{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:R2VMSR2WPRGNDYKZY246GE67MA","short_pith_number":"pith:R2VMSR2W","schema_version":"1.0","canonical_sha256":"8eaac947567c4cd1e159c6b9e313df600d29d55ae8d4472ff462c8435a0a0127","source":{"kind":"arxiv","id":"1102.0276","version":3},"attestation_state":"computed","paper":{"title":"Higher rank Brill-Noether theory on sections of K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Angela Ortega, Gavril Farkas","submitted_at":"2011-02-01T20:57:48Z","abstract_excerpt":"We discuss the role of K3 surfaces in the context of Mercat's conjecture in higher rank Brill-Noether theory. Using liftings of Koszul classes, we show that Mercat's conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether-Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercat's conjecture in rank 3 fails even for curves lying on K3 surfaces with Picard number 1. Finally, we provide a detailed proof of Mercat's conjecture in rank 2 for general curves of genus 11, and describe explicitly the action of the Fourier-Muk"},"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":"1102.0276","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-01T20:57:48Z","cross_cats_sorted":[],"title_canon_sha256":"67f617c4681f729c1461a0968bdd88db1a5ef47dd669b5ea6d40387d21409580","abstract_canon_sha256":"306cb6d35f2f26a9b656ceb303dd984e380d64a3ef43a58b3936fa814b6bc7aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:29.722456Z","signature_b64":"l3wN3EoU7b9Q2Dkb9J0oklO2NZ+ZRwOonEXq1/N9UyUncmJgpzUl4lvOyifhg160RYLWCUjqiSGc3P8OOE5kBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8eaac947567c4cd1e159c6b9e313df600d29d55ae8d4472ff462c8435a0a0127","last_reissued_at":"2026-05-18T03:43:29.721913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:29.721913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher rank Brill-Noether theory on sections of K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Angela Ortega, Gavril Farkas","submitted_at":"2011-02-01T20:57:48Z","abstract_excerpt":"We discuss the role of K3 surfaces in the context of Mercat's conjecture in higher rank Brill-Noether theory. Using liftings of Koszul classes, we show that Mercat's conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether-Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercat's conjecture in rank 3 fails even for curves lying on K3 surfaces with Picard number 1. Finally, we provide a detailed proof of Mercat's conjecture in rank 2 for general curves of genus 11, and describe explicitly the action of the Fourier-Muk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0276","kind":"arxiv","version":3},"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":"1102.0276","created_at":"2026-05-18T03:43:29.721997+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.0276v3","created_at":"2026-05-18T03:43:29.721997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0276","created_at":"2026-05-18T03:43:29.721997+00:00"},{"alias_kind":"pith_short_12","alias_value":"R2VMSR2WPRGN","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"R2VMSR2WPRGNDYKZ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"R2VMSR2W","created_at":"2026-05-18T12:26:39.201973+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/R2VMSR2WPRGNDYKZY246GE67MA","json":"https://pith.science/pith/R2VMSR2WPRGNDYKZY246GE67MA.json","graph_json":"https://pith.science/api/pith-number/R2VMSR2WPRGNDYKZY246GE67MA/graph.json","events_json":"https://pith.science/api/pith-number/R2VMSR2WPRGNDYKZY246GE67MA/events.json","paper":"https://pith.science/paper/R2VMSR2W"},"agent_actions":{"view_html":"https://pith.science/pith/R2VMSR2WPRGNDYKZY246GE67MA","download_json":"https://pith.science/pith/R2VMSR2WPRGNDYKZY246GE67MA.json","view_paper":"https://pith.science/paper/R2VMSR2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.0276&json=true","fetch_graph":"https://pith.science/api/pith-number/R2VMSR2WPRGNDYKZY246GE67MA/graph.json","fetch_events":"https://pith.science/api/pith-number/R2VMSR2WPRGNDYKZY246GE67MA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R2VMSR2WPRGNDYKZY246GE67MA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R2VMSR2WPRGNDYKZY246GE67MA/action/storage_attestation","attest_author":"https://pith.science/pith/R2VMSR2WPRGNDYKZY246GE67MA/action/author_attestation","sign_citation":"https://pith.science/pith/R2VMSR2WPRGNDYKZY246GE67MA/action/citation_signature","submit_replication":"https://pith.science/pith/R2VMSR2WPRGNDYKZY246GE67MA/action/replication_record"}},"created_at":"2026-05-18T03:43:29.721997+00:00","updated_at":"2026-05-18T03:43:29.721997+00:00"}