Akihiro Koide

Geometric-Series Valuations and Frobenius Initial Forms for the Krattenthaler–Müller Sequence

This paper resolves Conjecture 43 of Krattenthaler and Müller concerning the p-adic divisibility of the auxiliary integer sequence arising in Romik’s hypergeometric description of the Taylor coefficients of the Jacobi theta constant. A uniform valuation theorem is proved for ever...

Profinite Vanishing of Fixed Columns in Romik's Matrix: Conjecture 47(2) and the Pure-Periodicity Clause in Conjecture 47(1)

This paper studies the fixed-column sequences in Romik’s matrix that appear in Conjecture 47 of Krattenthaler and Müller. It proves Conjecture 47(2) and establishes a stronger conclusion: every fixed-column sequence is eventually zero modulo every prescribed integer. Equivalently...

Geometric-Series Valuations and Frobenius Initial Forms for the Krattenthaler–Müller Sequence

This paper resolves Conjecture 43 of Krattenthaler and Müller concerning the p-adic divisibility of the auxiliary integer sequence arising in Romik’s hypergeometric description of the Taylor coefficients of the Jacobi theta constant. A uniform valuation theorem is proved for ever...

Positive-Definite Boundary Correlations and Fourier Zero Strips: Resolution of Csordas' Open Problem 4.12

This paper gives a necessary and sufficient positive-definiteness criterion for confining the zeros of Fourier transforms of real even kernels with super-Gaussian decay to a prescribed horizontal strip. The criterion is formulated in terms of explicit boundary correlation kernels...

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...

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...

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...

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...

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...

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 Xi 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...

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...

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...

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...

High-Order Center Failures of the Derivative Laguerre Inequalities for the Riemann Xi Kernel

This preprint studies the high-order behavior of the derivative Laguerre inequalities for the standard Jacobi-theta kernel associated with the Riemann Xi function. The paper focuses on the symmetry point at the origin and derives a three-term asymptotic expansion for the even der...