{"paper":{"title":"Positivity in classical enumerative geometry: a case study in synchronized AI-assisted mathematics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.NE"],"primary_cat":"math.AG","authors_text":"Gergely B\\'erczi, L\\'aszl\\'o M. Feh\\'er","submitted_at":"2026-05-24T21:56:27Z","abstract_excerpt":"We study the symmetric polynomial $\\prod_{\\alpha\\in A_{n,d}}\\bigl(1+\\alpha_1 x_1+\\cdots+\\alpha_n x_n\\bigr)$ where $A_{n,d}:=\\{\\alpha\\in\\mathbb{Z}_{\\ge 0}^n:|\\alpha|=d\\}$, which is the total Chern class of $\\mathrm{Sym}^d(\\mathbb{C}^n)$, viewed as a torus representation whose Chern roots are the weights $\\alpha_1 x_1+\\cdots+\\alpha_n x_n$ for $\\alpha\\in A_{n,d}$. Its homogeneous degree-$k$ part $c_k(n,d)$ is the $k$-th Chern class of $\\mathrm{Sym}^d(\\mathbb{C}^n)$. These Chern classes, together with their coefficients in various symmetric function bases, play a central role in enumerative geomet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25271","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/2605.25271/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"}