{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EOZVORH5CLBMS327H2GXHW46CM","short_pith_number":"pith:EOZVORH5","schema_version":"1.0","canonical_sha256":"23b35744fd12c2c96f5f3e8d73db9e1329e6afe2a4c94268b23cddae9c1af57a","source":{"kind":"arxiv","id":"1709.06736","version":2},"attestation_state":"computed","paper":{"title":"The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CO","authors_text":"Martha Precup, Megumi Harada","submitted_at":"2017-09-20T06:57:50Z","abstract_excerpt":"We define a subclass of Hessenberg varieties called abelian Hessenberg varieties, inspired by the theory of abelian ideals in a Lie algebra developed by Kostant and Peterson. We give an inductive formula for the $S_n$-representation on the cohomology of an abelian regular semisimple Hessenberg variety with respect to the action defined by Tymoczko. Our result implies that a graded version of the Stanley-Stembridge conjecture holds in the abelian case, and generalizes results obtained by Shareshian-Wachs and Teff. Our proof uses previous work of Stanley, Gasharov, Shareshian-Wachs, and Brosnan-"},"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":"1709.06736","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-20T06:57:50Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"54671c6415726085a81205ce9f8b182cb2b96493174f4ff5f88048aa6f20cf26","abstract_canon_sha256":"a3d7ac36daa3453ae2874fdbe41797afb2cc75c72d2bd730f8797bd379671977"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:18.932412Z","signature_b64":"yyblCi0t4Q7h/cpKKiYpiY6r4QZTYUv7tV7gbnoFdiOE4y/mV4U3e6/Z8+tI99eLZAMepFKzmbI8j6YicN4xCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23b35744fd12c2c96f5f3e8d73db9e1329e6afe2a4c94268b23cddae9c1af57a","last_reissued_at":"2026-05-18T00:27:18.931901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:18.931901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CO","authors_text":"Martha Precup, Megumi Harada","submitted_at":"2017-09-20T06:57:50Z","abstract_excerpt":"We define a subclass of Hessenberg varieties called abelian Hessenberg varieties, inspired by the theory of abelian ideals in a Lie algebra developed by Kostant and Peterson. We give an inductive formula for the $S_n$-representation on the cohomology of an abelian regular semisimple Hessenberg variety with respect to the action defined by Tymoczko. Our result implies that a graded version of the Stanley-Stembridge conjecture holds in the abelian case, and generalizes results obtained by Shareshian-Wachs and Teff. Our proof uses previous work of Stanley, Gasharov, Shareshian-Wachs, and Brosnan-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06736","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":"1709.06736","created_at":"2026-05-18T00:27:18.931981+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.06736v2","created_at":"2026-05-18T00:27:18.931981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06736","created_at":"2026-05-18T00:27:18.931981+00:00"},{"alias_kind":"pith_short_12","alias_value":"EOZVORH5CLBM","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EOZVORH5CLBMS327","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EOZVORH5","created_at":"2026-05-18T12:31:12.930513+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/EOZVORH5CLBMS327H2GXHW46CM","json":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM.json","graph_json":"https://pith.science/api/pith-number/EOZVORH5CLBMS327H2GXHW46CM/graph.json","events_json":"https://pith.science/api/pith-number/EOZVORH5CLBMS327H2GXHW46CM/events.json","paper":"https://pith.science/paper/EOZVORH5"},"agent_actions":{"view_html":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM","download_json":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM.json","view_paper":"https://pith.science/paper/EOZVORH5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.06736&json=true","fetch_graph":"https://pith.science/api/pith-number/EOZVORH5CLBMS327H2GXHW46CM/graph.json","fetch_events":"https://pith.science/api/pith-number/EOZVORH5CLBMS327H2GXHW46CM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM/action/storage_attestation","attest_author":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM/action/author_attestation","sign_citation":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM/action/citation_signature","submit_replication":"https://pith.science/pith/EOZVORH5CLBMS327H2GXHW46CM/action/replication_record"}},"created_at":"2026-05-18T00:27:18.931981+00:00","updated_at":"2026-05-18T00:27:18.931981+00:00"}