Kenshirou Moriwaki

Explicit Right-Kernel Supports in Two-Prime Rédei Layers: An r4=1 Criterion and Conditional CFRAC Redundancy

We give an explicit treatment of right-kernel supports in two-prime pure Rédei layers for discriminants D = 4Ap1p2, with emphasis on the case r4 = 1. A unified four-bit formula describes the column-normalized 4-by-4 Rédei matrix, and an exhaustive classification identifies the no...

Shaped Heights on Pell Unit Orbits: Monotone Dynamics, Depth Recovery, and Sharp Small-Height Bounds

Let N = ℓM ≡ 3 (mod 4) be the product of distinct odd primes 3 ≤ ℓ < M, and let a₀ = floor(√N). We study positive integral solutions X² − Ny² = σcℓ, X = a₀y + t, where c ∈ {1,2}. A description by the height t alone is not valid: multiplication by the positive fundamental unit pre...

Shaped Heights on Pell Unit Orbits: Monotone Dynamics, Depth Recovery, and Sharp Small-Height Bounds

Let N = ℓM ≡ 3 (mod 4) be the product of distinct odd primes 3 ≤ ℓ < M, and put a₀ = ⌊√N⌋. We study positive integral solutions of X² − Ny² = σcℓ, X = a₀y + t, where c ∈ {1,2}. A description by the height t alone is not valid: multiplication by the positive fundamental unit prese...

Unconditional Half-Density at Minimum 2-Class Depth in a Two-Prime Layer III+ Family

We prove unconditionally that the minimum-depth event (e=2) has limiting conditional density (1/2) in a two-prime Layer III+ family. The Layer III+ character sum is decomposed into four components. Three ancillary components are realized as tempered quadratic or cyclic-quartic ch...

Explicit 8-Rank Criteria in a Squarefree Composite Family: Rédei Kernels, Artin Symbols, and Continued-Fraction Centers

We study the narrow class group of real quadratic fields with fundamental discriminant D = 4AB, where A is a prime congruent to 7 modulo 8 and B = p₁p₂ is a product of two distinct primes lying either both in 1 modulo 8 or both in 7 modulo 8. A single four-bit formula is obtained...

The Jacobi-positive squarefree odd semiprimes: a complete parametrisation

Let N = ℓM with 3 ≤ ℓ < M distinct odd primes and let 𝒥(N) be the set of denominators Q_k in the period of the continued fraction of √N whose Jacobi symbol (Q_k/N) equals +1. A previous paper (DOI 10.5281/zenodo.21285697) proved that 𝒥(N) = {1} forces the period length L to lie i...