Akihiro Koide

Low-Rank Segre Geometry, Automorphism Groups, and Complement Cohomology of a Binary Two-Step Algebra

This paper determines the intrinsic geometry, symmetry structure, and complement cohomology of an explicit forty-three-dimensional two-step nilpotent associative algebra over the binary field and of its associated algebra group. The contraction ranks of the induced quadratic map...

Low-Rank Segre Geometry, Automorphism Groups, and Complement Cohomology of a Binary Two-Step Algebra

This paper determines the intrinsic geometry, symmetry structure, and complement cohomology of an explicit forty-three-dimensional two-step nilpotent associative algebra over the binary field and of its associated algebra group. The contraction ranks of the induced quadratic map...

A Nonsplit Special 2-Group Extension Governed by the 2×2 Matrix-Multiplication Tensor

This paper determines the extension structure of the full linear stabilizer of an explicit configuration of 1,024 six-dimensional subspaces over the binary field. The configuration was introduced in the preceding paper Exact Linear Symmetry of a Four-Core Rank-Metric Sunflower Co...

Higher Dyadic Residual Ranks for the Romik Hypergeometric Quotient

This paper determines the eighth and ninth dyadic residual layers arising from the Romik hypergeometric quotient and gives exact finite-state and Cartier-module descriptions valid for every index. The minimal Cartier dimensions of the eighth and ninth residual sequences are prove...

Higher Dyadic Residual Ranks for the Romik Hypergeometric Quotient

This paper determines the eighth and ninth dyadic residual layers arising from the Romik hypergeometric quotient and gives exact finite-state and Cartier-module descriptions valid for every index. The minimal Cartier dimensions of the eighth and ninth residual sequences are prove...

Exact Linear Symmetry of a Four-Core Rank-Metric Sunflower Configuration

This paper constructs and analyzes an explicit configuration of 1,024 six-dimensional subspaces over the binary field. The configuration is assembled from four tensor cores, a four-dimensional rank-metric center code, and two affine parameters. The intersection structure determin...

A Nonsplit Special 2-Group Extension Governed by the 2×2 Matrix-Multiplication Tensor

This paper determines the extension structure of the full linear stabilizer of an explicit configuration of 1,024 six-dimensional subspaces over the binary field. The configuration was introduced in the preceding paper Exact Linear Symmetry of a Four-Core Rank-Metric Sunflower Co...

Heat-Driven Descent and Re-Entrant Pólya-Frequency Obstructions for the Riemann Autocorrelation Kernel

This paper studies finite-order total positivity for a heat-deformed autocorrelation constructed from the classical Riemann–Jacobi kernel. Although every kernel in the family remains positive definite, the results show that positive definiteness does not prevent the appearance of...

A Fractional p-Adic Perturbation Bridge for a Supercongruence of Long

This preprint proves the modular hypergeometric supercongruence stated by Ling Long as Conjecture 5, equation (14). It establishes the conjecture for every prime at least seven by constructing a direct congruence bridge from Long’s nonintegral hypergeometric datum to a standard R...

A Fractional p-Adic Perturbation Bridge for a Supercongruence of Long

This preprint proves the modular hypergeometric supercongruence stated by Ling Long as Conjecture 5, equation (14). It establishes the conjecture for every prime at least seven by constructing a direct congruence bridge from Long’s nonintegral hypergeometric datum to a standard R...

Continuous Dual Hahn Structure in the Riemann–Xi Center Transport: Sharp Supercongruences and Exact p-Adic Dynamics

This preprint studies the arithmetic and finite-characteristic structure of the center transport associated with the standard Riemann–Jacobi kernel for the Riemann Xi function. The center transport is shown to admit an exact description in terms of a specific family of continuous...

Harmonic Theta-Mode Dominance and Superlinear Real-Zero Growth for the Riemann–Jacobi Kernel

This preprint studies the real-zero growth of high derivatives of the standard Riemann–Jacobi kernel associated with the Riemann Xi function. The main result proves that the number of distinct real zeros of the derivatives grows faster than any fixed linear multiple of the deriva...

Harmonic Theta-Mode Dominance and Superlinear Real-Zero Growth for the Riemann–Jacobi Kernel

This preprint studies the real-zero growth of high derivatives of the standard Riemann–Jacobi kernel associated with the Riemann Xi function. The main result proves that the number of distinct real zeros of the derivatives grows faster than any fixed linear multiple of the deriva...

Continuous Dual Hahn Structure in the Riemann–Xi Center Transport: Sharp Supercongruences and Exact p-Adic Dynamics

This preprint studies the arithmetic and finite-characteristic structure of the center transport associated with the standard Riemann–Jacobi kernel for the Riemann Xi function. The center transport is shown to admit an exact description in terms of a specific family of continuous...

A Counterexample to Csordas' Open Problem 4.13 for the Riemann ξ-Kernel

This preprint gives a negative answer to Csordas’ Open Problem 4.13 concerning derivative Laguerre inequalities for the Jacobi theta kernel associated with the Riemann xi-function. At the symmetry point, the proposed inequalities are proved to hold through derivative order eight...

Arithmetic of CM Center Polynomials for the Riemann Xi Kernel

This preprint studies the arithmetic structure of the even derivatives at the symmetry center of the standard Jacobi-theta kernel associated with the Riemann Xi function. Using Romik’s centered expansion of the Jacobi theta constant, the paper constructs a family of rational poly...

Finite-Characteristic Dynamics of Riemann Xi Center Polynomials and Splitting in Q(i)

This preprint studies the finite-characteristic dynamics of the center-polynomial family associated with the even derivatives of the standard Jacobi-theta kernel for the Riemann Xi function. Using Romik’s centered expansion of the Jacobi theta constant, the paper places the cente...

A Counterexample to an Off-Axis Wiener Criterion for the Laguerre–Pólya Class and a Corrected Jensen Correlation Kernel

This preprint examines an off-axis Wiener criterion for the Laguerre–Pólya class proposed by Dimitrov and Xu. It identifies a missing complex factor in the Fourier transform of an odd kernel, which reverses the sign of one of the second-order correlation terms used in the publish...

The First Failure of the Derivative Laguerre Inequalities for the Riemann Xi Kernel

This preprint studies the derivative Laguerre inequalities for the standard kernel associated with the Riemann Xi function, in connection with Csordas’ Open Problem 4.13. The paper proves that the inequalities hold globally for the first eight derivative shifts. It then shows tha...

Power-Saving Center-Failure Counts for the Derivative Laguerre Inequalities of the Riemann Xi Kernel

This preprint studies the asymptotic number of failures of the derivative Laguerre inequalities at the symmetry point of the standard Jacobi-theta kernel associated with the Riemann Xi function. Building on a previous transition analysis, it strengthens the known qualitative coun...