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Namely, we prove that $$\\mathrm{Fte}(R) \\le \\lceil \\log_p(2n_0)\\rceil + \\mathrm{HSL}(R),$$ where $n_0$ is the integer such that $\\frak m^{n_0} \\, H^i_{\\frak m}(R) = 0$ for all $i < \\mathrm{dim}(R)$, and $\\lceil x\\rceil$ is the smallest integer that is greater than or equal to $x$."},"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":"2605.29544","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AC","submitted_at":"2026-05-28T07:56:38Z","cross_cats_sorted":[],"title_canon_sha256":"0aa321fd4fdc3d994f8845a9a018df95e1e4c38385a2fada0ba72463225e1f00","abstract_canon_sha256":"067fd747856449539e7372cb81fe8638e3fabbfeb977bce042a8b8da09fc1c7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:05:46.252263Z","signature_b64":"cqh7rhlgTylBQgSyLAMJ1lBqs849lamHJgnp3et74lO5RaaLRp/iYfNlpCNJnsyjRyIY1VVGkULZ67xY5gqzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"032e3d3befc5083de4d03da423e0f1a781793c2e26afa0f795a4295e2c94fa30","last_reissued_at":"2026-05-29T01:05:46.251425Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:05:46.251425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp bound for the Frobenius test exponents in generalized Cohen-Macaulay local rings","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Duong Thi Huong, Pham Hung Quy","submitted_at":"2026-05-28T07:56:38Z","abstract_excerpt":"Let $(R,\\frak m)$ be a generalized Cohen-Macaulay local ring of prime characteristic $p$. 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