Shin Tamaki

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.

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.

A Noncommutative Model of Meaning Generation: Δ, π₁, Representation Theory, and Curvature

This paper presents a noncommutative model of meaning generation based on singularities in rationality space, fundamental-group cycles, unitary representations, and curvature. The framework explains contextual reversal, interiority, taboo dynamics, and humor as geometric effects...

A Noncommutative Model of Meaning Generation: Δ, π₁, Representation Theory, and Curvature

This paper presents a noncommutative model of meaning generation based on singularities in rationality space, fundamental-group cycles, unitary representations, and curvature. The framework explains contextual reversal, interiority, taboo dynamics, and humor as geometric effects...

Pre‑Generative Causal Model: A Categorical Isomorphism between the Egg Model and the Minkowski Causal Lattice

This report establishes a categorical isomorphism between the Egg Model and the Minkowski causal lattice, showing that their generative operators correspond under a functor preserving causal order, thereby yielding a unified pre‑generative architecture consistent with FRLT’s null...

Pre‑Generative Causal Model: A Categorical Isomorphism between the Egg Model and the Minkowski Causal Lattice

This report establishes a categorical isomorphism between the Egg Model and the Minkowski causal lattice, showing that their generative operators correspond under a functor preserving causal order, thereby yielding a unified pre‑generative architecture consistent with FRLT’s null...

Generative and Braid-Based Unification of Magnetic Topology via the Pivot–Null–Braid Architecture

This work presents a generative, braid-based unification of magnetic topology using the pivot–null–braid architecture, showing how helical, frustrated, and skyrmionic structures arise from a single nonlinear sequence governing winding, boundaries, and causal spin organization.

Holonomic D‑Modules on Complex Curves and Mirror Pullback : A Structure‑Preserving Comparison via Automorphisms

This paper introduces the mirror pullback of holonomic D‑modules on complex curves, a structure‑preserving comparison defined via automorphisms. It maintains one‑dimensional thickness, transforms monodromy naturally, and provides a new framework consistent with the Riemann–Hilber...

A Unified Generative Theory of Crystal Formation via Pivot–Hole Geometry and D-Modules

This paper presents a unified generative theory of crystal formation integrating pivot–hole geometry, D-modules, torsion, Frobenius angles, and derived layering, reconstructing band structures as spectral data and formalizing crystal generation as a derived functorial process.

A Unified Generative Theory of Crystal Formation via Pivot–Hole Geometry and D-Modules

This paper presents a unified generative theory of crystal formation integrating pivot–hole geometry, D-modules, torsion, Frobenius angles, and derived layering, reconstructing band structures as spectral data and formalizing crystal generation as a derived functorial process.

A Groupoid-Level Equivalence of Phase, Null, and Galois Structures

We show that layered circle, null, and Galois structures become isomorphic groupoids within a reduced model. Using pushout encounters and a discrete pivot, phase geometry, causal propagation, and Galois symmetry collapse into a single algebraic pattern.

Biological Morphogenesis Governed by a Complex Generative Index

Biological morphogenesis is described using a complex generative index whose real and imaginary parts govern growth and chirality. Its induced monodromy field organizes spirals, layers, and branches, yielding a unified dynamical and singularity-based framework for biological form...

Holonomic D‑Modules on Complex Curves and Mirror Pullback : A Structure‑Preserving Comparison via Automorphisms

This paper introduces the mirror pullback of holonomic D‑modules on complex curves, a structure‑preserving comparison defined via automorphisms. It maintains one‑dimensional thickness, transforms monodromy naturally, and provides a new framework consistent with the Riemann–Hilber...

Biological Morphogenesis Governed by a Complex Generative Index

Biological morphogenesis is described using a complex generative index whose real and imaginary parts govern growth and chirality. Its induced monodromy field organizes spirals, layers, and branches, yielding a unified dynamical and singularity-based framework for biological form...

Generative and Braid-Based Unification of Magnetic Topology via the Pivot–Null–Braid Architecture

This work presents a generative, braid-based unification of magnetic topology using the pivot–null–braid architecture, showing how helical, frustrated, and skyrmionic structures arise from a single nonlinear sequence governing winding, boundaries, and causal spin organization.

A Groupoid-Level Equivalence of Phase, Null, and Galois Structures

We show that layered circle, null, and Galois structures become isomorphic groupoids within a reduced model. Using pushout encounters and a discrete pivot, phase geometry, causal propagation, and Galois symmetry collapse into a single algebraic pattern.

The Hyperbolic, Eisenstein–Lattice, and FRLT Interpretation of the Figure‑Eight Choreography in the Three‑Body Problem

The figure‑eight three‑body choreography is reformulated using a complex shape parameter matching the hyperbolic structure of the figure‑eight knot complement. Its action becomes a hyperbolic geodesic functional, and the Eisenstein lattice’s unique fixed point serves as the FRLT...

S⁴-Membrane Intelligence: A Universal-Layer–Pivot–Groupoid Architecture for Generative Structural AI

This work introduces an AI architecture where intelligence emerges from structural growth across a universal layer, pivot field, S⁴ membrane, and contact groupoid. Domain cones embed into this geometry, enabling reversible cross‑domain reasoning and higher‑order coherence formali...

The Hyperbolic, Eisenstein–Lattice, and FRLT Interpretation of the Figure‑Eight Choreography in the Three‑Body Problem

The figure‑eight three‑body choreography is reformulated using a complex shape parameter matching the hyperbolic structure of the figure‑eight knot complement. Its action becomes a hyperbolic geodesic functional, and the Eisenstein lattice’s unique fixed point serves as the FRLT...