{"paper":{"title":"The rank-five Peterson hit problem, the fifth Singer transfer, and a geometric generator in unoriented cobordism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc","submitted_at":"2026-07-21T07:55:16Z","abstract_excerpt":"The Peterson hit problem seeks a minimal set of generators for the polynomial algebra $P_s = \\mathbb{F}_2[x_1,\\dots,x_s]$ as an unstable module over the mod-2 Steenrod algebra $\\mathcal{A}$. For rank five, general admissible bases fail, and the interplay between Kameko periodicity and modular invariants becomes computationally complex. In this paper, we study the rank-five cohit module in the generic family $N_d = 27\\cdot 2^d - 5$. Exact sparse elimination in degree $49$ processes $292825$ monomials, yielding a hit rank of $289969$ and a cohit dimension of $2856$. We determine the exact weight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20566","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/2607.20566/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"}