{"paper":{"title":"Real-rootedness of the Poincar\\'e polynomials of $\\overline{\\mathcal M}_{0,n}$: an AI-assisted proof","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.NE"],"primary_cat":"math.AG","authors_text":"Gergely B\\'erczi, Young-Hoon Kiem","submitted_at":"2026-05-27T22:26:05Z","abstract_excerpt":"We prove real-rootedness for the Poincar\\'e polynomial \\[\n  P_n(t)=\\sum_{i=0}^{n-3} \\dim H^{2i}(\\overline{\\mathcal M}_{0,n};\\mathbb{Q})t^i \\] of the Deligne--Mumford moduli space $\\overline{\\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli. The proof starts from the Keel--Manin--Getzler recurrence, but its main new idea is a bivariate deformation $F_m(y,t)$ of the Poincar\\'e polynomial. This deformation reveals a hidden interlacing structure not visible in the one-variable recurrence. For fixed $t<0$, the zero set of $F_m$ in the $y$-direc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29151","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/2605.29151/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"}