{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:B2DX5SVGHZDJUPKK54NYMKSSQJ","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":"bb2437ca1f60586618129f33f5c9d37c07362b97f1602b5cd5d01367f3e2131c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-16T13:58:33Z","title_canon_sha256":"2d089c7f8c181e1441f186c197f824362b0841fd6bfb00e29d93472ee3197b96"},"schema_version":"1.0","source":{"id":"1603.05104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05104","created_at":"2026-05-18T01:18:58Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05104v1","created_at":"2026-05-18T01:18:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05104","created_at":"2026-05-18T01:18:58Z"},{"alias_kind":"pith_short_12","alias_value":"B2DX5SVGHZDJ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"B2DX5SVGHZDJUPKK","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"B2DX5SVG","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:7a3deaa6bdcb15fd44a8d256f156de2fe093578f032df0d64adc09eb490dbfc3","target":"graph","created_at":"2026-05-18T01:18:58Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate the $W_2(k)$-liftability of singular schemes. We prove constructibility of the locus of $W_2(k)$-liftable schemes in a flat family $X \\to S$. Moreover, we construct an explicit $W_2(k)$-lifting of a Frobenius split scheme $X$ over a perfect field $k$, reproving Bhatt's existential result. Furthermore, we study existence of liftings of the Frobenius morphism. In particular, we prove that in dimension $n \\geq 4$ ordinary double points do not admit a $W_2(k)$-lifting compatible with Frobenius, and that canonical surface singularities are Frobenius liftable. Combined with Bhatt's re","authors_text":"Maciej Zdanowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-16T13:58:33Z","title":"Liftability of singularities and their Frobenius morphism modulo $p^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05104","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8dd6ca6d50c4dced4ebd46c7e8ae249eb7c54b251582811b82e59c6f69fb90d5","target":"record","created_at":"2026-05-18T01:18:58Z","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":"bb2437ca1f60586618129f33f5c9d37c07362b97f1602b5cd5d01367f3e2131c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-16T13:58:33Z","title_canon_sha256":"2d089c7f8c181e1441f186c197f824362b0841fd6bfb00e29d93472ee3197b96"},"schema_version":"1.0","source":{"id":"1603.05104","kind":"arxiv","version":1}},"canonical_sha256":"0e877ecaa63e469a3d4aef1b862a52824ea1cad1808e376a65a773ea1b0ad58d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e877ecaa63e469a3d4aef1b862a52824ea1cad1808e376a65a773ea1b0ad58d","first_computed_at":"2026-05-18T01:18:58.033894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:58.033894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AZzFfqsebGAD9XmPtPG8jy4uNkXX1Ribz2QM3eQ0PaYDG46wU+ML8bozjh1vptpTY6k0WpwKre9V+d4IkJbeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:58.034398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dd6ca6d50c4dced4ebd46c7e8ae249eb7c54b251582811b82e59c6f69fb90d5","sha256:7a3deaa6bdcb15fd44a8d256f156de2fe093578f032df0d64adc09eb490dbfc3"],"state_sha256":"e1bf8becb1d0fd6ed07f05fa8a6970f54ce6447ce7aad2d44231fccb2f909f04"}