{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZP4DGQR6LDZPOIHO4BZAFY7PR6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0eab478ca895bc3f5ee04ca7af8cedde93608e43991307e395865c2e63e6d061","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-04-21T15:04:53Z","title_canon_sha256":"1a0da4460ef63f7dbb38148f27e5d27fbe63b8ac5bbb5fbda13056212bc04366"},"schema_version":"1.0","source":{"id":"2604.19546","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.19546","created_at":"2026-06-10T01:11:00Z"},{"alias_kind":"arxiv_version","alias_value":"2604.19546v3","created_at":"2026-06-10T01:11:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.19546","created_at":"2026-06-10T01:11:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZP4DGQR6LDZP","created_at":"2026-06-10T01:11:00Z"},{"alias_kind":"pith_short_16","alias_value":"ZP4DGQR6LDZPOIHO","created_at":"2026-06-10T01:11:00Z"},{"alias_kind":"pith_short_8","alias_value":"ZP4DGQR6","created_at":"2026-06-10T01:11:00Z"}],"graph_snapshots":[{"event_id":"sha256:d735cb8615efba51b957fc0f109b943b5525292eb44eae0d87551676a6b2776c","target":"graph","created_at":"2026-06-10T01:11:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"under Langer type positivity assumptions, we prove that π∗(D,x)⟶π∗(X,x) is an isomorphism for ∗∈{S,N,EN,F, EF,Loc,ELoc,ét,Eét,uni} over perfect fields."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The Langer-type positivity assumptions on the divisor D that are invoked for the isomorphism statements."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Under Langer-type positivity assumptions the fundamental group scheme of an ample divisor D is isomorphic to that of X for many variants including etale, unipotent, and local versions over perfect fields."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Langer positivity assumptions ensure that fundamental group schemes of ample divisors are isomorphic to those of the ambient schemes."}],"snapshot_sha256":"bca3f5ac8666faa80b973527b23e823be3da0f01966bffb5dfcc7d1d1dc06a4c"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-20T02:49:02.471029Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2604.19546/integrity.json","findings":[],"snapshot_sha256":"0f6ea496a2ceb61d506fa4be1d0dcc341263f4e2344b4d1d0eaf844aa121c149","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $k$ be a field, $X$ a connected scheme proper over $k$, $D\\subsetneq X$ an ample effective connected divisor, $x\\in D(k)$. For Tannakian categories $\\mathcal{C}_X$ and $\\mathcal{C}_D$ whose objects consist of vector bundles on $X$ and $D$ respectively, we establish general Tannakian criteria for the natural homomorphism \\(\\pi(\\mathcal{C}_D,x)\\to \\pi(\\mathcal{C}_X,x)\\) to be faithfully flat, a closed immersion, or an isomorphism. As applications, under Langer type positivity assumptions, we prove that \\(\\pi^{\\ast}(D,x)\\longrightarrow \\pi^{\\ast}(X,x)\\) is an isomorphism for $\\ast\\in\\{S,N,EN,","authors_text":"Lingguang Li, Niantao Tian","cross_cats":[],"headline":"Langer positivity assumptions ensure that fundamental group schemes of ample divisors are isomorphic to those of the ambient schemes.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-04-21T15:04:53Z","title":"The Lefschetz Type Theorem For Fundamental Group Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.19546","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-10T01:54:02.650228Z","id":"907e3d4b-e47d-42a6-b73a-bd477eeddb0a","model_set":{"reader":"grok-4.3"},"one_line_summary":"Under Langer-type positivity assumptions the fundamental group scheme of an ample divisor D is isomorphic to that of X for many variants including etale, unipotent, and local versions over perfect fields.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Langer positivity assumptions ensure that fundamental group schemes of ample divisors are isomorphic to those of the ambient schemes.","strongest_claim":"under Langer type positivity assumptions, we prove that π∗(D,x)⟶π∗(X,x) is an isomorphism for ∗∈{S,N,EN,F, EF,Loc,ELoc,ét,Eét,uni} over perfect fields.","weakest_assumption":"The Langer-type positivity assumptions on the divisor D that are invoked for the isomorphism statements."}},"verdict_id":"907e3d4b-e47d-42a6-b73a-bd477eeddb0a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1e77cae7699570976d276254162907ef11e27a43dd1c6c436897177c4014b892","target":"record","created_at":"2026-06-10T01:11:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0eab478ca895bc3f5ee04ca7af8cedde93608e43991307e395865c2e63e6d061","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-04-21T15:04:53Z","title_canon_sha256":"1a0da4460ef63f7dbb38148f27e5d27fbe63b8ac5bbb5fbda13056212bc04366"},"schema_version":"1.0","source":{"id":"2604.19546","kind":"arxiv","version":3}},"canonical_sha256":"cbf833423e58f2f720eee07202e3ef8f9c7e164bdb8dfefd039ec6233bb32d3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbf833423e58f2f720eee07202e3ef8f9c7e164bdb8dfefd039ec6233bb32d3a","first_computed_at":"2026-06-10T01:11:00.511406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:11:00.511406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0FJQEoTZrFpbx9yCvJpSp0/bajOK0iHGvtlZMJzalVsT29utgXD+bGAyuRd4Ct2oRhITSgn40Btju+EHh4xSCg==","signature_status":"signed_v1","signed_at":"2026-06-10T01:11:00.512498Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.19546","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e77cae7699570976d276254162907ef11e27a43dd1c6c436897177c4014b892","sha256:d735cb8615efba51b957fc0f109b943b5525292eb44eae0d87551676a6b2776c"],"state_sha256":"eeba459be5349d529af9376e8f87b80cb9adda05717d8660aee5c717bed78b91"}