Research

hott-riemann-hypothesis-vol6

A Lean 4 reduction of the Riemann Hypothesis via Yoneda detection and Hardy model spaces. Volume VI.

foundational-reformulation

A categorical-condensed reconstruction program for geometry, quantum theory, and kinetic theory

topological-phases-of-matter

Six-paper research program: topological phases of matter in a condensed-mathematics paradigm — condensed moduli stacks of Hamiltonians, uniform spectral gaps, solid K-theory, bordism realizability; with Haskell verification suites and a sorry-free Lean 4 library.

topological-phases-of-matter-chatgpt

Six-paper research program on topological phases in condensed mathematics, with reviewed PDFs, Haskell checks, Lean interfaces, and a static research site.

condensed-representation-theory-of-physics

Toward a Condensed Representation Theory of Physics — a modular 7-part series on condensed mathematics, representation theory, and emergent spacetime (LaTeX + Haskell + Lean + Next.js).

math-qg-representation-library

Quantum gravity as reconstruction from invariant representation structures — 12 regime papers + synthesis, with Haskell + Lean verification

mathematics-physical-representation

A modular research library reading a Goncharov-style Lie coalgebra as the decomposition law of physical observables: five peer-reviewed, formally-verified (Haskell + Lean 4) papers plus a synthesis.

math-phy-library

A Math->Physics Representation Library: six formally-verified papers + a modular synthesis (LaTeX, Haskell/Lean verification, agy+Codex review, Next.js site).

hott-riemann-hypothesis-vol5

Using homotopy type theory and condensed mathematics to attack the Riemann Hypothesis with machine-checked formal proof. Final volume of a five-part programme. RH formally reduced to two named open problems, proven equivalent inside the condensed (∞,1)-topos. 239 verified Lean theorems, zero invalid.

hott-riemann-hypothesis-vol4

Volume IV — From formulation to formal proof: actually proving the OQ1, OQ3, OQ5 theorems via Lean 4 + Cubical Agda + rzk + Haskell. 62 valid / 0 invalid / 29 incomplete machine-checked theorems verified by Codex gpt-5.5 xhigh.

hott-foundations-mathematics

HoTT Foundations of Mathematics, Volume II — six open problems unified toward ζ(s)=0 as a HoTT-native statement. 7 papers + synthesis (176pp), Haskell verification, Lean proofs, Next.js site.

emergent-spacetime-dynamics

A modular four-part research series formalizing emergent phases of matter from information through category theory.

hott-hallucination-research

Hallucination–Homotopy Correspondence: A complete HoTT framework for AI hallucination detection and prevention. 3 papers, verified Haskell, live website.

dna-lang

DNA-Lang: A typed programming language for biological systems. 8 research papers + Haskell implementations mapping DNA sequence categories to programming language constructs.

yoneda-constraint

The Yoneda Constraint as a universal axiom: unifying Godel, the measurement problem, compiler bootstrap, and AI alignment under one categorical principle.

yoneda-ai

Category-theoretic foundations for open problems in quantum mechanics, gravity, and observer theory — 6 papers applying the Yoneda Constraint

time-compression-paradox

The Time Compression Paradox: A formal analysis of why AI increases rather than eliminates work. Four-paper research series (~91 pages) by Matthew Long, YonedaAI Research Collective.

yoneda-ai-web

YonedaAI Research Collective website — yonedaai.com — 16 peer-reviewed papers on category-theoretic quantum foundations

categorical-architecture-qp

The Categorical Architecture of Quantum Perspectivism: Topoi, Logic, and Dynamics [math-ph] — 27pp peer-reviewed paper with Haskell formalization

open-problems-qp

Open Problems in Quantum Perspectivism: From Category Structure to Experimental Signatures [quant-ph] — 32pp peer-reviewed paper with Haskell formalization

entanglement-complementarity-measurement

Entanglement, Complementarity, and Measurement as Categorical Phenomena [quant-ph] — 27pp peer-reviewed paper with Haskell formalization

technical-constructions-qp

Technical Constructions in Quantum Perspectivism: Complex Amplitudes, Gleason, and Decoherence [math-ph] — 26pp peer-reviewed paper with Haskell formalization

yoneda-constraint-quantum-structure

Deriving Quantum Mechanics from the Yoneda Constraint [quant-ph] — 36pp peer-reviewed paper with Haskell formalization

philosophical-implications-qp

Philosophical Implications of Quantum Perspectivism: Structural Realism and the Primacy of Relation [physics.hist-ph] — 26pp peer-reviewed paper with Haskell formalization

connections-existing-frameworks

Quantum Perspectivism and Its Relations: RQM, QBism, Many-Worlds, and Topos Theory [quant-ph] — 32pp peer-reviewed paper with Haskell formalization

yoneda-physical-content

The Yoneda Lemma as Physical Law: Identity, Relation, and the Structure of Reality [math.CT] — 29pp peer-reviewed paper with Haskell formalization

quantum-gravity-emergent-spacetime

Quantum Gravity and Emergent Spacetime from Perspectival Structure [hep-th] — 29pp peer-reviewed paper with Haskell formalization

crisis-of-foundations

The Crisis of Quantum Foundations: Why Physics Needs the Yoneda Constraint [quant-ph] — 27pp peer-reviewed paper with Haskell formalization

type-safe-biophysics

Type-Safe Biophysics: The Protein Folding Problem as Type Inference - Why AlphaFold Works and What It Teaches Us About Machine Learning. A novel framework connecting protein folding to type theory.

