{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:XCNAKFC6HPYEUQ4X4X5D4BWKOX","short_pith_number":"pith:XCNAKFC6","schema_version":"1.0","canonical_sha256":"b89a05145e3bf04a4397e5fa3e06ca75cd444210c213e3de119f138b6b5f6566","source":{"kind":"arxiv","id":"math/9904102","version":1},"attestation_state":"computed","paper":{"title":"Restriction of stable rank two vector bundles in arbitrary characteristic","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Georg Hein","submitted_at":"1999-04-20T13:21:42Z","abstract_excerpt":"Let $X$ be a smooth variety defined over an algebraically closed field of arbitrary characteristic and $\\O_X(H)$ be a very ample line bundle on $X$. We show that for a semistable $X$-bundle $E$ of rank two, there exists an integer $m$ depending only on $\\Delta(E).H^{\\dim(X)-2}$ and $H^{\\dim(X)}$ such that the restriction of $E$ to a general divisor in $|mH|$ is again semistable. As corollaries we obtain boundedness results, and weak versions of Bogomolov's theorem and Kodaira's vanishing theorem for surfaces in arbitrary characteristic."},"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":"math/9904102","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1999-04-20T13:21:42Z","cross_cats_sorted":[],"title_canon_sha256":"245b18817b31eb2273048adacfafed4009c130ad59a831c3217a22f5773a560e","abstract_canon_sha256":"3dc5ec4c867d0d2abe2f486dca2fa63d1c88ebe5d39548f60b9f6980ea1cc302"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:33.111478Z","signature_b64":"X6Ift9rUDiUgfiFLOm0bATrr+4kJyMrxD/vht2GpfZDPHSmIHDkgN3KCimNrR94e7n9K+j4G12JHet1siUS5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b89a05145e3bf04a4397e5fa3e06ca75cd444210c213e3de119f138b6b5f6566","last_reissued_at":"2026-05-18T01:05:33.110814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:33.110814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Restriction of stable rank two vector bundles in arbitrary characteristic","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Georg Hein","submitted_at":"1999-04-20T13:21:42Z","abstract_excerpt":"Let $X$ be a smooth variety defined over an algebraically closed field of arbitrary characteristic and $\\O_X(H)$ be a very ample line bundle on $X$. We show that for a semistable $X$-bundle $E$ of rank two, there exists an integer $m$ depending only on $\\Delta(E).H^{\\dim(X)-2}$ and $H^{\\dim(X)}$ such that the restriction of $E$ to a general divisor in $|mH|$ is again semistable. As corollaries we obtain boundedness results, and weak versions of Bogomolov's theorem and Kodaira's vanishing theorem for surfaces in arbitrary characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9904102","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":"math/9904102","created_at":"2026-05-18T01:05:33.110905+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9904102v1","created_at":"2026-05-18T01:05:33.110905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9904102","created_at":"2026-05-18T01:05:33.110905+00:00"},{"alias_kind":"pith_short_12","alias_value":"XCNAKFC6HPYE","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_16","alias_value":"XCNAKFC6HPYEUQ4X","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_8","alias_value":"XCNAKFC6","created_at":"2026-05-18T12:25:49.631198+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/XCNAKFC6HPYEUQ4X4X5D4BWKOX","json":"https://pith.science/pith/XCNAKFC6HPYEUQ4X4X5D4BWKOX.json","graph_json":"https://pith.science/api/pith-number/XCNAKFC6HPYEUQ4X4X5D4BWKOX/graph.json","events_json":"https://pith.science/api/pith-number/XCNAKFC6HPYEUQ4X4X5D4BWKOX/events.json","paper":"https://pith.science/paper/XCNAKFC6"},"agent_actions":{"view_html":"https://pith.science/pith/XCNAKFC6HPYEUQ4X4X5D4BWKOX","download_json":"https://pith.science/pith/XCNAKFC6HPYEUQ4X4X5D4BWKOX.json","view_paper":"https://pith.science/paper/XCNAKFC6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9904102&json=true","fetch_graph":"https://pith.science/api/pith-number/XCNAKFC6HPYEUQ4X4X5D4BWKOX/graph.json","fetch_events":"https://pith.science/api/pith-number/XCNAKFC6HPYEUQ4X4X5D4BWKOX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XCNAKFC6HPYEUQ4X4X5D4BWKOX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XCNAKFC6HPYEUQ4X4X5D4BWKOX/action/storage_attestation","attest_author":"https://pith.science/pith/XCNAKFC6HPYEUQ4X4X5D4BWKOX/action/author_attestation","sign_citation":"https://pith.science/pith/XCNAKFC6HPYEUQ4X4X5D4BWKOX/action/citation_signature","submit_replication":"https://pith.science/pith/XCNAKFC6HPYEUQ4X4X5D4BWKOX/action/replication_record"}},"created_at":"2026-05-18T01:05:33.110905+00:00","updated_at":"2026-05-18T01:05:33.110905+00:00"}