YonedaAI Research Collective

Category-theoretic foundations for open problems in quantum mechanics, gravity, and observer theory.

This repository contains a systematic research program applying the Yoneda Constraint — a category-theoretic framework based on the Yoneda lemma — to six foundational problems in physics. Each paper includes formal proofs, accompanying Haskell implementations, and Gemini-reviewed peer feedback.

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Papers

Paper	Pages	Category
Black Hole Information Paradox	26	hep-th
Hidden Variable Debates	27	quant-ph
Measurement Problem	28	quant-ph
Wigner's Friend	32	quant-ph
Horizon Problems	33	hep-th
Limits of Quantum Gravity Observation	33	gr-qc

Total: 179 pages across 6 papers

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Core Framework

The Yoneda Constraint reformulates fundamental physics problems as category-theoretic obstructions:

• Measurement categories encode observer-system interactions as morphisms
• Representable presheaves characterize accessible knowledge via the Yoneda embedding
• Kan extension deficits quantify information loss at epistemic horizons
• Cohomological obstructions unify no-go theorems (Bell, Kochen-Specker, PBR) as presheaf failures

Each paper builds on a shared mathematical vocabulary from category theory (AQFT, topos theory, enriched categories) and connects to the broader YonedaAI research program.

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Repository Structure

yoneda-ai/
  sources/              # Original .tex research papers (knowledge base inputs)
  papers/
    latex/              # New papers (.tex source)
    pdf/                # Compiled papers (.pdf)
  reviews/              # Gemini CLI peer review reports
  src/
    black-hole-information-paradox/    # Haskell: representable functors, Page curve
    hidden-variable-debates/           # Haskell: Bell/KS verification, Kan extensions
    measurement-problem/               # Haskell: Born rule, decoherence, obstruction
    wigners-friend/                    # Haskell: presheaf irreconcilability, CHSH
    horizon-problems/                  # Haskell: causal categories, horizon deficits
    limits-quantum-gravity-observation/# Haskell: QG obstructions, entropy bounds

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Key Results

• Presheaf Irreconcilability Theorem — Friend's and Wigner's presheaves are provably non-isomorphic (Wigner's Friend)
• Measurement Obstruction Theorem — The measurement problem is a Yoneda obstruction with cohomological invariant (Measurement Problem)
• Three Independent Yoneda Obstructions to Planck-scale observation: gravitational horizon, diffeomorphism gauge, holographic saturation (QG Limits)
• Unified No-Go Framework — Bell, Kochen-Specker, PBR, von Neumann, and Free Will theorems as presheaf obstructions (Hidden Variables)
• Horizon Classification — All horizon types (cosmological, event, Rindler, de Sitter, holographic) as accessible subcategory inclusions with Kan extension deficits (Horizon Problems)
• Page Curve as Kan Extension — Island formula emerges as the left Kan extension along the inclusion of the radiation subsystem (Black Hole Information)

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Building

Papers

cd papers/latex
pdflatex -interaction=nonstopmode <paper>.tex
pdflatex -interaction=nonstopmode <paper>.tex  # second pass for references

Haskell Code

cd src/<subject>
ghc -o main Main.hs
./main

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Authors

Matthew Long The YonedaAI Collaboration YonedaAI Research Collective Chicago, IL matthew@yonedaai.com | yonedaai.com

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Methodology

Papers were generated using a multi-agent pipeline:

1. Knowledge Base Agent — ingested 7 source .tex files into a structured knowledge base
2. 6 Worker Agents — each wrote a 20+ page paper with Haskell code from the Yoneda Constraint perspective
3. Gemini CLI Peer Review — each paper reviewed by Google Gemini for mathematical correctness, clarity, and completeness
4. Revision Pass — all reviewer feedback addressed and incorporated
5. PDF Compilation — LaTeX compiled with GrokRxiv DOI sidebars

See agent-execution-plan.md for the reusable execution schema.

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License

All rights reserved. For academic use and citation, please contact the authors.