{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DBFSCYMQQX5CAZWPM2I5FLBBNI","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":"0fec1c585ee9e821119cd740a752b7652ada06e3f2dfcfba4c47d5072bbf2690","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-29T12:27:26Z","title_canon_sha256":"7cbdbefb800784146c25576da2ffa2666f4e857fd19e7dfbb851a26f18057a74"},"schema_version":"1.0","source":{"id":"1202.6528","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6528","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6528v3","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6528","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"DBFSCYMQQX5C","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"DBFSCYMQQX5CAZWP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"DBFSCYMQ","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:f5ec012988298d26294e908accb9492129457a1a3c0bf53221ce28d1f0bca087","target":"graph","created_at":"2026-05-18T02:29:25Z","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 (X,H) be a polarized smooth projective surface satisfying H^1(X,O_X)=0 and let F be either a rank one torsion-free sheaf or a rank two {\\mu}H-stable vector bundle on X. Assume that c_1(F)/=0. In this article it is shown that the rank two, respectively rank four tautological sheaf F^{[2]} associated with F on the Hilbert square X^{[2]} is {\\mu}-stable with respect to a certain polarization.","authors_text":"Malte Wandel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-29T12:27:26Z","title":"Stability of tautological bundles on the Hilbert scheme of two points on a surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6528","kind":"arxiv","version":3},"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:b88794de70373fa501872710af88f3845dab24bb99a6f09be0c644c4b346ce75","target":"record","created_at":"2026-05-18T02:29:25Z","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":"0fec1c585ee9e821119cd740a752b7652ada06e3f2dfcfba4c47d5072bbf2690","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-29T12:27:26Z","title_canon_sha256":"7cbdbefb800784146c25576da2ffa2666f4e857fd19e7dfbb851a26f18057a74"},"schema_version":"1.0","source":{"id":"1202.6528","kind":"arxiv","version":3}},"canonical_sha256":"184b21619085fa2066cf6691d2ac216a3400abd22a6b130e9dcfc053cff8b49b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"184b21619085fa2066cf6691d2ac216a3400abd22a6b130e9dcfc053cff8b49b","first_computed_at":"2026-05-18T02:29:25.473977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:25.473977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O6G3GP8+R10SMZ2Rbi85vpa2eNYCfoTJAoh4cQV2a/oeUpk8SJ3KLJX0E1iPmqeCtxBCP0n2shfybPb45LmQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:25.474394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6528","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b88794de70373fa501872710af88f3845dab24bb99a6f09be0c644c4b346ce75","sha256:f5ec012988298d26294e908accb9492129457a1a3c0bf53221ce28d1f0bca087"],"state_sha256":"c2b0e1e0a76a7e2a6851d8086653d06cfde14a93b130c08fd9cf05186aafcc8c"}