{"paper":{"title":"Strata of Ecological Coexistence via Grassmannians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Georgy Scholten, Giulio Zucal, Kexin Wang, Pierre A. Haas, T\\\"urk\\\"u \\\"Ozl\\\"um \\c{C}elik","submitted_at":"2025-08-29T18:05:55Z","abstract_excerpt":"We study the Lotka--Volterra system from the perspective of computational algebraic geometry, focusing on equilibria that are both feasible and stable. These conditions stratifies the parameter space in $\\mathbb{R}\\times\\mathbb{R}^{n\\times n}$ with the feasible-stable semialgebraic sets. We encode them on the real Grassmannian ${\\rm Gr}_{\\mathbb{R}}(n,2n)$ via a parameter matrix representation, and use oriented matroid theory to develop an algorithm, combining Grassmann--Pl{\\\"u}cker relations with branching under feasibility and stability constraints. This symbolic approach determines whether "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.00165","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/2509.00165/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"}