{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FKRY5B3W7K4S5ORC3C4ONKTGFH","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":"d9b327c39055e24ccbb7ecac2f27887112415b5ba769ff450d827bc073332442","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-06T12:45:06Z","title_canon_sha256":"339c62657b6cefda062b25a6d737bc6979582ed2600b79c87f27c9754da46be9"},"schema_version":"1.0","source":{"id":"1312.1844","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1844","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1844v4","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1844","created_at":"2026-05-18T01:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"FKRY5B3W7K4S","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FKRY5B3W7K4S5ORC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FKRY5B3W","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:c930a76f38af0a7850c43eda8cf29636b192d90e25731de0bc802a8904bd0ee7","target":"graph","created_at":"2026-05-18T01:30:15Z","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 $C$ be a smooth projective complex curve of genus $g \\geq 2$. We investigate the Brill-Noether locus consisting of stable bundles of rank 2 and determinant $L$ of odd degree $d$ having at least $k$ independent sections. This locus possesses a virtual fundamental class. We show that in many cases this class is non-zero, which implies that the Brill-Noether locus is non-empty. For many values of $d$ and $k$ the result is best possible. We obtain more precise results for $k\\le5$. An appendix contains the proof of a combinatorial lemma which we need.","authors_text":"H. Lange, P. E. Newstead, V. Strehl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-06T12:45:06Z","title":"Non-emptiness of Brill-Noether loci in M(2,L)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1844","kind":"arxiv","version":4},"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":"sha256:18d8cecb7b702cbdb74d5783cb8b50467b8a1450211bca1ff99526914e935e93","target":"record","created_at":"2026-05-18T01:30:15Z","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":"d9b327c39055e24ccbb7ecac2f27887112415b5ba769ff450d827bc073332442","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-06T12:45:06Z","title_canon_sha256":"339c62657b6cefda062b25a6d737bc6979582ed2600b79c87f27c9754da46be9"},"schema_version":"1.0","source":{"id":"1312.1844","kind":"arxiv","version":4}},"canonical_sha256":"2aa38e8776fab92eba22d8b8e6aa6629cdd98a59c7f97aa77728ac7c5e3ae9c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2aa38e8776fab92eba22d8b8e6aa6629cdd98a59c7f97aa77728ac7c5e3ae9c7","first_computed_at":"2026-05-18T01:30:15.691340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:15.691340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UTob1ZrDnra56675vL39eJLdfF3ko8hVFXyWRYMHcFYDeospq2tRvGOitjDNLeIKL4zUuoL0Xp2Hlcby0Ou0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:15.691823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1844","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18d8cecb7b702cbdb74d5783cb8b50467b8a1450211bca1ff99526914e935e93","sha256:c930a76f38af0a7850c43eda8cf29636b192d90e25731de0bc802a8904bd0ee7"],"state_sha256":"f9dcda84b4fdda1b90e6f211e066b0d54f238325930207284a371b3737de79ac"}