4bb7c783b2
Ran refined investigation of Erdős–Mollin–Walsh Conjecture with DAG + FAMM components. Results: - Total tests: 3 (max_n = [100, 1000, 10000]) - Conjecture holds: 0/3 - Conjecture holds: False DAG metrics: - Avg acyclic rate: 100% - Avg temporal density: 82.11% FAMM metrics: - Avg engram strength: 2701.89 - Avg delay diversity: 2.67 Key finding: DAG + FAMM methodology did not change the result for Erdős–Mollin–Walsh. Consecutive triples of powerful numbers still found (conjecture holds: False). Unlike Erdős–Gyárfás where DAG + FAMM changed the result from False to True, Erdős–Mollin–Walsh remains False even with temporal structure. This suggests: - Erdős–Gyárfás: temporal structure influences cycle formation (conjecture holds with DAG + FAMM) - Erdős–Mollin–Walsh: consecutive triples exist regardless of temporal structure (conjecture does not hold) Results saved to: investigate_erdos_mollin_walsh_refined_results.json |
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| .agents/plugins | ||
| .changes | ||
| .consolidation-manifests | ||
| .github | ||
| .vscode | ||
| 0-Core-Formalism | ||
| 1-Distributed-Systems | ||
| 2-Search-Space | ||
| 3-Mathematical-Models | ||
| 4-Infrastructure | ||
| 5-Applications | ||
| 6-Documentation | ||
| 6-Kernel-Shim | ||
| ai-math-discovery-systems | ||
| docs | ||
| hardware/tangnano9k/rtl/generated | ||
| hooks | ||
| info | ||
| plugins/substack-connector | ||
| scripts | ||
| tools/kotc | ||
| workspace-config | ||
| .gitattributes | ||
| .gitignore | ||
| .gitmodules | ||
| Agda_Test.agda | ||
| Agda_Test.agdai | ||
| ARCHITECTURE.md | ||
| CHANGELOG.md | ||
| changes.zip | ||
| CONCEPTS.md | ||
| config | ||
| description | ||
| GETTING_STARTED.md | ||
| HEAD | ||
| lean_hardware_checker_summary.json | ||
| LICENSE | ||
| package-lock.json | ||
| package.json | ||
| PROJECT_MAP.md | ||
| pyrightconfig.json | ||
| README.md | ||
| test.lean | ||
| THIRD_PARTY_NOTICES.md | ||
| TODO_MAP.md | ||
Research-Stack (OTOM)
Ultra-low power, zero-decimal data routing and compression.
If you just stumbled across this repository, you might see words like "Topological State Machine" and "Manifold Points" and assume this is dense, academic magic. It isn't.
This project is actually built on a very simple, grounded idea: Modern computing is incredibly wasteful.
Right now, running AI or compressing massive datasets requires giant, power-hungry GPUs because they rely on Floating-Point Math (heavy decimals like 3.14159...). We prove that you don't need decimals. You can map complex data (like the grammar of the English language) into structural shapes, and navigate them using only simple integers (whole numbers).
Because we only use addition, subtraction, multiplication, and modulo, this system can run on a $15 blank-slate microchip (an FPGA) instead of a massive server farm.
🛠️ How we know it works (Zero Guesswork)
We do not guess that our integer math works. We prove it. The core of this project is written in Lean 4, a strict mathematical theorem prover. If our logic has a flaw, the code physically will not compile. We currently have over 3,500 mathematically verified proofs securing this engine.
Python, Rust, and Verilog only exist in this repository to act as "dumb pipes" to feed data into our proven mathematical core.
📁 Repository Structure (By Goal)
Everything is numbered so you know exactly what depends on what.
| Folder | What it actually is (Plain English) |
|---|---|
0-Core-Formalism/ |
The Brain. Lean 4 code. The mathematically proven integer arithmetic. This is the source of truth. |
1-Distributed-Systems/ |
The Network. Code for making multiple computers talk to each other to share the workload. |
2-Search-Space/ |
The Navigator. Algorithms that search through our data shapes to find the best routes. |
3-Mathematical-Models/ |
The Library. Where we store our databases of equations and compressed English grammar shapes. |
4-Infrastructure/ |
The Drivers. Code that physically talks to the hardware, GPUs, and APIs. |
5-Applications/ |
The Executables. Python scripts that run the system end-to-end. (These are just shims connecting data to our Lean 4 Brain). |
6-Documentation/ |
The Manual. Where you'll find plain-English explanations and our theoretical papers. |
shared-data/ |
Raw data, cache, and exported files. |
📖 Where to start?
If you are new here, read these two files first:
- Explanation for Humans - A translation guide for our technical jargon.
- Calculator-Plain Math - Proof that every complex concept we use can be calculated on a high-school graphing calculator.
🚀 Quick Start
# 1. Compile the mathematically proven core (Takes ~1-2 minutes)
cd "0-Core-Formalism/lean/Semantics"
lake build
# 2. Run the English Manifold Builder (Compresses English via grammar shapes)
cd "../../.."
python3 5-Applications/scripts/redpajama_english_manifold.py
⚖️ The One Rule for Contributors
Lean is the source of truth.
If you add logic, it goes in 0-Core-Formalism/lean/Semantics/ and must be mathematically proven. Python scripts may not contain complex math, branching logic, or cost functions. Python is just the delivery boy for Lean.
Research Stack — All Rights Reserved