{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:H5UAMBVXEVCXT743PLPWOMPB76","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":"accc1611f33126ac072a5c9f724a39747e4c4ea1a266c7d6a21466b2f956e65d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-19T15:42:08Z","title_canon_sha256":"30f3899002054eb011734d1574b5720bca315aef7f7c4956d8a6aee07ff9688e"},"schema_version":"1.0","source":{"id":"1501.04526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04526","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04526v1","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04526","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"pith_short_12","alias_value":"H5UAMBVXEVCX","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H5UAMBVXEVCXT743","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H5UAMBVX","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:1eff78c8d8191009ccbad8ec0c3bbff26141330f5f807a21c84d7e622e011e5b","target":"graph","created_at":"2026-05-18T02:29:08Z","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":"In 1983, Faltings proved that there are only finitely many abelian varieties over a number field of fixed dimension and with good reduction outside a given set of places. In this paper, we consider the analogous problem for other algebraic groups and their homogeneous spaces, such as flag varieties.","authors_text":"Ariyan Javanpeykar, Daniel Loughran","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-19T15:42:08Z","title":"Good reduction of algebraic groups and flag varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04526","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:e9106901e433823d043f0a5fb3dfd50c209419944f55b21214b712f8f8edc67b","target":"record","created_at":"2026-05-18T02:29:08Z","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":"accc1611f33126ac072a5c9f724a39747e4c4ea1a266c7d6a21466b2f956e65d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-01-19T15:42:08Z","title_canon_sha256":"30f3899002054eb011734d1574b5720bca315aef7f7c4956d8a6aee07ff9688e"},"schema_version":"1.0","source":{"id":"1501.04526","kind":"arxiv","version":1}},"canonical_sha256":"3f680606b7254579ff9b7adf6731e1ffae3a3c605a3aedb7fea3aacba660d0aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f680606b7254579ff9b7adf6731e1ffae3a3c605a3aedb7fea3aacba660d0aa","first_computed_at":"2026-05-18T02:29:08.797458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:08.797458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AgDJpTTHYxe/A16zN8jb21Fqid+T1mtOeWWcCsLw/4fzfDVwdIBWzqEdpZNa4+TT80tEIQwuwa9tJCvZ11oTDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:08.798075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9106901e433823d043f0a5fb3dfd50c209419944f55b21214b712f8f8edc67b","sha256:1eff78c8d8191009ccbad8ec0c3bbff26141330f5f807a21c84d7e622e011e5b"],"state_sha256":"a558524509562ffe921ca58255f1de6917a062a8eedb6e3794a3e38895c9e611"}