{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BN5E37V6PC6K65F7YG4TYI3Y4X","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":"66a000b9151e2b041861079cfeb5d58f398b1899fc8aeb5e0a535b662756f0f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-05T15:16:16Z","title_canon_sha256":"d7694ba3e9de86d31cfff68bcda962b469ce509edc486439ecbca4cc80804273"},"schema_version":"1.0","source":{"id":"1502.01604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01604","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01604v1","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01604","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"pith_short_12","alias_value":"BN5E37V6PC6K","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BN5E37V6PC6K65F7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BN5E37V6","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:4b127d42928040483e16c60130f6ef8e2c31051fbeff280273cce3705fa27d08","target":"graph","created_at":"2026-05-18T02:27:51Z","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"},"paper":{"abstract_excerpt":"We extend the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. In particular, for a finite and totally ramified extension $F/\\mathbb Q_p$, and an arbitrary finite extension $K/F$, we construct a general class of infinite and totally wildly ramified extensions $K_\\infty/K$ so that the functor $V\\mapsto V|_{G_{K_\\infty}}$ is fully-faithfull on the category of $F$-crystalline representations $V$. We also establish a new classification of $F$-Barsotti-Tate groups via Kisin modules of height 1 which allows more general lifts of","authors_text":"Bryden Cais, Tong Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-05T15:16:16Z","title":"On F-crystalline representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01604","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:ad03e03542ab95142cb77710869bc337951eb3b059e4adeeda1f1602bb05bba5","target":"record","created_at":"2026-05-18T02:27:51Z","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":"66a000b9151e2b041861079cfeb5d58f398b1899fc8aeb5e0a535b662756f0f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-05T15:16:16Z","title_canon_sha256":"d7694ba3e9de86d31cfff68bcda962b469ce509edc486439ecbca4cc80804273"},"schema_version":"1.0","source":{"id":"1502.01604","kind":"arxiv","version":1}},"canonical_sha256":"0b7a4dfebe78bcaf74bfc1b93c2378e5f3fbd6bf71aa7378980d702af0f799c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b7a4dfebe78bcaf74bfc1b93c2378e5f3fbd6bf71aa7378980d702af0f799c1","first_computed_at":"2026-05-18T02:27:51.697133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:51.697133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2LRYDIjW1XmUZ8WwjleK2YsuUmzs78szdBTcTC21nkDEdWjOYM3K8nojcme4t38ayz1G8tA/sNkAvZJbsVTWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:51.697706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad03e03542ab95142cb77710869bc337951eb3b059e4adeeda1f1602bb05bba5","sha256:4b127d42928040483e16c60130f6ef8e2c31051fbeff280273cce3705fa27d08"],"state_sha256":"2784c2cb37f5ad78414cf20c87a6d84741a8c68b19bd18ff79c7b307add25bb5"}