type-safe-physics

Type-Safe Physics: A framework for expressing physics with mathematical rigor using type theory, category theory, and formal verification. Includes paper, Haskell implementations, and educational resources.

functorial-fission

A Functorial Formulation of Nuclear Fission: Category theory meets nuclear physics with type-safe Haskell implementation

standard-model

Standard Model research: modular physics framework for matter, anti-matter, and gauge unification

minimal-runtime-axiom

The Minimal Runtime Axiom: Runtime is proof of ignorance. A type-theoretic and category-theoretic formalization.

quantum-perspectivism-haskell

Complete Haskell implementation of Quantum Perspectivism — categorical framework for foundational physics via the Yoneda Constraint. 42 modules, 11-step derivation chain from Yoneda Lemma to Schrödinger equation.

emergent_spacetime

Investigating emergent spacetime through simulations and theoretical models to understand its origins.

yonedaai-industry-research

YonedaAI Methodology: Mitigating AI Code Generation Limitations through Risk-Aware Engineering, Golden Paths, and Enterprise AI Governance Frameworks

black_hole_info_paradox_resolution

A formal resolution to the Black Hole Information Paradox through information-theoretic foundations

modular-physics

A compositional framework for fundamental physics laws based on information-theoretic principles

ai_theory

Advancing the theoretical foundations of Artificial Intelligence through interdisciplinary research. This repository bridges AI, mathematics, and information theory, exploring innovative concepts that shape the future of AI systems. Contributions are welcome!

chain-of-intent

Chain of Intent (CoI): Novel AI alignment framework treating intent as mathematically transformable objects. Implements semantic preservation theorems, safety verification, and clarification protocols for LLMs.

functorial-physics

Explore theoretical physics through functorial frameworks, unifying mathematical structures and physical phenomena.

first-law-entanglement

Rigorous Haskell proof of the First Law of Entanglement (δS_A = δ⟨K_A⟩) - the quantum information principle showing how spacetime emerges from entanglement.

unified_foundations_of_mathematics

A deep dive into the universal underpinnings of mathematics, seeking to unify set theory, category theory, logic, and more under a cohesive framework

quantum_unification

Investigations into unifying quantum mechanics with broader physical theories, exploring foundational concepts and beyond.

quantum_database_theory

Cutting-edge exploration of quantum-enhanced database operations using principles of quantum computing. Join us! #quantum #database #technology

proof_as_code_qec

Compositional quantum error correction pipeline in Haskell, integrating topological, penalty-based, and type-theoretic QEC with code-based verification....

proof_as_code_math_physics

Explore math and physics concepts through code with examples in calculus, mechanics, and electromagnetism. Haskell and Coq used.

proof_as_code

A repository showcasing the power of using code to generate and verify mathematical proofs and assertions. Technologies: Python, Jupyter Notebooks. Standout ...

quantum-topological-qec

Quantum topological QEC: Explore algorithms for error correction in quantum systems using topological properties. #QEC #topological- codes

derived-functors-qec

Derived Functors and Quantum Error Correction: A Homotopy-Theoretic Approach

database_theory

Advancing database theory through interdisciplinary research. Explore mathematical frameworks like Topos Theory, functional programming, and the Langlands program applied to modern database challenges. This repository houses papers and resources for researchers and developers pushing the boundaries of database design and architecture.

FunctorialHamiltonians

A repository exploring Hamiltonian mechanics using category theory and functors. It demonstrates the construction and transformation of Hamiltonians through functorial mappings, bridging mathematical physics and algebraic structures. Ideal for researchers in quantum mechanics and advanced algebra.

QuantumFlow

QuantumFlow – A Python library for simulating derived Hamiltonians in quantum fields, lattice QCD, quantum circuits, and biophysics. Supports tensor-driven computations, phase space visualizations, and higher-order corrections to classical and quantum systems.

on_the_same_origin_of_quantum_physics_and_general_relativity_expanded_with_code

Code For Unified Physics

geometric_langlands_conjecture_expanded

Comprehensive resources and explorations of the Geometric Langlands Conjecture, bridging number theory, geometry, and representation theory.

mathematical_physics

An interdisciplinary collection of resources on the nexus of advanced mathematics and theoretical physics, with an emphasis on fundamental principles.