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We show that $B^4(2,K_C)$ it has an irreducible component $\\mathcal B$ of dimension $3g-13$ on a general curve $C$ of genus $g\\geq 8$. Moreover, we show that for the general element $[E]$ of $\\mathcal B$, $E$ fits in a exact sequence $0\\to\\mathcal O_C(D)\\to E\\to K_C(-D)\\to 0$, with $D$ a general effective divisor of degree three, and the corresponding "},"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":"1411.4155","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-15T15:22:57Z","cross_cats_sorted":[],"title_canon_sha256":"1d6e1132a5385088274e521a2a68c149f1ff0b463f1f209845f589e2a434f2f7","abstract_canon_sha256":"4e4a6e6248e513a99578a2c9d29635ef1d297805296abcd97f28a27db39a82c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:28.501207Z","signature_b64":"jKP7/oLl1ikFtLmbXD8slb74lrXGAVnqxYQQaAWWPh5p5XUPP62Nc5g5ykM73jPlQw6r7mj/MC6wxzsN60EyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00dd0fb60db29885d05f9bd39e316292a07a7527129e04fff1c7d993305da9cc","last_reissued_at":"2026-05-18T02:20:28.500544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:28.500544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on Ruled surfaces and rank two bundles with canonical determinant and 4 sections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abel Castorena, Graciela Reyes-Ahumada","submitted_at":"2014-11-15T15:22:57Z","abstract_excerpt":"Let $C$ be a smooth irreducible complex projective curve of genus $g$ and let $B^k(2,K_C)$ be the Brill-Noether loci parametrizing classes of (semi)-stable vector bundles $E$ of rank two with canonical determinant over $C$ with $h^0(C,E)\\geq k$. We show that $B^4(2,K_C)$ it has an irreducible component $\\mathcal B$ of dimension $3g-13$ on a general curve $C$ of genus $g\\geq 8$. Moreover, we show that for the general element $[E]$ of $\\mathcal B$, $E$ fits in a exact sequence $0\\to\\mathcal O_C(D)\\to E\\to K_C(-D)\\to 0$, with $D$ a general effective divisor of degree three, and the corresponding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4155","kind":"arxiv","version":2},"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":"1411.4155","created_at":"2026-05-18T02:20:28.500640+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.4155v2","created_at":"2026-05-18T02:20:28.500640+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4155","created_at":"2026-05-18T02:20:28.500640+00:00"},{"alias_kind":"pith_short_12","alias_value":"ADOQ7NQNWKMI","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"ADOQ7NQNWKMILUC7","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"ADOQ7NQN","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ADOQ7NQNWKMILUC7TPJZ4MLCSK","json":"https://pith.science/pith/ADOQ7NQNWKMILUC7TPJZ4MLCSK.json","graph_json":"https://pith.science/api/pith-number/ADOQ7NQNWKMILUC7TPJZ4MLCSK/graph.json","events_json":"https://pith.science/api/pith-number/ADOQ7NQNWKMILUC7TPJZ4MLCSK/events.json","paper":"https://pith.science/paper/ADOQ7NQN"},"agent_actions":{"view_html":"https://pith.science/pith/ADOQ7NQNWKMILUC7TPJZ4MLCSK","download_json":"https://pith.science/pith/ADOQ7NQNWKMILUC7TPJZ4MLCSK.json","view_paper":"https://pith.science/paper/ADOQ7NQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.4155&json=true","fetch_graph":"https://pith.science/api/pith-number/ADOQ7NQNWKMILUC7TPJZ4MLCSK/graph.json","fetch_events":"https://pith.science/api/pith-number/ADOQ7NQNWKMILUC7TPJZ4MLCSK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ADOQ7NQNWKMILUC7TPJZ4MLCSK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ADOQ7NQNWKMILUC7TPJZ4MLCSK/action/storage_attestation","attest_author":"https://pith.science/pith/ADOQ7NQNWKMILUC7TPJZ4MLCSK/action/author_attestation","sign_citation":"https://pith.science/pith/ADOQ7NQNWKMILUC7TPJZ4MLCSK/action/citation_signature","submit_replication":"https://pith.science/pith/ADOQ7NQNWKMILUC7TPJZ4MLCSK/action/replication_record"}},"created_at":"2026-05-18T02:20:28.500640+00:00","updated_at":"2026-05-18T02:20:28.500640+00:00"}