{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:G4ZWCCURIGPUHU4EPV52MQ2QD7","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":"70eb8577bcc5bf847182bda1e8686a2ea2b1819a92b4b16f7d082806e37924fd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-09-22T01:49:24Z","title_canon_sha256":"549337716853bd849621664930d36f9d62b9c52afea9cc00741b2e6e2ba49ea9"},"schema_version":"1.0","source":{"id":"2109.10483","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.10483","created_at":"2026-07-05T03:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"2109.10483v2","created_at":"2026-07-05T03:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.10483","created_at":"2026-07-05T03:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"G4ZWCCURIGPU","created_at":"2026-07-05T03:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"G4ZWCCURIGPUHU4E","created_at":"2026-07-05T03:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"G4ZWCCUR","created_at":"2026-07-05T03:22:12Z"}],"graph_snapshots":[{"event_id":"sha256:98f3f1448fac84f8e284ef3dd6748918acfb4da173d54e6d61a092ae60b7c86d","target":"graph","created_at":"2026-07-05T03:22:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.10483/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use Bott-Samelson resolutions of Schubert varieties in Grassmannians along with equiariant localization techniques to show that the factorial Schur functions and the factorial Grothendieck polynomials represent Schubert classes in equivariant cohomology and equivariant K-theory respectively.","authors_text":"David Oetjen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-09-22T01:49:24Z","title":"Factorial Schur and Grothendieck polynomials from Bott Samelson varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10483","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:ab795cab869bd2f80e71ce0ba1594cc8840e58c13bad4da08c9a266e147647f7","target":"record","created_at":"2026-07-05T03:22:12Z","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":"70eb8577bcc5bf847182bda1e8686a2ea2b1819a92b4b16f7d082806e37924fd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-09-22T01:49:24Z","title_canon_sha256":"549337716853bd849621664930d36f9d62b9c52afea9cc00741b2e6e2ba49ea9"},"schema_version":"1.0","source":{"id":"2109.10483","kind":"arxiv","version":2}},"canonical_sha256":"3733610a91419f43d3847d7ba643501ffd299a6bf06711e95df14e40af8ff881","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3733610a91419f43d3847d7ba643501ffd299a6bf06711e95df14e40af8ff881","first_computed_at":"2026-07-05T03:22:12.756719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:22:12.756719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uy/bluAzI5ioY7ofRVWAmuUAfM8mpZqwd1ebsmr7slYVg2cVvkTvXNUzTgjGCtDqhm2za8vjmecKH8bVy93EAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:22:12.757130Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.10483","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab795cab869bd2f80e71ce0ba1594cc8840e58c13bad4da08c9a266e147647f7","sha256:98f3f1448fac84f8e284ef3dd6748918acfb4da173d54e6d61a092ae60b7c86d"],"state_sha256":"22fea5ae0899ee9d1a7b3a30dbe23eb8c1131294af3f3d95ca375f96c123bad8"}