{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ZOYEFCECPIVKWXMQQPNWFJQI4P","short_pith_number":"pith:ZOYEFCEC","schema_version":"1.0","canonical_sha256":"cbb04288827a2aab5d9083db62a608e3cad12437ac93c55812bf0a5f8cb2e79b","source":{"kind":"arxiv","id":"1905.08555","version":6},"attestation_state":"computed","paper":{"title":"Breuil-Kisin modules and integral $p$-adic Hodge theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hui Gao","submitted_at":"2019-05-21T11:21:26Z","abstract_excerpt":"We construct a category of Breuil-Kisin $G_K$-modules to classify integral semi-stable Galois representations. Our theory uses Breuil-Kisin modules and Breuil-Kisin-Fargues modules with Galois actions, and can be regarded as the algebraic avatar of the integral $p$-adic cohomology theories of Bhatt-Morrow-Scholze and Bhatt-Scholze. As a key ingredient, we classify Galois representations that are of finite $E(u)$-height."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.08555","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-21T11:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"7f6311b2d4113269653fe6a3bb1165c9ca5568a7ab890f224e7a8ac74c7ccbe6","abstract_canon_sha256":"3cbef080fc781acc20021f19fb4ff11f5fc13e32b900d6130624cca582931c37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:45:48.063038Z","signature_b64":"TqcLF4qdK7ZuUGp9ZGCyvxNEjrCBx32FJOd6ORtrPqJvSnVhmpR6iu8jTN1f4Ay/MvxWKF+DRdDKmw/iWISxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbb04288827a2aab5d9083db62a608e3cad12437ac93c55812bf0a5f8cb2e79b","last_reissued_at":"2026-07-05T10:45:48.062588Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:45:48.062588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Breuil-Kisin modules and integral $p$-adic Hodge theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hui Gao","submitted_at":"2019-05-21T11:21:26Z","abstract_excerpt":"We construct a category of Breuil-Kisin $G_K$-modules to classify integral semi-stable Galois representations. Our theory uses Breuil-Kisin modules and Breuil-Kisin-Fargues modules with Galois actions, and can be regarded as the algebraic avatar of the integral $p$-adic cohomology theories of Bhatt-Morrow-Scholze and Bhatt-Scholze. As a key ingredient, we classify Galois representations that are of finite $E(u)$-height."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08555","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.08555/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.08555","created_at":"2026-07-05T10:45:48.062644+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.08555v6","created_at":"2026-07-05T10:45:48.062644+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08555","created_at":"2026-07-05T10:45:48.062644+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZOYEFCECPIVK","created_at":"2026-07-05T10:45:48.062644+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZOYEFCECPIVKWXMQ","created_at":"2026-07-05T10:45:48.062644+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZOYEFCEC","created_at":"2026-07-05T10:45:48.062644+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.07185","citing_title":"Moduli stacks of \\'etale (phi,Gamma)-modules and the existence of crystalline lifts","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZOYEFCECPIVKWXMQQPNWFJQI4P","json":"https://pith.science/pith/ZOYEFCECPIVKWXMQQPNWFJQI4P.json","graph_json":"https://pith.science/api/pith-number/ZOYEFCECPIVKWXMQQPNWFJQI4P/graph.json","events_json":"https://pith.science/api/pith-number/ZOYEFCECPIVKWXMQQPNWFJQI4P/events.json","paper":"https://pith.science/paper/ZOYEFCEC"},"agent_actions":{"view_html":"https://pith.science/pith/ZOYEFCECPIVKWXMQQPNWFJQI4P","download_json":"https://pith.science/pith/ZOYEFCECPIVKWXMQQPNWFJQI4P.json","view_paper":"https://pith.science/paper/ZOYEFCEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.08555&json=true","fetch_graph":"https://pith.science/api/pith-number/ZOYEFCECPIVKWXMQQPNWFJQI4P/graph.json","fetch_events":"https://pith.science/api/pith-number/ZOYEFCECPIVKWXMQQPNWFJQI4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZOYEFCECPIVKWXMQQPNWFJQI4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZOYEFCECPIVKWXMQQPNWFJQI4P/action/storage_attestation","attest_author":"https://pith.science/pith/ZOYEFCECPIVKWXMQQPNWFJQI4P/action/author_attestation","sign_citation":"https://pith.science/pith/ZOYEFCECPIVKWXMQQPNWFJQI4P/action/citation_signature","submit_replication":"https://pith.science/pith/ZOYEFCECPIVKWXMQQPNWFJQI4P/action/replication_record"}},"created_at":"2026-07-05T10:45:48.062644+00:00","updated_at":"2026-07-05T10:45:48.062644+00:00"}