{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NC44ROXVTRBLVW6JXDUFX34N63","short_pith_number":"pith:NC44ROXV","schema_version":"1.0","canonical_sha256":"68b9c8baf59c42badbc9b8e85bef8df6cf5d6ce696cd2bdeca14237ac0feeac4","source":{"kind":"arxiv","id":"1603.05593","version":2},"attestation_state":"computed","paper":{"title":"An introduction to affine Grassmannians and the geometric Satake equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Xinwen Zhu","submitted_at":"2016-03-17T17:56:28Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.05593","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-17T17:56:28Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1fc322a50efbc1404129ee0cdbecbe184eccc4179a581671fbd8dd1d2616524d","abstract_canon_sha256":"8bf19aef83b96e5b6322e3080115d1cef1ca5ef541c848bbd1567b49f252c329"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:46.772186Z","signature_b64":"f/+jFE4k7BPidA778i6W1XEAgDOKPzTtWBLolSU1UIyHF2uTQmkfF6vY28AfWFGusWe6BtsCjKUeKJvwXSm9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68b9c8baf59c42badbc9b8e85bef8df6cf5d6ce696cd2bdeca14237ac0feeac4","last_reissued_at":"2026-05-18T01:17:46.771518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:46.771518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An introduction to affine Grassmannians and the geometric Satake equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Xinwen Zhu","submitted_at":"2016-03-17T17:56:28Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05593","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.05593","created_at":"2026-05-18T01:17:46.771615+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.05593v2","created_at":"2026-05-18T01:17:46.771615+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05593","created_at":"2026-05-18T01:17:46.771615+00:00"},{"alias_kind":"pith_short_12","alias_value":"NC44ROXVTRBL","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NC44ROXVTRBLVW6J","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NC44ROXV","created_at":"2026-05-18T12:30:32.724797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NC44ROXVTRBLVW6JXDUFX34N63","json":"https://pith.science/pith/NC44ROXVTRBLVW6JXDUFX34N63.json","graph_json":"https://pith.science/api/pith-number/NC44ROXVTRBLVW6JXDUFX34N63/graph.json","events_json":"https://pith.science/api/pith-number/NC44ROXVTRBLVW6JXDUFX34N63/events.json","paper":"https://pith.science/paper/NC44ROXV"},"agent_actions":{"view_html":"https://pith.science/pith/NC44ROXVTRBLVW6JXDUFX34N63","download_json":"https://pith.science/pith/NC44ROXVTRBLVW6JXDUFX34N63.json","view_paper":"https://pith.science/paper/NC44ROXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.05593&json=true","fetch_graph":"https://pith.science/api/pith-number/NC44ROXVTRBLVW6JXDUFX34N63/graph.json","fetch_events":"https://pith.science/api/pith-number/NC44ROXVTRBLVW6JXDUFX34N63/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NC44ROXVTRBLVW6JXDUFX34N63/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NC44ROXVTRBLVW6JXDUFX34N63/action/storage_attestation","attest_author":"https://pith.science/pith/NC44ROXVTRBLVW6JXDUFX34N63/action/author_attestation","sign_citation":"https://pith.science/pith/NC44ROXVTRBLVW6JXDUFX34N63/action/citation_signature","submit_replication":"https://pith.science/pith/NC44ROXVTRBLVW6JXDUFX34N63/action/replication_record"}},"created_at":"2026-05-18T01:17:46.771615+00:00","updated_at":"2026-05-18T01:17:46.771615+00:00"}