{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VFQ7YVKXDIEU74XOE33QZTPNKY","short_pith_number":"pith:VFQ7YVKX","schema_version":"1.0","canonical_sha256":"a961fc55571a094ff2ee26f70ccded562a436ecb30b243ccf5823d4b179441d6","source":{"kind":"arxiv","id":"1611.09506","version":2},"attestation_state":"computed","paper":{"title":"On the existence of Ulrich bundles on geometrically ruled surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Gianfranco Casnati","submitted_at":"2016-11-29T06:36:21Z","abstract_excerpt":"Let $S$ be a geometrically ruled surface with invariant $e$ on a curve $C$. We deal with Ulrich line bundles and $\\mu$-stable special Ulrich bundles of rank $2$ on $S$ when $e\\ge0$, slightly extending a recent result due to M. Aprodu, L. Costa and R.M. Mir\\'o-Roig. If $C$ is elliptic, we also prove that $S$ always supports Ulrich bundles of rank at most $2$, without any restriction on $e$. Finally, we show that in many cases $S$ supports families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$."},"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":"1611.09506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-29T06:36:21Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"5ae95cb8e765c359c40137f82eb46b46f8259f62b2934c02f49e875c6835e659","abstract_canon_sha256":"574ca68185d502f6a8db0c14a11149420849e60cef7b9a9bda3393b90c79cc33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:11.671805Z","signature_b64":"I/n7xLsujcW8byx17JN/Ui66txt5bYqiM1rDggsWXdkLm4j649Izm3jkqTZ4WCiYVJIBuOCLhHsJosmb3eaNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a961fc55571a094ff2ee26f70ccded562a436ecb30b243ccf5823d4b179441d6","last_reissued_at":"2026-05-18T00:56:11.671370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:11.671370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence of Ulrich bundles on geometrically ruled surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Gianfranco Casnati","submitted_at":"2016-11-29T06:36:21Z","abstract_excerpt":"Let $S$ be a geometrically ruled surface with invariant $e$ on a curve $C$. We deal with Ulrich line bundles and $\\mu$-stable special Ulrich bundles of rank $2$ on $S$ when $e\\ge0$, slightly extending a recent result due to M. Aprodu, L. Costa and R.M. Mir\\'o-Roig. If $C$ is elliptic, we also prove that $S$ always supports Ulrich bundles of rank at most $2$, without any restriction on $e$. Finally, we show that in many cases $S$ supports families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09506","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":"1611.09506","created_at":"2026-05-18T00:56:11.671435+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.09506v2","created_at":"2026-05-18T00:56:11.671435+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09506","created_at":"2026-05-18T00:56:11.671435+00:00"},{"alias_kind":"pith_short_12","alias_value":"VFQ7YVKXDIEU","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VFQ7YVKXDIEU74XO","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VFQ7YVKX","created_at":"2026-05-18T12:30:48.956258+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/VFQ7YVKXDIEU74XOE33QZTPNKY","json":"https://pith.science/pith/VFQ7YVKXDIEU74XOE33QZTPNKY.json","graph_json":"https://pith.science/api/pith-number/VFQ7YVKXDIEU74XOE33QZTPNKY/graph.json","events_json":"https://pith.science/api/pith-number/VFQ7YVKXDIEU74XOE33QZTPNKY/events.json","paper":"https://pith.science/paper/VFQ7YVKX"},"agent_actions":{"view_html":"https://pith.science/pith/VFQ7YVKXDIEU74XOE33QZTPNKY","download_json":"https://pith.science/pith/VFQ7YVKXDIEU74XOE33QZTPNKY.json","view_paper":"https://pith.science/paper/VFQ7YVKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.09506&json=true","fetch_graph":"https://pith.science/api/pith-number/VFQ7YVKXDIEU74XOE33QZTPNKY/graph.json","fetch_events":"https://pith.science/api/pith-number/VFQ7YVKXDIEU74XOE33QZTPNKY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VFQ7YVKXDIEU74XOE33QZTPNKY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VFQ7YVKXDIEU74XOE33QZTPNKY/action/storage_attestation","attest_author":"https://pith.science/pith/VFQ7YVKXDIEU74XOE33QZTPNKY/action/author_attestation","sign_citation":"https://pith.science/pith/VFQ7YVKXDIEU74XOE33QZTPNKY/action/citation_signature","submit_replication":"https://pith.science/pith/VFQ7YVKXDIEU74XOE33QZTPNKY/action/replication_record"}},"created_at":"2026-05-18T00:56:11.671435+00:00","updated_at":"2026-05-18T00:56:11.671435+00:00"}