{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6AUQTYFPTBG4WSRKJLG5E6JL4Q","short_pith_number":"pith:6AUQTYFP","canonical_record":{"source":{"id":"1609.04490","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-15T01:46:05Z","cross_cats_sorted":[],"title_canon_sha256":"37b3ab9dcb655545ca8b5114b2d71928a424eed11f6f115ac9d9b3b129de5b0a","abstract_canon_sha256":"7d61bf55ca616e37e74249f1272e295e74a24dc74d0c5067c5bfac38aabe10aa"},"schema_version":"1.0"},"canonical_sha256":"f02909e0af984dcb4a2a4acdd2792be435b4ca6ce3764460c891d4e2637c3853","source":{"kind":"arxiv","id":"1609.04490","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04490","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04490v2","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04490","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"pith_short_12","alias_value":"6AUQTYFPTBG4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6AUQTYFPTBG4WSRK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6AUQTYFP","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6AUQTYFPTBG4WSRKJLG5E6JL4Q","target":"record","payload":{"canonical_record":{"source":{"id":"1609.04490","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-15T01:46:05Z","cross_cats_sorted":[],"title_canon_sha256":"37b3ab9dcb655545ca8b5114b2d71928a424eed11f6f115ac9d9b3b129de5b0a","abstract_canon_sha256":"7d61bf55ca616e37e74249f1272e295e74a24dc74d0c5067c5bfac38aabe10aa"},"schema_version":"1.0"},"canonical_sha256":"f02909e0af984dcb4a2a4acdd2792be435b4ca6ce3764460c891d4e2637c3853","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:52.292368Z","signature_b64":"ZgiwsLISMiYcOcq4dVBGni7TuwCgNdp8qnzWX1QklKRmIhUimd/57WSSGcwMHuc4x3DCwgNw8fBSFIAZT7zqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f02909e0af984dcb4a2a4acdd2792be435b4ca6ce3764460c891d4e2637c3853","last_reissued_at":"2026-05-18T00:44:52.291649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:52.291649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.04490","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5O9f4C/wGV3enzprAH4fwWqIf1UhU4ji/+anr4WJwbh4q0gIsXBm41/SniekvJI518u9WWuQBuayLGsUop38Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:38:16.804656Z"},"content_sha256":"4b3373ef5e8ad1c392c00e1f906250d95d2f2bada48835135534c14ba4f15b9e","schema_version":"1.0","event_id":"sha256:4b3373ef5e8ad1c392c00e1f906250d95d2f2bada48835135534c14ba4f15b9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6AUQTYFPTBG4WSRKJLG5E6JL4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lattices in crystalline representations and Kisin modules associated with iterate extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yoshiyasu Ozeki","submitted_at":"2016-09-15T01:46:05Z","abstract_excerpt":"Cais and Liu extended the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. Based on their theory, we classify lattices in crystalline representations by Kisin modules with additional structures under a Cais-Liu's setting. Furthermore, we give a geometric interpretation of Kisin modules of height one in terms of Dieudonn\\'e crystals of $p$-divisible groups, and show a full faithfulness theorem for a restriction functor on torsion crystalline representations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04490","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H0qd7EZ7bHApKjtV5DvMWhSWCg0Hqn4rYNI6SSpsJ0kFnsO84SAr40LhFyEsJ8x/GwWAFfFWlbljpd4RGrSKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:38:16.805009Z"},"content_sha256":"e66269de9cca473d72a72b8ba3d26d7c74728c49e4c91cc99a1f8c180789b612","schema_version":"1.0","event_id":"sha256:e66269de9cca473d72a72b8ba3d26d7c74728c49e4c91cc99a1f8c180789b612"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6AUQTYFPTBG4WSRKJLG5E6JL4Q/bundle.json","state_url":"https://pith.science/pith/6AUQTYFPTBG4WSRKJLG5E6JL4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6AUQTYFPTBG4WSRKJLG5E6JL4Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T04:38:16Z","links":{"resolver":"https://pith.science/pith/6AUQTYFPTBG4WSRKJLG5E6JL4Q","bundle":"https://pith.science/pith/6AUQTYFPTBG4WSRKJLG5E6JL4Q/bundle.json","state":"https://pith.science/pith/6AUQTYFPTBG4WSRKJLG5E6JL4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6AUQTYFPTBG4WSRKJLG5E6JL4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6AUQTYFPTBG4WSRKJLG5E6JL4Q","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":"7d61bf55ca616e37e74249f1272e295e74a24dc74d0c5067c5bfac38aabe10aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-15T01:46:05Z","title_canon_sha256":"37b3ab9dcb655545ca8b5114b2d71928a424eed11f6f115ac9d9b3b129de5b0a"},"schema_version":"1.0","source":{"id":"1609.04490","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04490","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04490v2","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04490","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"pith_short_12","alias_value":"6AUQTYFPTBG4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6AUQTYFPTBG4WSRK","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6AUQTYFP","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:e66269de9cca473d72a72b8ba3d26d7c74728c49e4c91cc99a1f8c180789b612","target":"graph","created_at":"2026-05-18T00:44:52Z","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":"Cais and Liu extended the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. Based on their theory, we classify lattices in crystalline representations by Kisin modules with additional structures under a Cais-Liu's setting. Furthermore, we give a geometric interpretation of Kisin modules of height one in terms of Dieudonn\\'e crystals of $p$-divisible groups, and show a full faithfulness theorem for a restriction functor on torsion crystalline representations.","authors_text":"Yoshiyasu Ozeki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-15T01:46:05Z","title":"Lattices in crystalline representations and Kisin modules associated with iterate extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04490","kind":"arxiv","version":2},"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":"sha256:4b3373ef5e8ad1c392c00e1f906250d95d2f2bada48835135534c14ba4f15b9e","target":"record","created_at":"2026-05-18T00:44:52Z","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":"7d61bf55ca616e37e74249f1272e295e74a24dc74d0c5067c5bfac38aabe10aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-15T01:46:05Z","title_canon_sha256":"37b3ab9dcb655545ca8b5114b2d71928a424eed11f6f115ac9d9b3b129de5b0a"},"schema_version":"1.0","source":{"id":"1609.04490","kind":"arxiv","version":2}},"canonical_sha256":"f02909e0af984dcb4a2a4acdd2792be435b4ca6ce3764460c891d4e2637c3853","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f02909e0af984dcb4a2a4acdd2792be435b4ca6ce3764460c891d4e2637c3853","first_computed_at":"2026-05-18T00:44:52.291649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:52.291649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgiwsLISMiYcOcq4dVBGni7TuwCgNdp8qnzWX1QklKRmIhUimd/57WSSGcwMHuc4x3DCwgNw8fBSFIAZT7zqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:52.292368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04490","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b3373ef5e8ad1c392c00e1f906250d95d2f2bada48835135534c14ba4f15b9e","sha256:e66269de9cca473d72a72b8ba3d26d7c74728c49e4c91cc99a1f8c180789b612"],"state_sha256":"479fabbbe847679ffc26a99ecebd3071a8750172c93a87db9cb77a567dd92744"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p+4hdyn2OdbsN8M9Xhq7bVx2VjNX70MR0qY3YilkYDqlehsJr0+6pFsGEcMzEdS59xuyzN67FS9QNSNA+Q98CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:38:16.806858Z","bundle_sha256":"f20b454d74fc5e3552a0569d13a0c6bde736e408ebe3256fb3336ff112aa3c16"}}