Fixed-unit Kummer twists in the AR16 D4 search: certified twins and negative controls

| This reproducibility note studies fixed-unit Kummer twists in a finite AR16 pilot. It distinguishes three evidence levels: the published w281 same-group pair; a newly certified but previously unpublished p=41 same-group pair; and raw exploratory p=349 and p=173 controls showing that no general class-number or class-group invariance law follows from the pilot. For p=41, a one-sided octic class-group certificate, fully certified proper D4 subfields, explicit norm-one units, and Arb regulator intervals prove Cl(L10)=Cl(L15)=Z/32Z plus Z/4Z and h=128. The package includes scripts, logs, checksums, and a MacBook cross-machine rerun of the lower-bound portion. No priority claim or general invariance theorem is made.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-17
DOI
https://doi.org/10.5281/zenodo.22808065
Primary Topic
Formal Methods in Verification
Type
article
Field-Weighted Citation Impact
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article

Fixed-unit Kummer twists in the AR16 D4 search: certified twins and negative controls

Kenshirou Moriwaki
Zenodo (CERN European Organization for Nuclear Research)
Formal Methods in Verification
article

Fixed-unit Kummer twists in the AR16 D4 search: certified twins and negative controls

Kenshirou Moriwaki
article en

Abstract

| This reproducibility note studies fixed-unit Kummer twists in a finite AR16 pilot. It distinguishes three evidence levels: the published w281 same-group pair; a newly certified but previously unpublished p=41 same-group pair; and raw exploratory p=349 and p=173 controls showing that no general class-number or class-group invariance law follows from the pilot. For p=41, a one-sided octic class-group certificate, fully certified proper D4 subfields, explicit norm-one units, and Arb regulator intervals prove Cl(L10)=Cl(L15)=Z/32Z plus Z/4Z and h=128. The package includes scripts, logs, checksums, and a MacBook cross-machine rerun of the lower-bound portion. No priority claim or general invariance theorem is made.

Zenodo (CERN European Organization for Nuclear Research)
Hokkaido Research Organization (JP)
Gender equality
Openalex Percentile: Top 8%
Formal Methods in Verification
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