{"paper":{"title":"On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The authors prove a fermionic-bosonic duality that confirms the conjectural fermionic formula for the Macdonald index in Argyres-Douglas theories of type (A1, D2k+1).","cross_cats":["hep-th","math.NT"],"primary_cat":"math.CO","authors_text":"Chanh Tran, Shane Chern, Tanay Wakhare","submitted_at":"2026-05-04T05:55:10Z","abstract_excerpt":"We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type $(A_1, D_{2k+1})$, thereby yielding a conjectural fermionic formula due to Andrews et al. Our duality is built upon a new conjugate Bailey pair to be established using techniques from orthogonal polynomials and basic hypergeometric series. In addition, this fermionic formula implies another sum-like expression independently conjectured by Andrews et al. and Kim et al. for the same Macdonald index."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type (A1, D2k+1), thereby yielding a conjectural fermionic formula due to Andrews et al.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The new conjugate Bailey pair constructed via orthogonal polynomials and basic hypergeometric series exactly matches the structure of the Macdonald index for the specific (A1, D2k+1) theories without further restrictions or adjustments.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proof of a fermionic-bosonic duality for the Macdonald index in (A1, D2k+1) Argyres-Douglas theories via a new conjugate Bailey pair from orthogonal polynomials and hypergeometric series.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The authors prove a fermionic-bosonic duality that confirms the conjectural fermionic formula for the Macdonald index in Argyres-Douglas theories of type (A1, D2k+1).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"73d694019f1fce91cba6702d2ea461595c49bc167afc1e63f1eb6cd453f91b8c"},"source":{"id":"2605.02251","kind":"arxiv","version":2},"verdict":{"id":"a190811e-19cf-4aa9-8e55-8d5473f3e8dd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T18:48:00.495996Z","strongest_claim":"We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type (A1, D2k+1), thereby yielding a conjectural fermionic formula due to Andrews et al.","one_line_summary":"Proof of a fermionic-bosonic duality for the Macdonald index in (A1, D2k+1) Argyres-Douglas theories via a new conjugate Bailey pair from orthogonal polynomials and hypergeometric series.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The new conjugate Bailey pair constructed via orthogonal polynomials and basic hypergeometric series exactly matches the structure of the Macdonald index for the specific (A1, D2k+1) theories without further restrictions or adjustments.","pith_extraction_headline":"The authors prove a fermionic-bosonic duality that confirms the conjectural fermionic formula for the Macdonald index in Argyres-Douglas theories of type (A1, D2k+1)."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.02251/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T16:35:27.226597Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T03:31:23.062290Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T16:31:22.789488Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6b2623ad9a73cbbb1a872b6faf9c1faa883dfe8a5cf1236208c07dcf13d0299e"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"da853ca6671a84b6545723ba06725fdc493b81641ace0d63e0ce8275614f69c3"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}