{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5Z2DW74NWIJQIQLTI5F5Y4HQG5","short_pith_number":"pith:5Z2DW74N","schema_version":"1.0","canonical_sha256":"ee743b7f8db213044173474bdc70f0375891d8aeb67ff027ee8ec36ccf0a423d","source":{"kind":"arxiv","id":"1311.3014","version":2},"attestation_state":"computed","paper":{"title":"Monk's Rule and Giambelli's Formula for Peterson Varieties of All Lie Types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elizabeth Drellich","submitted_at":"2013-11-13T04:35:01Z","abstract_excerpt":"A Peterson variety is a subvariety of the flag variety $G/B$ which appears in the construction of the quantum cohomology of partial flag varieties. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H_{S^1}^*(Pet)$ and identify the ring generators. In type $A$ Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli's formula for multiplication in the cohomology ring. This paper gives Monk's rule and Giambelli's formula for all Lie types."},"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":"1311.3014","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-13T04:35:01Z","cross_cats_sorted":[],"title_canon_sha256":"a78a1b67629bcea79852bfdc3d5140835c99dc60a1f81c74bf5a8d5961ae1d59","abstract_canon_sha256":"75e5345a841e68f10cb58500dfecb4306607b6ba41ab04b60a3b9f1d484b53ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:52.323772Z","signature_b64":"yr06TfoWEgbSQtubpaJhLSs93u5Esl4Iss3Daji5wZONcqr63SD/QumC0+WQBkP+26yVE8bFqlRO1sr6tdJbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee743b7f8db213044173474bdc70f0375891d8aeb67ff027ee8ec36ccf0a423d","last_reissued_at":"2026-05-18T02:43:52.323337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:52.323337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monk's Rule and Giambelli's Formula for Peterson Varieties of All Lie Types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elizabeth Drellich","submitted_at":"2013-11-13T04:35:01Z","abstract_excerpt":"A Peterson variety is a subvariety of the flag variety $G/B$ which appears in the construction of the quantum cohomology of partial flag varieties. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H_{S^1}^*(Pet)$ and identify the ring generators. In type $A$ Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli's formula for multiplication in the cohomology ring. This paper gives Monk's rule and Giambelli's formula for all Lie types."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3014","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":"1311.3014","created_at":"2026-05-18T02:43:52.323396+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.3014v2","created_at":"2026-05-18T02:43:52.323396+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3014","created_at":"2026-05-18T02:43:52.323396+00:00"},{"alias_kind":"pith_short_12","alias_value":"5Z2DW74NWIJQ","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5Z2DW74NWIJQIQLT","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5Z2DW74N","created_at":"2026-05-18T12:27:34.582898+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/5Z2DW74NWIJQIQLTI5F5Y4HQG5","json":"https://pith.science/pith/5Z2DW74NWIJQIQLTI5F5Y4HQG5.json","graph_json":"https://pith.science/api/pith-number/5Z2DW74NWIJQIQLTI5F5Y4HQG5/graph.json","events_json":"https://pith.science/api/pith-number/5Z2DW74NWIJQIQLTI5F5Y4HQG5/events.json","paper":"https://pith.science/paper/5Z2DW74N"},"agent_actions":{"view_html":"https://pith.science/pith/5Z2DW74NWIJQIQLTI5F5Y4HQG5","download_json":"https://pith.science/pith/5Z2DW74NWIJQIQLTI5F5Y4HQG5.json","view_paper":"https://pith.science/paper/5Z2DW74N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.3014&json=true","fetch_graph":"https://pith.science/api/pith-number/5Z2DW74NWIJQIQLTI5F5Y4HQG5/graph.json","fetch_events":"https://pith.science/api/pith-number/5Z2DW74NWIJQIQLTI5F5Y4HQG5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5Z2DW74NWIJQIQLTI5F5Y4HQG5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5Z2DW74NWIJQIQLTI5F5Y4HQG5/action/storage_attestation","attest_author":"https://pith.science/pith/5Z2DW74NWIJQIQLTI5F5Y4HQG5/action/author_attestation","sign_citation":"https://pith.science/pith/5Z2DW74NWIJQIQLTI5F5Y4HQG5/action/citation_signature","submit_replication":"https://pith.science/pith/5Z2DW74NWIJQIQLTI5F5Y4HQG5/action/replication_record"}},"created_at":"2026-05-18T02:43:52.323396+00:00","updated_at":"2026-05-18T02:43:52.323396+00:00"}