{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EJSG7V7HOJI7NBBQS6PJKWLXDR","short_pith_number":"pith:EJSG7V7H","canonical_record":{"source":{"id":"1412.3032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-09T17:53:51Z","cross_cats_sorted":[],"title_canon_sha256":"1609461d005dcdb07e9cf171dbe3dd2e05d9d69574063111e92516c8ea551770","abstract_canon_sha256":"d4117a2b637d728a70d2cd1b1b909108a6c3b98dcaf78aac974737fb46a1849b"},"schema_version":"1.0"},"canonical_sha256":"22646fd7e77251f68430979e9559771c4e002581accf0ea48dae5a1cf1a11361","source":{"kind":"arxiv","id":"1412.3032","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3032","created_at":"2026-05-18T02:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3032v1","created_at":"2026-05-18T02:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3032","created_at":"2026-05-18T02:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"EJSG7V7HOJI7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EJSG7V7HOJI7NBBQ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EJSG7V7H","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EJSG7V7HOJI7NBBQS6PJKWLXDR","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-09T17:53:51Z","cross_cats_sorted":[],"title_canon_sha256":"1609461d005dcdb07e9cf171dbe3dd2e05d9d69574063111e92516c8ea551770","abstract_canon_sha256":"d4117a2b637d728a70d2cd1b1b909108a6c3b98dcaf78aac974737fb46a1849b"},"schema_version":"1.0"},"canonical_sha256":"22646fd7e77251f68430979e9559771c4e002581accf0ea48dae5a1cf1a11361","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:45.147928Z","signature_b64":"KW6Ey1DBz2N3FbPGu4LlP20V3qx6cmlxPEo2KFbSrZ1MMgHr2Xw+T8kMshl50O2MIZ3qdSZol1mIJK/cn/nvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22646fd7e77251f68430979e9559771c4e002581accf0ea48dae5a1cf1a11361","last_reissued_at":"2026-05-18T02:31:45.147191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:45.147191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3032","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGmBF1tMKW2m1OiHL0dencyy5DQfyWI5G4Yy9fYwhO6JFxl9q5qDU2d3WMhHvi/bc6lxG9SXCLHXvY4S/ZFTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:02:08.368734Z"},"content_sha256":"966a57524fe607f7ea3a45c020f00e1ff4f4b0f6f1abe3259d5f9d74fb61a04b","schema_version":"1.0","event_id":"sha256:966a57524fe607f7ea3a45c020f00e1ff4f4b0f6f1abe3259d5f9d74fb61a04b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EJSG7V7HOJI7NBBQS6PJKWLXDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Truncated Barsotti-Tate Groups and Displays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eike Lau, Thomas Zink","submitted_at":"2014-12-09T17:53:51Z","abstract_excerpt":"We define truncated displays over rings in which a prime p is nilpotent, we associate crystals to truncated displays, and we define functors from truncated displays to truncated Barsotti-Tate groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3032","kind":"arxiv","version":1},"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":"2026-05-18T02:31:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PlD/VxvKLjHrZpN7wMHr/5c5OYcak8ZkZ3TsBVAOObO76qRmmuERFua3z1BY9qrHyNRZf+ZPAOv6r2oSYMStBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:02:08.369093Z"},"content_sha256":"a5e4017c75c60c2f3de1bd53d18436ac6fcbe9848f829430120098d7e647d58f","schema_version":"1.0","event_id":"sha256:a5e4017c75c60c2f3de1bd53d18436ac6fcbe9848f829430120098d7e647d58f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJSG7V7HOJI7NBBQS6PJKWLXDR/bundle.json","state_url":"https://pith.science/pith/EJSG7V7HOJI7NBBQS6PJKWLXDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJSG7V7HOJI7NBBQS6PJKWLXDR/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":"2026-05-26T20:02:08Z","links":{"resolver":"https://pith.science/pith/EJSG7V7HOJI7NBBQS6PJKWLXDR","bundle":"https://pith.science/pith/EJSG7V7HOJI7NBBQS6PJKWLXDR/bundle.json","state":"https://pith.science/pith/EJSG7V7HOJI7NBBQS6PJKWLXDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJSG7V7HOJI7NBBQS6PJKWLXDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EJSG7V7HOJI7NBBQS6PJKWLXDR","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":"d4117a2b637d728a70d2cd1b1b909108a6c3b98dcaf78aac974737fb46a1849b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-09T17:53:51Z","title_canon_sha256":"1609461d005dcdb07e9cf171dbe3dd2e05d9d69574063111e92516c8ea551770"},"schema_version":"1.0","source":{"id":"1412.3032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3032","created_at":"2026-05-18T02:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3032v1","created_at":"2026-05-18T02:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3032","created_at":"2026-05-18T02:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"EJSG7V7HOJI7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EJSG7V7HOJI7NBBQ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EJSG7V7H","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:a5e4017c75c60c2f3de1bd53d18436ac6fcbe9848f829430120098d7e647d58f","target":"graph","created_at":"2026-05-18T02:31:45Z","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 define truncated displays over rings in which a prime p is nilpotent, we associate crystals to truncated displays, and we define functors from truncated displays to truncated Barsotti-Tate groups.","authors_text":"Eike Lau, Thomas Zink","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-09T17:53:51Z","title":"Truncated Barsotti-Tate Groups and Displays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3032","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":"sha256:966a57524fe607f7ea3a45c020f00e1ff4f4b0f6f1abe3259d5f9d74fb61a04b","target":"record","created_at":"2026-05-18T02:31:45Z","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":"d4117a2b637d728a70d2cd1b1b909108a6c3b98dcaf78aac974737fb46a1849b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-09T17:53:51Z","title_canon_sha256":"1609461d005dcdb07e9cf171dbe3dd2e05d9d69574063111e92516c8ea551770"},"schema_version":"1.0","source":{"id":"1412.3032","kind":"arxiv","version":1}},"canonical_sha256":"22646fd7e77251f68430979e9559771c4e002581accf0ea48dae5a1cf1a11361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22646fd7e77251f68430979e9559771c4e002581accf0ea48dae5a1cf1a11361","first_computed_at":"2026-05-18T02:31:45.147191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:45.147191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KW6Ey1DBz2N3FbPGu4LlP20V3qx6cmlxPEo2KFbSrZ1MMgHr2Xw+T8kMshl50O2MIZ3qdSZol1mIJK/cn/nvBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:45.147928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:966a57524fe607f7ea3a45c020f00e1ff4f4b0f6f1abe3259d5f9d74fb61a04b","sha256:a5e4017c75c60c2f3de1bd53d18436ac6fcbe9848f829430120098d7e647d58f"],"state_sha256":"ba8be2130ae183d0fa505bf1775e5e35ea74a716d6996aa9c060a1752484bbb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VqiZENE1mZ68/QSFqWXw/5F5A4qwHbx9fhH83wVPqkKFnvrJHwA4R/tMIFVPeUQrJFzJuWMrFNows4ME5QrLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:02:08.371556Z","bundle_sha256":"de1437d9507ea9bdcc3c3c0b1e63c47f5009884a8f5b90992140976259bf1f7e"}}