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We also classify simple cuspidal quasi-Poisson modules over the Lie-Rinehart pair (dot A, dot fk) and show that each such module is a tensor module dot A ot Omega for an admissible gl(m+1,n)-module Omega via a prescribed action.","one_line_summary":"Defines quasi-Poisson modules over Lie-Rinehart pairs and establishes a bijection with Harish-Chandra modules, classifying simple cuspidal examples as tensor modules over gl(m+1,n).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The specific algebraic setup with dot A = C[t1^{pm1},...,tm^{pm1}] ot Lambda_n and the restriction to cuspidal simple modules; the correspondence and classification are stated only for this choice of Lie-Rinehart pair and module class, so the result depends on these structural choices holding exactly as defined.","pith_extraction_headline":"Simple cuspidal quasi-Poisson modules over a Lie-Rinehart pair correspond one-to-one with simple cuspidal Harish-Chandra modules."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16950/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T19:52:11.225259Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:18.920208Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:10:41.565141Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.239049Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.322616Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f3acd02164fd51026740cbff1ad1637431a8d296d170a57a99d26d4fd195be17"},"references":{"count":13,"sample":[{"doi":"","year":2022,"title":"Billig, Towards Kac-Van de Leur conjecture: locality of superconfo rmal algebras , Advances in Mathe- matics 400 (2022), 108295","work_id":"96cfa5c8-4f65-47fe-999d-a41e68a66fe7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"Y. 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