This preprint studies a q-supercongruence conjecture of Guo and Schlosser concerning fourth-power cyclotomic divisibility of truncated basic hypergeometric sums. The conjecture as originally stated is shown to fail in an admissible even-parameter case. The paper identifies the source of this failure and proves a strong...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
SAE-HPC Suite 1.1 is a reproducible research software package for structure-aware exact-arithmetic workflows. It combines byte-exact state compression, owner optimization, finite-horizon plan selection, robust-regret certification, retained benchmark evidence, and fresh local systems validation. The release includes C+...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
SAE-HPC Suite 1.1 is a reproducible research software package for structure-aware exact-arithmetic workflows. It combines byte-exact state compression, owner optimization, finite-horizon plan selection, robust-regret certification, retained benchmark evidence, and fresh local systems validation. The release includes C+...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This paper determines the exact order of the polynomial system introduced by Ho and Nguyen in the study of singularities and parameter convergence rates for overfitted Gaussian mixtures. The result resolves the general order predicted from the previously known two- and three-component cases. The upper bound is proved b...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This paper constructs an explicit three-component skew-normal mixture that approaches a single non-Gaussian skew-normal distribution while its parameter distance is of first order and its total variation distance is of sixth order. The construction disproves the fourth-order Wasserstein inverse bound conjectured by Ho...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This paper studies concise symmetric cubic tensors of minimal border rank. It establishes a general polar-defect obstruction for tensors that are 111-abundant but not 111-sharp, and combines this obstruction with the low-dimensional geometry of cubic hypersurfaces with vanishing Hessian. As a result, every concise 111-...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This paper studies concise symmetric cubic tensors of minimal border rank. It establishes a general polar-defect obstruction for tensors that are 111-abundant but not 111-sharp, and combines this obstruction with the low-dimensional geometry of cubic hypersurfaces with vanishing Hessian. As a result, every concise 111-...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This work gives a complete dimension and defectivity classification for homoscedastic Gaussian moment varieties over an algebraically closed field of characteristic zero. It proves that these varieties have the expected dimension for every moment order at least four and combines this result with the known cubic classif...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This work gives a complete dimension and defectivity classification for homoscedastic Gaussian moment varieties over an algebraically closed field of characteristic zero. It proves that these varieties have the expected dimension for every moment order at least four and combines this result with the known cubic classif...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This revised preprint studies the derivative Laguerre quantities associated with the Jacobi theta kernel in the Fourier representation of the Riemann xi-function. It gives exact rational certificates showing that the ninth quantity is negative throughout a nontrivial interval around the symmetry point, with the certifi...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This revised preprint studies the derivative Laguerre quantities associated with the Jacobi theta kernel in the Fourier representation of the Riemann xi-function. It gives exact rational certificates showing that the ninth quantity is negative throughout a nontrivial interval around the symmetry point, with the certifi...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
This article studies one-parameter degenerations of chains of nilpotent Jordan blocks joined along their socle vectors. It gives a complete Smith-normal-form description of the associated self-extension torsion for arbitrary chain length and all nonnegative edge valuations. The result includes an explicit path-matching...
Akihiro Koide· Zenodo (CERN European Organi...· 0 citations
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