🧠 Geometry‑Driven AI Memory (Working Papers)

Independent research on AI memory systems, information geometry, and the "physical properties" of semantic data.
Status: 🚧 Work‑in‑progress – looking for collaborators and friendly reviewers, especially on the math derivations.

🔍 Why AI-Co-Discovery Works

1. Symbolic Co-Pilot: LLMs excel at tensor algebra and code scaffolding.
2. Error Injection: Prompt LLMs to break proofs; humans patch the gaps.
3. Rapid Iteration: Compress 3-week derivations into 3-hour Socratic loops.

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Table of Contents

Project	Paper	DOI	Code	Blog	Status
CHEESE Contextual Hierarchy for Embedding Enhancement & Semantic Enrichment	paper.md		cheese/cheese_minimal.py	Medium	📝 Draft (unpublished)
BREAD Bundles, Relations, Embeddings, And Dimensions	paper.md		bread/bread_minimal.py	Medium	📝 Draft (unpublished)
SMoGE Structured Multi‑Geometric Expertise	Private		Available on request	-	📝 Draft (private)
L‑Shape Lossless Hierarchical Representation	Private		Available on request	-	📝 Draft (private)
Geometric Phase Transitions The Instant Transformation from Euclidean to Hyperbolic Space at Layer 1	README.md		geometric-phase-transitions/	-	✅ Published
Hyperbolic Helices Why Transformers Can't Count: Geometric Patterns of Semantic Uncertainty	preprint.pdf		helices/	-	✅ Published

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Running the Code

This repository uses UV for Python dependency management with a workspace configuration. All papers share common dependencies while maintaining their own specific requirements.

Quick Start

# Install UV (if not already installed)
curl -LsSf https://astral.sh/uv/install.sh | sh

# Install all dependencies
uv sync

# Run any paper from the root directory
uv run python helices/code/prototype_implementation.py
uv run python bread/bread_minimal.py
uv run python cheese/cheese_minimal.py

The workspace automatically manages:

• Shared dependencies (numpy, matplotlib, rich, sentence-transformers)
• Paper-specific requirements in each folder's pyproject.toml
• Single lockfile for reproducible environments

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License

IMPORTANT: This repository uses multiple licenses. See LICENSE for details.

• Papers/Documentation: LICENSE_PAPERS - CC BY-NC-SA 4.0 (no commercial use, share-alike)
• Code: LICENSE_CODE - Apache 2.0 with Non-Commercial rider
• helices/ folder: CC BY 4.0 (as published on Zenodo)

Patent Notice

No patent license—express or implied—is granted by distribution of this repository. Some concepts are covered by U.S. provisional patent applications filed in 2025. Any commercial use requires a separate patent license.

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Contributing / Feedback

I'm a self‑taught software engineer using AI‑assisted tooling orchestrated and validated by myself, to the best of my ability.
If you're comfortable with differential geometry, hyperbolic embeddings, or LLM memory, I'd love a sanity check or collaboration. Open an issue or email me (address in author: field of the papers).

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Citation

@misc{gardner2025geomemory,
  author    = {James Gardner},
  title     = {Geometry-Driven AI Memory Systems},
  year      = {2025},
  howpublished = {GitHub},
  url       = {https://github.com/jamestexas/papers}
}