{"paper":{"title":"Canonical Lattices of Integer Relations Associated to Rational Fans: Wall Generation and a Two-Step Support Filtration","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Daisuke Ishii, Rizwan Jahangir","submitted_at":"2026-01-09T09:53:35Z","abstract_excerpt":"We study the lattice $L_{\\mathrm{rel}}(\\Sigma)=\\ker\\big(\\mathbb{Z}^{\\Sigma(1)}\\to N\\big)$ of integer relations among the primitive ray generators of a rational fan $\\Sigma$, from an intrinsic, coordinate-free point of view. For each cone $\\tau\\in\\Sigma$ we introduce the \\emph{star-supported} sublattice $L_{\\mathrm{rel}}(\\operatorname{Star}(\\tau))$ of relations whose support lies in the star of $\\tau$, and we organize these by codimension into a support filtration $F_\\bullet L_{\\mathrm{rel}}(\\Sigma)$. Our main result is a sharp local generation theorem: for a complete fan the relation lattice i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.05678","kind":"arxiv","version":2},"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/2601.05678/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"}