{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:WOR56MAKQR74BAFQZXXHYYKBE4","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":"58e6094c3f7525d830d28002151fe3720e1f4b13f29bfd71c07eb7edf3ced388","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-02-04T18:13:43Z","title_canon_sha256":"35492ec78ae615ec928ba04c29871a20744b3d648855d065cb4b3b899de4c41b"},"schema_version":"1.0","source":{"id":"2102.02788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.02788","created_at":"2026-07-05T02:12:51Z"},{"alias_kind":"arxiv_version","alias_value":"2102.02788v1","created_at":"2026-07-05T02:12:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.02788","created_at":"2026-07-05T02:12:51Z"},{"alias_kind":"pith_short_12","alias_value":"WOR56MAKQR74","created_at":"2026-07-05T02:12:51Z"},{"alias_kind":"pith_short_16","alias_value":"WOR56MAKQR74BAFQ","created_at":"2026-07-05T02:12:51Z"},{"alias_kind":"pith_short_8","alias_value":"WOR56MAK","created_at":"2026-07-05T02:12:51Z"}],"graph_snapshots":[{"event_id":"sha256:ce3c292c8781d5662836175d8a83404a94ac8cea57322a0a53f350efd7c632b4","target":"graph","created_at":"2026-07-05T02:12:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.02788/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, a sequel to \"Global Frobenius Liftability I\" (math:1708:03777v2), we continue the development of a comprehensive theory of Frobenius liftings modulo $p^2$. We study compatibility of divisors and closed subschemes with Frobenius liftings, Frobenius liftings of blow-ups, descent under quotients by some group actions, stability under base change, and the properties of associated F-splittings. Consequently, we characterise Frobenius liftable surfaces and Fano threefolds, confirming the conjecture stated in our previous paper.","authors_text":"Jakub Witaszek, Maciej Zdanowicz, Piotr Achinger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-02-04T18:13:43Z","title":"Global Frobenius Liftability II: Surfaces and Fano Threefolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.02788","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":"sha256:27999d08e40165c280cdeea4e33e73167bd772aa53e99d2f615ecf7ef237373c","target":"record","created_at":"2026-07-05T02:12:51Z","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":"58e6094c3f7525d830d28002151fe3720e1f4b13f29bfd71c07eb7edf3ced388","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-02-04T18:13:43Z","title_canon_sha256":"35492ec78ae615ec928ba04c29871a20744b3d648855d065cb4b3b899de4c41b"},"schema_version":"1.0","source":{"id":"2102.02788","kind":"arxiv","version":1}},"canonical_sha256":"b3a3df300a847fc080b0cdee7c61412721d5b6e5ea378d43d43ac7ff7695b660","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3a3df300a847fc080b0cdee7c61412721d5b6e5ea378d43d43ac7ff7695b660","first_computed_at":"2026-07-05T02:12:51.542267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:12:51.542267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pDTsPF9R83zZybnZK4bczC1L7K7ekT8Y+acZe72VrYngoyPJUK8msM5ma14Z8h2Go56HfdWitaWjgxXLcVyICw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:12:51.542714Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.02788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27999d08e40165c280cdeea4e33e73167bd772aa53e99d2f615ecf7ef237373c","sha256:ce3c292c8781d5662836175d8a83404a94ac8cea57322a0a53f350efd7c632b4"],"state_sha256":"546ac1f19a15a4d149470f2f937bf6304071a1a8cd1656eae64a53894bf1594b"}