA6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"F3XSHRKA","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:F3XSHRKALEFYRXA6JQM5CMLVDO","target":"record","payload":{"canonical_record":{"source":{"id":"math/0107182","kind":"arxiv","version":11},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2001-07-24T23:38:06Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"800b32c6c3598ca5ffdf11aba2c897ba87415608fc9d85377982232e1c0f48d6","abstract_canon_sha256":"93450da4b7a3169ee8d384e96b043d9444de11c6ccb57673ae876a83ebc622cf"},"schema_version":"1.0"},"canonical_sha256":"2eef23c540590b88dc1e4c19d131751baa8ecbebea7b7cff8411671843ce74c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:02.898236Z","signature_b64":"nXlBCIohfCU3MRV51Ko1WlYyU3yPWzQAf+Hb2lOMzuN+Fd5/lrNSBOexjllWWOysF9m69qfxA++naZJ+CiPaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2eef23c540590b88dc1e4c19d131751baa8ecbebea7b7cff8411671843ce74c5","last_reissued_at":"2026-05-18T04:27:02.897583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:02.897583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0107182","source_version":11,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:27:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNS6YkeK32B6NzerymzQtt80PFAogfxz6KF+1B8WylsFlnt6WTMtJQuWlSFrmDSavydXj803CAKTtOycRw7nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:30:46.192828Z"},"content_sha256":"ef0abf3cde9e3dac0f9b2ea8b7368183b0896a55f7eaf291c97ffe51dceb2f54","schema_version":"1.0","event_id":"sha256:ef0abf3cde9e3dac0f9b2ea8b7368183b0896a55f7eaf291c97ffe51dceb2f54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:F3XSHRKALEFYRXA6JQM5CMLVDO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperholomorpic connections on coherent sheaves and stability","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Misha Verbitsky","submitted_at":"2001-07-24T23:38:06Z","abstract_excerpt":"Let $M$ be a hyperkaehler manifold, and $F$ a torsion-free and reflexive coherent sheaf on $M$. Assume that $F$ (outside of its singularities) admits a connection with a curvature which is invariant under the standard SU(2)-action on 2-forms. If the curvature is square-integrable, then $F$ is stable and its singularities are hyperkaehler subvarieties in $M$. Such sheaves (called hyperholomorphic sheaves) are well understood. In the present paper, we study sheaves admitting a connection with SU(2)-invariant curvature which is not necessarily square-integrable. This situation arises often, for i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107182","kind":"arxiv","version":11},"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":"2026-05-18T04:27:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FFXH6Gsyna73vMiPfqgdLUbjzxGS8sCNCZ+RB+L5VxTt3RFhb6jYcQ08GFmrphl41S2c7MaZWPYenCMvkktaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:30:46.193176Z"},"content_sha256":"4fc8948a05ba2cb4555418ea369aa0c29e9a10ab40f95846008c2760db3b5849","schema_version":"1.0","event_id":"sha256:4fc8948a05ba2cb4555418ea369aa0c29e9a10ab40f95846008c2760db3b5849"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3XSHRKALEFYRXA6JQM5CMLVDO/bundle.json","state_url":"https://pith.science/pith/F3XSHRKALEFYRXA6JQM5CMLVDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3XSHRKALEFYRXA6JQM5CMLVDO/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":"2026-06-01T17:30:46Z","links":{"resolver":"https://pith.science/pith/F3XSHRKALEFYRXA6JQM5CMLVDO","bundle":"https://pith.science/pith/F3XSHRKALEFYRXA6JQM5CMLVDO/bundle.json","state":"https://pith.science/pith/F3XSHRKALEFYRXA6JQM5CMLVDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3XSHRKALEFYRXA6JQM5CMLVDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:F3XSHRKALEFYRXA6JQM5CMLVDO","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":"93450da4b7a3169ee8d384e96b043d9444de11c6ccb57673ae876a83ebc622cf","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2001-07-24T23:38:06Z","title_canon_sha256":"800b32c6c3598ca5ffdf11aba2c897ba87415608fc9d85377982232e1c0f48d6"},"schema_version":"1.0","source":{"id":"math/0107182","kind":"arxiv","version":11}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0107182","created_at":"2026-05-18T04:27:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0107182v11","created_at":"2026-05-18T04:27:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0107182","created_at":"2026-05-18T04:27:02Z"},{"alias_kind":"pith_short_12","alias_value":"F3XSHRKALEFY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"F3XSHRKALEFYRXA6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"F3XSHRKA","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:4fc8948a05ba2cb4555418ea369aa0c29e9a10ab40f95846008c2760db3b5849","target":"graph","created_at":"2026-05-18T04:27:02Z","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 $M$ be a hyperkaehler manifold, and $F$ a torsion-free and reflexive coherent sheaf on $M$. Assume that $F$ (outside of its singularities) admits a connection with a curvature which is invariant under the standard SU(2)-action on 2-forms. If the curvature is square-integrable, then $F$ is stable and its singularities are hyperkaehler subvarieties in $M$. Such sheaves (called hyperholomorphic sheaves) are well understood. In the present paper, we study sheaves admitting a connection with SU(2)-invariant curvature which is not necessarily square-integrable. This situation arises often, for i","authors_text":"Misha Verbitsky","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2001-07-24T23:38:06Z","title":"Hyperholomorpic connections on coherent sheaves and stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107182","kind":"arxiv","version":11},"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:ef0abf3cde9e3dac0f9b2ea8b7368183b0896a55f7eaf291c97ffe51dceb2f54","target":"record","created_at":"2026-05-18T04:27:02Z","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":"93450da4b7a3169ee8d384e96b043d9444de11c6ccb57673ae876a83ebc622cf","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2001-07-24T23:38:06Z","title_canon_sha256":"800b32c6c3598ca5ffdf11aba2c897ba87415608fc9d85377982232e1c0f48d6"},"schema_version":"1.0","source":{"id":"math/0107182","kind":"arxiv","version":11}},"canonical_sha256":"2eef23c540590b88dc1e4c19d131751baa8ecbebea7b7cff8411671843ce74c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2eef23c540590b88dc1e4c19d131751baa8ecbebea7b7cff8411671843ce74c5","first_computed_at":"2026-05-18T04:27:02.897583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:02.897583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nXlBCIohfCU3MRV51Ko1WlYyU3yPWzQAf+Hb2lOMzuN+Fd5/lrNSBOexjllWWOysF9m69qfxA++naZJ+CiPaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:02.898236Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0107182","source_kind":"arxiv","source_version":11}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef0abf3cde9e3dac0f9b2ea8b7368183b0896a55f7eaf291c97ffe51dceb2f54","sha256:4fc8948a05ba2cb4555418ea369aa0c29e9a10ab40f95846008c2760db3b5849"],"state_sha256":"776c0225210ef20a30c6846e509ef98b6ef313f8cb0527ff93ab141886c430fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iz3gQnTeJrjgbjBA2lKCPnuOPHeSqCaIVWSeVZAELTMqiFzn9EEo2HOKyNd11BqjnQUOmQIaQccK4ifq7KxCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:30:46.195189Z","bundle_sha256":"1c8f442535b8948ad6508f048bc9e5b4f52b4322c0aef1e2bd95c8f6d3ae87de"}}