Shin Tamaki

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...

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...

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...

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...

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...

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).

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.

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 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...