{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EFWLJOZ27CFFSPXRAXBTYRISSA","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":"fe5fd9c06582a6b95afa33335dac247da67395da162212981191ef3e32370310","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-15T16:36:33Z","title_canon_sha256":"3c30828ef2f963a8645ec40891cfb00e8f3a73889fceea6573994427c227dada"},"schema_version":"1.0","source":{"id":"1010.3211","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3211","created_at":"2026-05-18T02:55:50Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3211v3","created_at":"2026-05-18T02:55:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3211","created_at":"2026-05-18T02:55:50Z"},{"alias_kind":"pith_short_12","alias_value":"EFWLJOZ27CFF","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EFWLJOZ27CFFSPXR","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EFWLJOZ2","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:c35d01743737bb4ebee42fc6ec4ecc591dbc3a8db85ceb2feb5474a29cd80cdf","target":"graph","created_at":"2026-05-18T02:55:50Z","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":"We prove that for a sufficiently ample line bundle $L$ on a surface $S$, the number of $\\delta$-nodal curves in a general $\\delta$-dimensional linear system is given by a universal polynomial of degree $\\delta$ in the four numbers $L^2,\\,L.K_S,\\,K_S^2$ and $c_2(S)$.\n  The technique is a study of Hilbert schemes of points on curves on a surface, using the BPS calculus of [PT3] and the computation of tautological integrals on Hilbert schemes by Ellingsrud, G\\\"ottsche and Lehn.\n  We are also able to weaken the ampleness required, from G\\\"ottsche's $(5\\delta-1)$-very ample to $\\delta$-very ample.","authors_text":"M. Kool, R. P. Thomas, V. Shende","cross_cats":["hep-th","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-15T16:36:33Z","title":"A short proof of the G\\\"ottsche conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3211","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":"sha256:8029741a9818a48b95cc53dbe45ff9e780e6692addc0aee60801ac3e50352aad","target":"record","created_at":"2026-05-18T02:55:50Z","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":"fe5fd9c06582a6b95afa33335dac247da67395da162212981191ef3e32370310","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-15T16:36:33Z","title_canon_sha256":"3c30828ef2f963a8645ec40891cfb00e8f3a73889fceea6573994427c227dada"},"schema_version":"1.0","source":{"id":"1010.3211","kind":"arxiv","version":3}},"canonical_sha256":"216cb4bb3af88a593ef105c33c45129013c793061d5d8f8f4e5f0a3899af46aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"216cb4bb3af88a593ef105c33c45129013c793061d5d8f8f4e5f0a3899af46aa","first_computed_at":"2026-05-18T02:55:50.173099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:50.173099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZvcYrS/lDchsL4Dh27KEMhcLdx8ZdIJVX6JxLDVkMEc+Lq9m6Vu/7e0bs/SVQFB3C5yMLL9Wp6/1+ioWRpm3Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:50.173584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3211","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8029741a9818a48b95cc53dbe45ff9e780e6692addc0aee60801ac3e50352aad","sha256:c35d01743737bb4ebee42fc6ec4ecc591dbc3a8db85ceb2feb5474a29cd80cdf"],"state_sha256":"1822b0384b00ab08d2c0586208e016c52434cdcdee96534df7ad7d4220c656c8"}