{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PGLIQWZ6U43IPE3KQQEFSGYDRM","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":"5eeef278f2d8ee34bf041e104fb8e8f50f08a07998d939cf7cfd3b7f729d2d3c","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-16T03:23:37Z","title_canon_sha256":"c66580b3a690a2fde993aaaf0d45632b8657afa40b488fb1e1b02928eeea0c81"},"schema_version":"1.0","source":{"id":"1301.3569","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3569","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3569v2","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3569","created_at":"2026-05-18T00:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"PGLIQWZ6U43I","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PGLIQWZ6U43IPE3K","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PGLIQWZ6","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:1b502bf9ef4f244315c9be1561b7e82f0e791983349c2007a47cb888d738f5bf","target":"graph","created_at":"2026-05-18T00:49:52Z","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":"This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled \"Affine Schubert Calculus\" that took place in July 2010 at the Fields Institute in Toronto, Ontario. The story of this research is told in three parts: 1. Primer on $k$-Schur Functions 2. Stanley symmetric functions and Peterson algebras 3. Affine Schubert calculus","authors_text":"Anne Schilling, Jennifer Morse, Luc Lapointe, Mark Shimozono, Mike Zabrocki, Thomas Lam","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-16T03:23:37Z","title":"$k$-Schur functions and affine Schubert calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3569","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:da23fb14b4c3b6ac6f2b1bf45ce1bcf5944fa7783f808b3ec0c5c466afc66c07","target":"record","created_at":"2026-05-18T00:49:52Z","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":"5eeef278f2d8ee34bf041e104fb8e8f50f08a07998d939cf7cfd3b7f729d2d3c","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-16T03:23:37Z","title_canon_sha256":"c66580b3a690a2fde993aaaf0d45632b8657afa40b488fb1e1b02928eeea0c81"},"schema_version":"1.0","source":{"id":"1301.3569","kind":"arxiv","version":2}},"canonical_sha256":"7996885b3ea73687936a8408591b038b29064eeef686c1a5d18841c59d893153","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7996885b3ea73687936a8408591b038b29064eeef686c1a5d18841c59d893153","first_computed_at":"2026-05-18T00:49:52.931895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:52.931895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M9trRKLcPgH9azEAqXMq9FG/vkKOiHrKgWXpBgdBS5+79EoviznOBcnb8d+5niPY1u9ezoLno3ZnrLM9sEaUBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:52.932454Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3569","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da23fb14b4c3b6ac6f2b1bf45ce1bcf5944fa7783f808b3ec0c5c466afc66c07","sha256:1b502bf9ef4f244315c9be1561b7e82f0e791983349c2007a47cb888d738f5bf"],"state_sha256":"8f52c8418658c37e26760e2122d2bb7766b3f2a32c41e74f6e79a3912aba29bc"}