{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3YRHU2G73OJPJ3RTRITVB5VUTR","short_pith_number":"pith:3YRHU2G7","schema_version":"1.0","canonical_sha256":"de227a68dfdb92f4ee338a2750f6b49c6ac739c5660891b07c7fb54cad765cab","source":{"kind":"arxiv","id":"1808.07577","version":1},"attestation_state":"computed","paper":{"title":"Natural Cohomology on $\\mathbb{P}^1 \\times \\mathbb{P}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pablo Solis","submitted_at":"2018-08-22T22:07:50Z","abstract_excerpt":"A vector bundle on a projective variety has a natural cohomology if for every twist its cohomology is concentrated in a single degree. Eisenbud and Schreyer conjectured there should be vector bundles on $\\mathbb{P}^1 \\times \\mathbb{P}^1$ with natural cohomology with respect to bundles $\\mathcal{O}(1,0),\\mathcal{O}(0,1)$ with prescribed Hilbert polynomial. We prove this conjecture."},"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":"1808.07577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-08-22T22:07:50Z","cross_cats_sorted":[],"title_canon_sha256":"403e43b44ea3e0b541bfdd5ea1627f1a487c8b3e8ce04212a025033635c8a087","abstract_canon_sha256":"5c12edaf6a08bfba68a35b5e1277f6d52cb2f0df2428322c76ca33c3625ecb73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:26.883270Z","signature_b64":"m97vER2vpm4ewA9K3chm6V7s2AEig/lzuyCH8X78EXzz0d/laMtoxnEGI9BgjhucVfVCgkUshGaub9jm+mpfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de227a68dfdb92f4ee338a2750f6b49c6ac739c5660891b07c7fb54cad765cab","last_reissued_at":"2026-05-18T00:07:26.882575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:26.882575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Natural Cohomology on $\\mathbb{P}^1 \\times \\mathbb{P}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pablo Solis","submitted_at":"2018-08-22T22:07:50Z","abstract_excerpt":"A vector bundle on a projective variety has a natural cohomology if for every twist its cohomology is concentrated in a single degree. Eisenbud and Schreyer conjectured there should be vector bundles on $\\mathbb{P}^1 \\times \\mathbb{P}^1$ with natural cohomology with respect to bundles $\\mathcal{O}(1,0),\\mathcal{O}(0,1)$ with prescribed Hilbert polynomial. We prove this conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07577","kind":"arxiv","version":1},"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":"1808.07577","created_at":"2026-05-18T00:07:26.882683+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.07577v1","created_at":"2026-05-18T00:07:26.882683+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07577","created_at":"2026-05-18T00:07:26.882683+00:00"},{"alias_kind":"pith_short_12","alias_value":"3YRHU2G73OJP","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"3YRHU2G73OJPJ3RT","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"3YRHU2G7","created_at":"2026-05-18T12:32:05.422762+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/3YRHU2G73OJPJ3RTRITVB5VUTR","json":"https://pith.science/pith/3YRHU2G73OJPJ3RTRITVB5VUTR.json","graph_json":"https://pith.science/api/pith-number/3YRHU2G73OJPJ3RTRITVB5VUTR/graph.json","events_json":"https://pith.science/api/pith-number/3YRHU2G73OJPJ3RTRITVB5VUTR/events.json","paper":"https://pith.science/paper/3YRHU2G7"},"agent_actions":{"view_html":"https://pith.science/pith/3YRHU2G73OJPJ3RTRITVB5VUTR","download_json":"https://pith.science/pith/3YRHU2G73OJPJ3RTRITVB5VUTR.json","view_paper":"https://pith.science/paper/3YRHU2G7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.07577&json=true","fetch_graph":"https://pith.science/api/pith-number/3YRHU2G73OJPJ3RTRITVB5VUTR/graph.json","fetch_events":"https://pith.science/api/pith-number/3YRHU2G73OJPJ3RTRITVB5VUTR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3YRHU2G73OJPJ3RTRITVB5VUTR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3YRHU2G73OJPJ3RTRITVB5VUTR/action/storage_attestation","attest_author":"https://pith.science/pith/3YRHU2G73OJPJ3RTRITVB5VUTR/action/author_attestation","sign_citation":"https://pith.science/pith/3YRHU2G73OJPJ3RTRITVB5VUTR/action/citation_signature","submit_replication":"https://pith.science/pith/3YRHU2G73OJPJ3RTRITVB5VUTR/action/replication_record"}},"created_at":"2026-05-18T00:07:26.882683+00:00","updated_at":"2026-05-18T00:07:26.882683+00:00"}