{"paper":{"title":"Coherent functors, powers of ideals, and asymptotic stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Dipankar Ghosh, Samarendra Sahoo, Siddhartha Pramanik, Souvik Dey, Tony J. Puthenpurakal","submitted_at":"2025-05-31T12:25:23Z","abstract_excerpt":"Let $R$ be a Noetherian ring, $I_1,\\ldots,I_r$ be ideals of $R$, and $N\\subseteq M$ be finitely generated $R$-modules. Let $S = \\bigoplus_{\\underline{n} \\in \\mathbb{N}^r} S_{\\underline{n}}$ be a Noetherian standard $\\mathbb{N}^r$-graded ring with $S_{\\underline{0}} = R$, and $\\mathcal{M} $ be a finitely generated $\\mathbb{Z}^r$-graded $S$-module. For $ \\underline{n} = (n_1,\\dots,n_r) \\in \\mathbb{N}^r$, set $G_{\\underline{n}} := \\mathcal{M}_{\\underline{n}}$ or $G_{\\underline{n}} := M/{\\bf I}^{\\underline{n}} N$, where ${\\bf I}^{\\underline{n}} = I_1^{n_1} \\cdots I_r^{n_r}$. Suppose $F$ is a coher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00529","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/2506.00529/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"}