{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NC44ROXVTRBLVW6JXDUFX34N63","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":"8bf19aef83b96e5b6322e3080115d1cef1ca5ef541c848bbd1567b49f252c329","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-17T17:56:28Z","title_canon_sha256":"1fc322a50efbc1404129ee0cdbecbe184eccc4179a581671fbd8dd1d2616524d"},"schema_version":"1.0","source":{"id":"1603.05593","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05593","created_at":"2026-05-18T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05593v2","created_at":"2026-05-18T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05593","created_at":"2026-05-18T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"NC44ROXVTRBL","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NC44ROXVTRBLVW6J","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NC44ROXV","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:81d612508e29601f49a23b263240b295b58a9eda62c29ad4273be73cf3cc4be1","target":"graph","created_at":"2026-05-18T01:17:46Z","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 introduce various affine Grassmannians, study their geometric properties, and give some applications. We also discuss the geometric Satake equivalence. These are the expanded lecture notes for a mini-course in 2015 PCMI summer school. References updated and more details added.","authors_text":"Xinwen Zhu","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-17T17:56:28Z","title":"An introduction to affine Grassmannians and the geometric Satake equivalence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05593","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:fef323b39801aa8c8d90eb2d25b1e23f323d828c24f8f878b31bd9bb2ae8f712","target":"record","created_at":"2026-05-18T01:17:46Z","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":"8bf19aef83b96e5b6322e3080115d1cef1ca5ef541c848bbd1567b49f252c329","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-17T17:56:28Z","title_canon_sha256":"1fc322a50efbc1404129ee0cdbecbe184eccc4179a581671fbd8dd1d2616524d"},"schema_version":"1.0","source":{"id":"1603.05593","kind":"arxiv","version":2}},"canonical_sha256":"68b9c8baf59c42badbc9b8e85bef8df6cf5d6ce696cd2bdeca14237ac0feeac4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68b9c8baf59c42badbc9b8e85bef8df6cf5d6ce696cd2bdeca14237ac0feeac4","first_computed_at":"2026-05-18T01:17:46.771518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:46.771518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f/+jFE4k7BPidA778i6W1XEAgDOKPzTtWBLolSU1UIyHF2uTQmkfF6vY28AfWFGusWe6BtsCjKUeKJvwXSm9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:46.772186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05593","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fef323b39801aa8c8d90eb2d25b1e23f323d828c24f8f878b31bd9bb2ae8f712","sha256:81d612508e29601f49a23b263240b295b58a9eda62c29ad4273be73cf3cc4be1"],"state_sha256":"d90a134d1f1cff67ee0c8ffb8c19a6084ea6322e3f35f2812abf06ca505ed393"}