Shin Tamaki

Generative Operators on Minkowski Lattices as a Foundational Model of Intelligence

Artificial intelligence is defined as a generative operator on Minkowski causal lattices, transforming discrete and continuous structures coherently. Reconfiguring null boundaries is isomorphic to nonlinear temporal order, establishing intelligence as causal-structural self-trans...

Generative Operators on Minkowski Lattices as a Foundational Model of Intelligence

Artificial intelligence is defined as a generative operator on Minkowski causal lattices, transforming discrete and continuous structures coherently. Reconfiguring null boundaries is isomorphic to nonlinear temporal order, establishing intelligence as causal-structural self-trans...

2-Bayesian Update as Homotopy Pushout in the Derived Category of 𝐷 𝑋

We study the update of Bayesian update maps (2-Bayesian update) by formulating update maps as morphisms in the derived category Db(DX). We show that deformations of update maps are classified by Ext1 and that the universal synthesis of multiple update maps is given by the homotop...

2-Bayesian Update as Homotopy Pushout in the Derived Category of 𝐷 𝑋

We study the update of Bayesian update maps (2-Bayesian update) by formulating update maps as morphisms in the derived category Db(DX). We show that deformations of update maps are classified by Ext1 and that the universal synthesis of multiple update maps is given by the homotop...

E‑Spacetime: A Noncommutative Entanglement Geometry Extending Einstein Gravity

E‑spacetime is a noncommutative geometry defined by [T,Si]=Θi, where time–space entanglement generates curvature. This framework unifies geometry, fields, gravity, and particles, and recovers GR, QFT, and Yang–Mills theory in the commutative limit.

E‑Spacetime: A Noncommutative Entanglement Geometry Extending Einstein Gravity

E‑spacetime is a noncommutative geometry defined by [T,Si]=Θi, where time–space entanglement generates curvature. This framework unifies geometry, fields, gravity, and particles, and recovers GR, QFT, and Yang–Mills theory in the commutative limit.

A Geometric Model of SU(2) via the Three‑Leaf Lemniscate and a Derivation of the Jacobi Identity

This paper presents a geometric model of SU(2) using a three‑leaf lemniscate. The trifolium’s orientation space forms S3, its infinitesimal rotations reproduce su(2), and the Jacobi identity arises naturally from the structure’s inherent 120∘ cyclic symmetry.

A Geometric Model of SU(2) via the Three‑Leaf Lemniscate and a Derivation of the Jacobi Identity

This paper presents a geometric model of SU(2) using a three‑leaf lemniscate. The trifolium’s orientation space forms S3, its infinitesimal rotations reproduce su(2), and the Jacobi identity arises naturally from the structure’s inherent 120∘ cyclic symmetry.

Bipolar Structure of the Lemniscate: Dual Images and Möbius Twist

The Bernoulli lemniscate exhibits a dual‑image structure generated by its two foci. A single normal‑field flip at the intersection produces a Möbius twist, converting locally distinct lobes into a globally unified image space through a nontrivial topological identification.

Symplectic Geometry and Curvature as Manifestations of the FRLT Pivot

Geometric structures—symplectic, curvature, Fedosov, and Kähler—arise as scalar, operator, higher‑order, and integrable manifestations of the FRLT pivot, unified by the generative formula R(X,Y)Z=Π(X,Y)(Z).

Symplectic Geometry and Curvature as Manifestations of the FRLT Pivot

Geometric structures—symplectic, curvature, Fedosov, and Kähler—arise as scalar, operator, higher‑order, and integrable manifestations of the FRLT pivot, unified by the generative formula R(X,Y)Z=Π(X,Y)(Z).

Artificial Satellite Orbit Generation Model for the Unification of Statistical Methods

This paper unifies major statistical methods through an orbit‑generation metaphor: an artificial satellite navigating an asteroid belt. Using FRLT’s local‑to‑global generative structure, diverse techniques are reinterpreted as procedures extracting one‑dimensional pivots guiding...

A Generative Reconstruction of Geometric Frustration as a Non‑Coherent Stable Structure of Low Consistency

This paper reconstructs geometric frustration as a generative, non‑coherent stable structure. By linking FRLT pivots, groupoid morphisms, signed‑graph holonomy, and Minkowski causality, it shows that low‑order states arise from proliferating non‑closure that stabilizes as a unifi...

A Generative Reconstruction of Geometric Frustration as a Non‑Coherent Stable Structure of Low Consistency

This paper reconstructs geometric frustration as a generative, non‑coherent stable structure. By linking FRLT pivots, groupoid morphisms, signed‑graph holonomy, and Minkowski causality, it shows that low‑order states arise from proliferating non‑closure that stabilizes as a unifi...

A Dispersive-field-valued 2-Morphism Framework for FRLT

This short communication introduces a dispersive‑field‑valued 2‑morphism framework for FRLT. By modeling local angular variation and global discrete jumps within a unified dispersive field D=U(1)×Z, FRLT’s generative pivots acquire a coherent 2‑categorical structure capturing loc...

A Generative Reconstruction of Geometric Frustration as a Non‑Coherent Stable Structure of Low Consistency

This paper reconstructs geometric frustration as a generative, non‑coherent stable structure. By linking FRLT pivots, groupoid morphisms, signed‑graph holonomy, and Minkowski causality, it shows that low‑order states arise from proliferating non‑closure that stabilizes as a unifi...

A Dispersive-field-valued 2-Morphism Framework for FRLT

This short communication introduces a dispersive‑field‑valued 2‑morphism framework for FRLT. By modeling local angular variation and global discrete jumps within a unified dispersive field D=U(1)×Z, FRLT’s generative pivots acquire a coherent 2‑categorical structure capturing loc...

A Generative Reconstruction of Geometric Frustration as a Non‑Coherent Stable Structure of Low Consistency

This paper reconstructs geometric frustration as a generative, non‑coherent stable structure. By linking FRLT pivots, groupoid morphisms, signed‑graph holonomy, and Minkowski causality, it shows that low‑order states arise from proliferating non‑closure that stabilizes as a unifi...

A Cubic Generative Model Unifying Logical, Quantum-Number, Magnetic, and Crystal Structures

This paper presents a unified cubic generative model linking logical transformations, quantum numbers, magnetic ordering, and crystal symmetries. Each domain shares three generative axes—negation, order, symmetry—forming an isomorphic Z2^3 structure. Embedding spdf orbitals, anti...

A Cubic Generative Model Unifying Logical, Quantum-Number, Magnetic, and Crystal Structures

This paper presents a unified cubic generative model linking logical transformations, quantum numbers, magnetic ordering, and crystal symmetries. Each domain shares three generative axes—negation, order, symmetry—forming an isomorphic Z2^3 structure. Embedding spdf orbitals, anti...