{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GDX42NK6XOGNNLDIEBJPPZ7NIS","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":"bcfb1b658aa208d3fb3c1b44a5e49446fc87507666fb1549b3f37fca75430028","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-02T14:49:38Z","title_canon_sha256":"20545abf0a0fb268cfe04ecf175b0a18ce501dc631342d31d79434946b9c348e"},"schema_version":"1.0","source":{"id":"1404.0577","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0577","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0577v2","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0577","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"GDX42NK6XOGN","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GDX42NK6XOGNNLDI","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GDX42NK6","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:09f0a747d243a75adfffda261975ba3ae3c7153179f71a0f2f5364147b362998","target":"graph","created_at":"2026-05-18T00:58:55Z","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 show that the zip stratification given by an arbitrary $\\Ghat$-zip over a scheme is pure. We deduce purity of the level-$m$-stratification for truncated Barsotti-Tate groups and purity of the Ekedahl-Oort stratification for special fibers of good models of Shimura varieties of Hodge type. We also show that all Ekedahl-Oort strata are quasi-affine schemes and generalize several properties of the Bruhat stratification from the PEL case to the case of Shimura varieties of Hodge type.","authors_text":"Torsten Wedhorn, Yaroslav Yatsyshyn","cross_cats":["math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-02T14:49:38Z","title":"Purity of Zip Strata with Applications to Ekedahl-Oort Strata of Shimura Varieties of Hodge Type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0577","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:be961d96038a25ed04c1a1870a0b4f08cc33d19b9e846a4cdc9bea747b1a668b","target":"record","created_at":"2026-05-18T00:58:55Z","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":"bcfb1b658aa208d3fb3c1b44a5e49446fc87507666fb1549b3f37fca75430028","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-02T14:49:38Z","title_canon_sha256":"20545abf0a0fb268cfe04ecf175b0a18ce501dc631342d31d79434946b9c348e"},"schema_version":"1.0","source":{"id":"1404.0577","kind":"arxiv","version":2}},"canonical_sha256":"30efcd355ebb8cd6ac682052f7e7ed44b895dcea596af46baf902e184ee4c125","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30efcd355ebb8cd6ac682052f7e7ed44b895dcea596af46baf902e184ee4c125","first_computed_at":"2026-05-18T00:58:55.744500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:55.744500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TaI5QnMYNDaDK6j9mwuKw4lBKxZBKy/wAHSKN+FVOiOSfEAjqOcMMpT5DwCI0oYB4nN+AE3gH+6C5xlugZDsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:55.744970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0577","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be961d96038a25ed04c1a1870a0b4f08cc33d19b9e846a4cdc9bea747b1a668b","sha256:09f0a747d243a75adfffda261975ba3ae3c7153179f71a0f2f5364147b362998"],"state_sha256":"8f9353882a612c2a53ada9d6d645a1f2a804b9d75fb3e294c3f0b2d1ace98ea5"}