{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:UBBXZYD2VIYULWRSMT2R7KSZH3","short_pith_number":"pith:UBBXZYD2","canonical_record":{"source":{"id":"math/0009252","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2000-09-01T00:00:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dc6f75a327444453f5804fc5976b5a5cd934754a4f28c26bca7b0f604c3e4387","abstract_canon_sha256":"e9a1dfb1071be4546d5ac608abf38d620e5a03a84d73a39c32d9d8a7ba01bc4d"},"schema_version":"1.0"},"canonical_sha256":"a0437ce07aaa3145da3264f51faa593ed2302aadb4e3e35d8816cd80b8fe6667","source":{"kind":"arxiv","id":"math/0009252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0009252","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0009252v1","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0009252","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"UBBXZYD2VIYU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"UBBXZYD2VIYULWRS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"UBBXZYD2","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:UBBXZYD2VIYULWRSMT2R7KSZH3","target":"record","payload":{"canonical_record":{"source":{"id":"math/0009252","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2000-09-01T00:00:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dc6f75a327444453f5804fc5976b5a5cd934754a4f28c26bca7b0f604c3e4387","abstract_canon_sha256":"e9a1dfb1071be4546d5ac608abf38d620e5a03a84d73a39c32d9d8a7ba01bc4d"},"schema_version":"1.0"},"canonical_sha256":"a0437ce07aaa3145da3264f51faa593ed2302aadb4e3e35d8816cd80b8fe6667","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:38.242612Z","signature_b64":"CCLmQ+9y+EMWPEnqWVozBgTkL6u8jR8mxtqdjjFSahpWrUqvRr5RQkWSTh9in+f0ULhF91IaAjz5+KYBU6yECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0437ce07aaa3145da3264f51faa593ed2302aadb4e3e35d8816cd80b8fe6667","last_reissued_at":"2026-05-18T01:05:38.241930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:38.241930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0009252","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":"2026-05-18T01:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rYUaL1m3xXiSAPj1RAYtSBQwR6hNdg9Qsdi4POmsjpdnSUwvtOfURuBMR/1En+ohrEW/wRbse5fsCQY0qQRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:04:02.669809Z"},"content_sha256":"75f46b4027e61a214b588caa0ee897477ebc67e6ba0df1a8285de276162c9a79","schema_version":"1.0","event_id":"sha256:75f46b4027e61a214b588caa0ee897477ebc67e6ba0df1a8285de276162c9a79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:UBBXZYD2VIYULWRSMT2R7KSZH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groupes p-divisibles, groupes finis et modules filtr\\'es","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Christophe Breuil","submitted_at":"2000-09-01T00:00:00Z","abstract_excerpt":"Let k be a perfect field of characteristic p>0. When p>2, Fontaine and Laffaille have classified p-divisibles groups and finite flat p-groups over the Witt vectors W(k) in terms of filtered modules. Still assuming p>2, we extend these classifications over an arbitrary complete discrete valuation ring A with unequal characteristic (0,p) and residue field k by using \"generalized\" filtered modules. In particular, there is no restriction on the ramification index. In the case k is included in \\bar{F}_p (and p>2), we then use this new classification to prove that any crystalline representation of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0009252","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":"2026-05-18T01:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EITKVKRE3MWklZxJg1wMowAd2yN4tGCVl/5iBvdbduDipEooXqdGFfsZDnNcN8ejmjLi/s4LjRx+Qc3rag5lAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:04:02.670464Z"},"content_sha256":"7608bbe5ed3051321aa416c397e6ac934117e286180b2fd9d5f4c1f7472117ca","schema_version":"1.0","event_id":"sha256:7608bbe5ed3051321aa416c397e6ac934117e286180b2fd9d5f4c1f7472117ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UBBXZYD2VIYULWRSMT2R7KSZH3/bundle.json","state_url":"https://pith.science/pith/UBBXZYD2VIYULWRSMT2R7KSZH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UBBXZYD2VIYULWRSMT2R7KSZH3/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":"2026-05-30T15:04:02Z","links":{"resolver":"https://pith.science/pith/UBBXZYD2VIYULWRSMT2R7KSZH3","bundle":"https://pith.science/pith/UBBXZYD2VIYULWRSMT2R7KSZH3/bundle.json","state":"https://pith.science/pith/UBBXZYD2VIYULWRSMT2R7KSZH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UBBXZYD2VIYULWRSMT2R7KSZH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:UBBXZYD2VIYULWRSMT2R7KSZH3","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":"e9a1dfb1071be4546d5ac608abf38d620e5a03a84d73a39c32d9d8a7ba01bc4d","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2000-09-01T00:00:00Z","title_canon_sha256":"dc6f75a327444453f5804fc5976b5a5cd934754a4f28c26bca7b0f604c3e4387"},"schema_version":"1.0","source":{"id":"math/0009252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0009252","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0009252v1","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0009252","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"UBBXZYD2VIYU","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"UBBXZYD2VIYULWRS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"UBBXZYD2","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:7608bbe5ed3051321aa416c397e6ac934117e286180b2fd9d5f4c1f7472117ca","target":"graph","created_at":"2026-05-18T01:05:38Z","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":"Let k be a perfect field of characteristic p>0. When p>2, Fontaine and Laffaille have classified p-divisibles groups and finite flat p-groups over the Witt vectors W(k) in terms of filtered modules. Still assuming p>2, we extend these classifications over an arbitrary complete discrete valuation ring A with unequal characteristic (0,p) and residue field k by using \"generalized\" filtered modules. In particular, there is no restriction on the ramification index. In the case k is included in \\bar{F}_p (and p>2), we then use this new classification to prove that any crystalline representation of t","authors_text":"Christophe Breuil","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2000-09-01T00:00:00Z","title":"Groupes p-divisibles, groupes finis et modules filtr\\'es"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0009252","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":"sha256:75f46b4027e61a214b588caa0ee897477ebc67e6ba0df1a8285de276162c9a79","target":"record","created_at":"2026-05-18T01:05:38Z","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":"e9a1dfb1071be4546d5ac608abf38d620e5a03a84d73a39c32d9d8a7ba01bc4d","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2000-09-01T00:00:00Z","title_canon_sha256":"dc6f75a327444453f5804fc5976b5a5cd934754a4f28c26bca7b0f604c3e4387"},"schema_version":"1.0","source":{"id":"math/0009252","kind":"arxiv","version":1}},"canonical_sha256":"a0437ce07aaa3145da3264f51faa593ed2302aadb4e3e35d8816cd80b8fe6667","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0437ce07aaa3145da3264f51faa593ed2302aadb4e3e35d8816cd80b8fe6667","first_computed_at":"2026-05-18T01:05:38.241930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:38.241930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CCLmQ+9y+EMWPEnqWVozBgTkL6u8jR8mxtqdjjFSahpWrUqvRr5RQkWSTh9in+f0ULhF91IaAjz5+KYBU6yECg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:38.242612Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0009252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75f46b4027e61a214b588caa0ee897477ebc67e6ba0df1a8285de276162c9a79","sha256:7608bbe5ed3051321aa416c397e6ac934117e286180b2fd9d5f4c1f7472117ca"],"state_sha256":"5a69b52ed126b2c81f984f56d785b2abe9a5e72ba397378e3812552898aabae9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pChdc61CoTQ2T4Gwc2evyYIBRaBxI5M3yy+vUOt8gg4AACidOzxKwl6WUszXLvXSiPk/mk+UgkXvve7lPYdKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:04:02.673556Z","bundle_sha256":"711a5529fc56e78e8515e8265645febbc94835f9837230ae6b63139363a00e3f"}}