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We prove that when $dim(X/{W})\\geq 2$ there exists an integer $d_0$, depending only on $X$, such that for any $d\\geq d_0$, any $Y\\in |H^{\\otimes d}|$ connected and smooth over ${W}$ and any $y\\in Y({W})$ the natural ${R}$-morphism of fundamental group schemes $\\pi_1(Y_R,y_R)\\to "},"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":"1111.3003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-13T12:08:00Z","cross_cats_sorted":[],"title_canon_sha256":"c4c83a3146581dedd63f05a8d19e64067cd5c976fa1b9262ba8a45499a427294","abstract_canon_sha256":"3d23866eac7c90cd668e881d088df89bd892deb1d43244c50ad32315762f5830"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:23.172606Z","signature_b64":"+12Nyxqx3yauH3wTFvPgHtOnDZmB7jmkuw4JBGh7UUdOveF66Y/LS/8fqGbH9XtWDKXTSsMk0Zf9qnsEgli7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b854017b4d815ef9ea8da09e7d089ea1ddbb1dd6077ddf2c4f4ee9295906b4f0","last_reissued_at":"2026-05-18T03:45:23.172097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:23.172097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Grothendieck-Lefschetz Theorem for a Family of Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Marco Antei, Vikram Mehta","submitted_at":"2011-11-13T12:08:00Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic $p>0$, $W$ the ring of Witt vectors over $k$ and ${R}$ the integral closure of $W$ in the algebraic closure ${\\bar{K}}$ of $K:=Frac(W)$; let moreover $X$ be a smooth, connected and projective scheme over $W$ and $H$ a relatively very ample line bundle over $X$. We prove that when $dim(X/{W})\\geq 2$ there exists an integer $d_0$, depending only on $X$, such that for any $d\\geq d_0$, any $Y\\in |H^{\\otimes d}|$ connected and smooth over ${W}$ and any $y\\in Y({W})$ the natural ${R}$-morphism of fundamental group schemes $\\pi_1(Y_R,y_R)\\to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3003","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":"1111.3003","created_at":"2026-05-18T03:45:23.172180+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.3003v1","created_at":"2026-05-18T03:45:23.172180+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3003","created_at":"2026-05-18T03:45:23.172180+00:00"},{"alias_kind":"pith_short_12","alias_value":"XBKAC62NQFPP","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"XBKAC62NQFPPT2UN","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"XBKAC62N","created_at":"2026-05-18T12:26:44.992195+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/XBKAC62NQFPPT2UNUCPH2CE6UH","json":"https://pith.science/pith/XBKAC62NQFPPT2UNUCPH2CE6UH.json","graph_json":"https://pith.science/api/pith-number/XBKAC62NQFPPT2UNUCPH2CE6UH/graph.json","events_json":"https://pith.science/api/pith-number/XBKAC62NQFPPT2UNUCPH2CE6UH/events.json","paper":"https://pith.science/paper/XBKAC62N"},"agent_actions":{"view_html":"https://pith.science/pith/XBKAC62NQFPPT2UNUCPH2CE6UH","download_json":"https://pith.science/pith/XBKAC62NQFPPT2UNUCPH2CE6UH.json","view_paper":"https://pith.science/paper/XBKAC62N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.3003&json=true","fetch_graph":"https://pith.science/api/pith-number/XBKAC62NQFPPT2UNUCPH2CE6UH/graph.json","fetch_events":"https://pith.science/api/pith-number/XBKAC62NQFPPT2UNUCPH2CE6UH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XBKAC62NQFPPT2UNUCPH2CE6UH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XBKAC62NQFPPT2UNUCPH2CE6UH/action/storage_attestation","attest_author":"https://pith.science/pith/XBKAC62NQFPPT2UNUCPH2CE6UH/action/author_attestation","sign_citation":"https://pith.science/pith/XBKAC62NQFPPT2UNUCPH2CE6UH/action/citation_signature","submit_replication":"https://pith.science/pith/XBKAC62NQFPPT2UNUCPH2CE6UH/action/replication_record"}},"created_at":"2026-05-18T03:45:23.172180+00:00","updated_at":"2026-05-18T03:45:23.172180+00:00"}