{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PGLIQWZ6U43IPE3KQQEFSGYDRM","short_pith_number":"pith:PGLIQWZ6","schema_version":"1.0","canonical_sha256":"7996885b3ea73687936a8408591b038b29064eeef686c1a5d18841c59d893153","source":{"kind":"arxiv","id":"1301.3569","version":2},"attestation_state":"computed","paper":{"title":"$k$-Schur functions and affine Schubert calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Anne Schilling, Jennifer Morse, Luc Lapointe, Mark Shimozono, Mike Zabrocki, Thomas Lam","submitted_at":"2013-01-16T03:23:37Z","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"},"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":"1301.3569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-16T03:23:37Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c66580b3a690a2fde993aaaf0d45632b8657afa40b488fb1e1b02928eeea0c81","abstract_canon_sha256":"5eeef278f2d8ee34bf041e104fb8e8f50f08a07998d939cf7cfd3b7f729d2d3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:52.932454Z","signature_b64":"M9trRKLcPgH9azEAqXMq9FG/vkKOiHrKgWXpBgdBS5+79EoviznOBcnb8d+5niPY1u9ezoLno3ZnrLM9sEaUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7996885b3ea73687936a8408591b038b29064eeef686c1a5d18841c59d893153","last_reissued_at":"2026-05-18T00:49:52.931895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:52.931895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$k$-Schur functions and affine Schubert calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Anne Schilling, Jennifer Morse, Luc Lapointe, Mark Shimozono, Mike Zabrocki, Thomas Lam","submitted_at":"2013-01-16T03:23:37Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3569","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":"1301.3569","created_at":"2026-05-18T00:49:52.931976+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.3569v2","created_at":"2026-05-18T00:49:52.931976+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3569","created_at":"2026-05-18T00:49:52.931976+00:00"},{"alias_kind":"pith_short_12","alias_value":"PGLIQWZ6U43I","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PGLIQWZ6U43IPE3K","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PGLIQWZ6","created_at":"2026-05-18T12:27:54.935989+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/PGLIQWZ6U43IPE3KQQEFSGYDRM","json":"https://pith.science/pith/PGLIQWZ6U43IPE3KQQEFSGYDRM.json","graph_json":"https://pith.science/api/pith-number/PGLIQWZ6U43IPE3KQQEFSGYDRM/graph.json","events_json":"https://pith.science/api/pith-number/PGLIQWZ6U43IPE3KQQEFSGYDRM/events.json","paper":"https://pith.science/paper/PGLIQWZ6"},"agent_actions":{"view_html":"https://pith.science/pith/PGLIQWZ6U43IPE3KQQEFSGYDRM","download_json":"https://pith.science/pith/PGLIQWZ6U43IPE3KQQEFSGYDRM.json","view_paper":"https://pith.science/paper/PGLIQWZ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.3569&json=true","fetch_graph":"https://pith.science/api/pith-number/PGLIQWZ6U43IPE3KQQEFSGYDRM/graph.json","fetch_events":"https://pith.science/api/pith-number/PGLIQWZ6U43IPE3KQQEFSGYDRM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PGLIQWZ6U43IPE3KQQEFSGYDRM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PGLIQWZ6U43IPE3KQQEFSGYDRM/action/storage_attestation","attest_author":"https://pith.science/pith/PGLIQWZ6U43IPE3KQQEFSGYDRM/action/author_attestation","sign_citation":"https://pith.science/pith/PGLIQWZ6U43IPE3KQQEFSGYDRM/action/citation_signature","submit_replication":"https://pith.science/pith/PGLIQWZ6U43IPE3KQQEFSGYDRM/action/replication_record"}},"created_at":"2026-05-18T00:49:52.931976+00:00","updated_at":"2026-05-18T00:49:52.931976+00:00"}