{"paper":{"title":"A proof of the Fields Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Andy Wilson, Brendon Rhoades, Satoshi Murai","submitted_at":"2025-05-29T22:00:09Z","abstract_excerpt":"The {\\em superspace ring} of rank $n$ is the algebra $\\Omega_n$ of differential forms on affine $n$-space. The algebra $\\Omega_n$ is bigraded with respect to polynomial and exterior degree and carries a natural action of the symmetric group $\\mathfrak{S}_n$. Modding out by $\\mathfrak{S}_n$-invariants with vanishing constant term yields the {\\em superspace coinvariant ring} $SR_n$. We prove that, as an ungraded $\\mathfrak{S}_n$-module, the space $SR_n$ is isomorphic to the sign-twisted permutation action of $\\mathfrak{S}_n$ on ordered set partitions of $\\{1,\\dots,n\\}$. We refine this result by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24027","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.24027/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}