Shin Tamaki

Complex Chirality and the Construction of Complex Monodromy

Complex chirality generates non‑commutative increments that converge at a univalence point p. A complex connection A records these increments, and its loop‑based closure yields the complex monodromy M(p), expressing local non‑abelian reciprocity.

Categorical Structures as Generative Geometry: A Unified Model of Duality, Thickness, EM/Kleisli Layers, ∞‑Stratification, and Curvature

This paper presents a generative geometric interpretation of categorical structures, where dualization forms layered depth, monads and comonads create thickness, EM/Kleisli yield four-layer organization, and ∞-categorical stratification and curvature describe higher-order deviati...

Imaginal Arithmetic Geometry: A Generative Reconstruction of Zeta and L-functions

We present imaginal arithmetic geometry, a generative framework in which Frobenius spectra produce emergent images whose global gluing yields zeta and L-functions, offering a unified structural interpretation of classical arithmetic phenomena.

Imaginal Number Theory A Spectral Unification of Arithmetic Geometry and Prime Emergence

Imaginal Number Theory unifies Frobenius and quaternionic spectra through a shared generative process of fluctuation, image formation, and spectral gluing, producing unified imaginal zeta and L-functions that coherently link arithmetic geometry with prime emergence.

Null Directional Derivations as Unified Generators in D-Module, Groupoid, and C ∗ -Algebra Frameworks

This paper shows that null directional derivations unify differential, geometric, and operator-algebraic structures by serving as common generators of D-modules, Lie groupoid flows, modular measures, and C∗-algebra derivations, yielding a coherent reconstruction of light-front dy...

Quaternionic Sato–Tate Field and Elliptic Interference in the Prime Density

We construct a quaternionic Sato–Tate field where Frobenius angles, SU(2) rotations, elliptic interference, and spiral geometry generate a unified prime-density model. The resulting kernel yields a PDE hierarchy linking D-modules, C\‑algebras, and null groupoid propagation.

Quaternionic Generative Geometry of Primes: Local–Global Hierarchy and Elliptic Interference

We present a unified framework where quaternionic generative geometry realizes the local layer of the number-theoretic hierarchy. Frobenius angles, SU(2) rotations, and elliptic interference form a prime-density field whose propagation yields a PDE hierarchy linking D-modules and...

Quaternionic Sato–Tate Field and Elliptic Interference in the Prime Density

We construct a quaternionic Sato–Tate field where Frobenius angles, SU(2) rotations, elliptic interference, and spiral geometry generate a unified prime-density model. The resulting kernel yields a PDE hierarchy linking D-modules, C\‑algebras, and null groupoid propagation.

Quaternionic Generative Geometry of Primes: Local–Global Hierarchy and Elliptic Interference

We present a unified framework where quaternionic generative geometry realizes the local layer of the number-theoretic hierarchy. Frobenius angles, SU(2) rotations, and elliptic interference form a prime-density field whose propagation yields a PDE hierarchy linking D-modules and...

Categorical Structures as Generative Geometry: A Unified Model of Duality, Thickness, EM/Kleisli Layers, ∞‑Stratification, and Curvature

This paper presents a generative geometric interpretation of categorical structures, where dualization forms layered depth, monads and comonads create thickness, EM/Kleisli yield four-layer organization, and ∞-categorical stratification and curvature describe higher-order deviati...

Imaginal Arithmetic Geometry: A Generative Reconstruction of Zeta and L-functions

We present imaginal arithmetic geometry, a generative framework in which Frobenius spectra produce emergent images whose global gluing yields zeta and L-functions, offering a unified structural interpretation of classical arithmetic phenomena.

Complex Chirality and the Construction of Complex Monodromy

Complex chirality generates non‑commutative increments that converge at a univalence point p. A complex connection A records these increments, and its loop‑based closure yields the complex monodromy M(p), expressing local non‑abelian reciprocity.

Unified Generative Number Theory

UGNT unifies generative geometry and field–response hierarchy, describing number-theoretic structures via curvature and admissibility on a single axis. Major phenomena, from Fermat to the Riemann Hypothesis, emerge as generative allowance or prohibition.

Unified Generative Geometry for Number Theory

Unified Generative Geometry identifies a single axis unifying local and global arithmetic structures. Curvature, image bundles, Frobenius angles, motivic geodesics, and Langlands symmetries appear as coherent generative images determining the variational structure of number‑theor...

Unified Generative Number Theory and Pontryagin Duality

This work unifies generative, dual, and limit structures in number theory using the FRLT pivot, Pontryagin duality, and limit geometries, showing the ABC conjecture arises naturally as the structural measure of arithmetic biduality failure.

Unified Generative Number Theory and Pontryagin Duality

This work unifies generative, dual, and limit structures in number theory using the FRLT pivot, Pontryagin duality, and limit geometries, showing the ABC conjecture arises naturally as the structural measure of arithmetic biduality failure.

Bi‑Tempo Poset

A bi‑tempo poset equips a partial order with two monotone endofunctors and a natural transformation encoding their interaction. Synchronization, asynchrony, and leap behavior arise from invertibility or failure of naturality.

Thick and Thin Globality: A Categorical Interpretation via Dictionary Sheaves and Sparse Selection

This paper contrasts thick globality from colimit gluing with thin globality from sparse selection in dictionary sheaves. We formalize selection as a right adjoint and show L1 regularization realizes this structure.

Cryptography and Optical Imaging as Dual Scattering Processes: A Categorical Formulation

This work formulates cryptography and optical imaging as dual scattering processes, modeling encryption, decryption, and imaging through scattering, Fourier duality, and anticommutation within a unified categorical framework.

Pushout Geometry of Galois, Étale, and Null Groupoids

We show that Galois, étale, and null groupoids share the same pushout geometry, yielding a unified local-to-global structure across arithmetic, algebraic, and Lorentzian settings via a common generative nucleus.