{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HRROKOAYNSU3RWBB6LXBS2XPKB","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":"acca29a89e619c4c89f41997c3f4856cbda55798edbc6e2ed6a6de29ad5713f6","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-30T20:28:19Z","title_canon_sha256":"4511ad63b1200f3a66ef88aa0c60bedc30ed36c012d74f78ac7558450f35bb3b"},"schema_version":"1.0","source":{"id":"1610.09706","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09706","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09706v3","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09706","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"pith_short_12","alias_value":"HRROKOAYNSU3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HRROKOAYNSU3RWBB","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HRROKOAY","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:8e87d2cf071a48a8ae6c6d40e32f1373783e94b0bdfc45033f630dc45d4d738e","target":"graph","created_at":"2026-05-17T23:50:34Z","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":"For a perfect field $k$ of characteristic $p>0$ and a smooth and proper formal scheme $\\mathscr{X}$ over the ring of integers of a finite and totally ramified extension $K$ of $W(k)[1/p]$, we propose a cohomological construction of the Breuil-Kisin modules attached to the $p$-adic \\'etale cohomology $H^i_{\\mathrm{\\'et}}(\\mathscr{X}_{\\overline{K}},\\mathbf{Z}_p)$. We then prove that our proposal works when $p>2$, $i < p-1$, and the crystalline cohomology of the special fiber of $\\mathscr{X}$ is torsion-free in degrees $i$ and $i+1$.","authors_text":"Bryden Cais, Tong Liu","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-30T20:28:19Z","title":"Breuil-Kisin Modules via crystalline cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09706","kind":"arxiv","version":3},"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":"sha256:158792fe521388683167297f3148651b5474990d4438e1b307adcd8f5efe6f89","target":"record","created_at":"2026-05-17T23:50:34Z","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":"acca29a89e619c4c89f41997c3f4856cbda55798edbc6e2ed6a6de29ad5713f6","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-30T20:28:19Z","title_canon_sha256":"4511ad63b1200f3a66ef88aa0c60bedc30ed36c012d74f78ac7558450f35bb3b"},"schema_version":"1.0","source":{"id":"1610.09706","kind":"arxiv","version":3}},"canonical_sha256":"3c62e538186ca9b8d821f2ee196aef5054984dc920db5f2df49f7785b72ac2b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c62e538186ca9b8d821f2ee196aef5054984dc920db5f2df49f7785b72ac2b7","first_computed_at":"2026-05-17T23:50:34.483633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:34.483633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EQUaeOzHI3MzUyTDRmiNXQJNHup0wqhiY7FBZc854+ZRjrVCt5UAGtlTXod4ZTXcexxKTAUy+ZF7iP1eLlf6CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:34.484115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09706","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:158792fe521388683167297f3148651b5474990d4438e1b307adcd8f5efe6f89","sha256:8e87d2cf071a48a8ae6c6d40e32f1373783e94b0bdfc45033f630dc45d4d738e"],"state_sha256":"c21fc95d7a06b19e275ae2c995bfb906962b339bbda7dd42d7941a8ac3c1eede"}