Founder, Kiara Inc.
Mathematical AI Systems Research

Building the mathematical foundations that expand human capability through AI.

🇺🇸 English | 🇯🇵 日本語 | 📚 Publications | 🧭 Research | 🚀 Projects | 🎤 Talks

Artificial intelligence should not merely automate work. It should systematically expand human capability.

My long-term research aims to establish a mathematical theory that explains:

• what AI can make accessible,
• what AI cannot make accessible,
• why these limits exist,
• and how those limits can be expanded.

Accessibility is treated here as the set of human capabilities made reachable through AI.

Understanding AI-enabled accessibility as a mathematical object rather than only a software feature.

Representative work

• The Accessibility Capability Boundary

  Introduces the Accessibility Capability Boundary (ACB), a theoretical framework for AI-generated accessibility systems. Browser-native single-file HTML prototypes demonstrate how LLMs reduce deployment barriers while revealing the remaining limits of autonomous accessibility computing.

• Maximum Formalism, Maximum Humanity

• GIGA for Sequential Art

Replacing heuristic engineering with AI systems whose behavior can be described, bounded, and verified mathematically.

Representative work

• Explainable PQC

  Presents a layered framework for making post-quantum cryptographic security assumptions more transparent through computational complexity, mathematical analysis, and empirical evaluation of lattice reduction algorithms.

• Toward Provably Safe Language Models

• Designing a Stable and Principled Kanban System

Developing mathematical structures motivated by toric geometry, lattice theory, and combinatorial topology.

Representative work

• Canonical Lattices of Integer Relations Associated to Rational Fans

  Develops a coordinate-free theory of integer relation lattices associated with rational fans and proves that all relations in complete fans are generated by wall-supported relations.

• Combinatorial Cycle Classes in the Intersection Cohomology of Projective Toric Varieties

  Studies combinatorial cycle classes in the BBFK framework and establishes generation results in low dimensions, clarifying connections between toric geometry and Hodge theory.

• Geometric Localization of Relation Lattices

Pure Mathematics
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Geometric & Combinatorial Structures
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Reliable Mathematical AI
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AI-enabled Accessibility
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Universal Human Capability

What are the mathematical limits of AI-enabled accessibility, and how can those limits be systematically expanded?

I welcome collaboration in:

• Mathematics
• Artificial Intelligence
• Human–Computer Interaction
• Accessibility
• Formal Verification
• Post-Quantum Cryptography
• Open-source Scientific Software

Mathematical AI · Accessibility · Formal Verification · Toric Geometry · Relation Lattices · Post-Quantum Cryptography · Human-AI Systems · Reliable AI