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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.20566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-07-21T07:55:16Z","cross_cats_sorted":[],"title_canon_sha256":"ab6241eabd2ee5957ea9e9c5a8a371371b10e17f56e623448e1daceb0484011b","abstract_canon_sha256":"047c072a2f59c4360d9cc2fe752a83bea97d310aa1dc0c34f61cd7ee8eb001fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T00:23:23.054198Z","signature_b64":"LEBEHzR7mLZ0V5/gb1cLPOyd6s+I8MFRA7ZI25yDPV/P2eH68QkdGoOCnFRjIWMwmpMnSu0A74bmYyGhKxCsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd53470e20019a21ca74de11c4305f92772c1bfbcf34cfe6f1f52db883dce34c","last_reissued_at":"2026-07-24T00:23:23.053323Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T00:23:23.053323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $2856$. 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