Shin Tamaki

Hyperbolic Knot Complements as Imaginary Thickness: Boundary Map Dynamics and PSL(2,R) Actions

This paper presents a cohomological model in which imaginary thickness arises from boundary map dynamics and aligns with hyperbolic actions of PSL(2,R). Knot complements provide the geometric setting that realizes these generative depth transformations. This work is licensed unde...

Topological Net-Field Representation of Squeezed Quantum States

We propose a topological Net Field that geometrically represents squeezed states, photon-number structure, and interference. Anisotropic tension, twist, and pivot nuclei reveal nonclassical features including negative Wigner regions, quiet bands, and knot-like entanglement. This...

QR and Householder Orthogonalization on Light-Cone Geometry

We reinterpret QR and Householder orthogonalization through light-cone geometry, showing how null-aligned reflections encode causal structure. This framework links orthogonalization to spacetime direction hierarchies, revealing a geometric basis for null-origin alignment. This wo...

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 Bi‑Tempo Poset: A Categorical Integration of Causality, Null Groupoids, and Higher‑Order Generative Dynamics

A bi‑tempo poset unifies hierarchical order, tempo, causality, and discontinuity. Through categorical integration with causal structures, null groupoids, and 2‑categories, it provides a coherent framework for irreversible propagation, boundary formation, and higher‑order generati...

The Bi‑Tempo Poset: A Categorical Integration of Causality, Null Groupoids, and Higher‑Order Generative Dynamics

A bi‑tempo poset unifies hierarchical order, tempo, causality, and discontinuity. Through categorical integration with causal structures, null groupoids, and 2‑categories, it provides a coherent framework for irreversible propagation, boundary formation, and higher‑order generati...

Null Dictionary Theory: Geometry, Groupoids, and Sparse Functorial Learning

We present Null Dictionary Theory, integrating Lorentzian null geometry, groupoid composition, and sparse functorial optimization. Sparse minimization yields minimal null subgroupoids, and the Sparse functor preserves geometric and algebraic structure, providing a unified foundat...

Null Dictionary Theory: Geometry, Groupoids, and Sparse Functorial Learning

We present Null Dictionary Theory, integrating Lorentzian null geometry, groupoid composition, and sparse functorial optimization. Sparse minimization yields minimal null subgroupoids, and the Sparse functor preserves geometric and algebraic structure, providing a unified foundat...

Set‑Generative AI: Braid Dynamics and Learning Phases

This paper presents a set‑generative AI model where braid dynamics on four‑component states produce distinct learning phases. The framework integrates double figure‑eight generation, non‑commutative propagation, and spectral regimes enabling coordination, pruning, exploration, an...

Quantum Optical Encryption Enabled by Four-Channel Metasurface Groupoid Structures

Quantum optical encryption is realized through four-channel metasurface scattering modeled as a groupoid structure. Encryption arises from composite morphisms, and decryption succeeds when the diagram closes. The same architecture extends to reversible unitary quantum operations.

Trusted Execution Environments as Generative Maps: A Groupoid-Theoretic Reformulation

Trusted Execution Environments are reformulated as generative maps f:Σ2→S3, where attestation becomes a pivot, key generation arises from SU(2), IGG ensures image integrity, and TEE transitions form a groupoid equivalent to Galois, étale, and null groupoids.

Topological Equivalence of Classical Generative Landscapes and Quantum Pyrochlore Phase Boundaries

Classical generative landscapes yield boundary stratifications satisfying braid relations. We show their boundary geometry is homeomorphic to quantum pyrochlore phase surfaces, with generating indices corresponding monotonically to critical exponents, revealing a structural equiv...

Quantum Optical Encryption Enabled by Four-Channel Metasurface Groupoid Structures

Quantum optical encryption is realized through four-channel metasurface scattering modeled as a groupoid structure. Encryption arises from composite morphisms, and decryption succeeds when the diagram closes. The same architecture extends to reversible unitary quantum operations.

Topological Equivalence of Classical Generative Landscapes and Quantum Pyrochlore Phase Boundaries

Classical generative landscapes yield boundary stratifications satisfying braid relations. We show their boundary geometry is homeomorphic to quantum pyrochlore phase surfaces, with generating indices corresponding monotonically to critical exponents, revealing a structural equiv...

Trusted Execution Environments as Generative Maps: A Groupoid-Theoretic Reformulation

Trusted Execution Environments are reformulated as generative maps f:Σ2→S3, where attestation becomes a pivot, key generation arises from SU(2), IGG ensures image integrity, and TEE transitions form a groupoid equivalent to Galois, étale, and null groupoids.

Set‑Generative AI: Braid Dynamics and Learning Phases

This paper presents a set‑generative AI model where braid dynamics on four‑component states produce distinct learning phases. The framework integrates double figure‑eight generation, non‑commutative propagation, and spectral regimes enabling coordination, pruning, exploration, an...

Local–Global Generative Structure of L-Functions: RH, Sato–Tate, and Langlands Reinterpreted

This paper presents a generative-theoretic reinterpretation of the Riemann Hypothesis, Sato–Tate Conjecture, and Langlands Correspondence, showing that their local, intermediate, and global behaviors arise as stability conditions within a single prime-centered hierarchical struct...

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.

Local–Global Generative Structure of L-Functions: RH, Sato–Tate, and Langlands Reinterpreted

This paper presents a generative-theoretic reinterpretation of the Riemann Hypothesis, Sato–Tate Conjecture, and Langlands Correspondence, showing that their local, intermediate, and global behaviors arise as stability conditions within a single prime-centered hierarchical struct...

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.