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README.md

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+# Chain-of-Thought as Sequential Conditional Probability Constriction
+
+## Author
+**Kevin T.N**  
+Email: jkdkr2439@gmail.com
+
+---
+
+## What is this?
+
+This repository contains a **theoretical / mathematical interpretation of Chain-of-Thought (CoT) prompting** for large language models.
+
+Instead of treating CoT as:
+- "reasoning"
+- "thinking step by step"
+- or a cognitive mechanism
+
+this work formalizes CoT as:
+
+> **A sequential conditional probability constriction process**,  
+> where each intermediate token re-conditions the model distribution,  
+> progressively narrowing entropy and steering probability mass.
+
+In short:
+- CoT does **not** add intelligence
+- It reshapes **how probability is conditioned and sampled**
+
+---
+
+## Who is this for?
+
+This work may be useful if you are:
+- A researcher working on **LLM interpretability**
+- Interested in **reasoning vs. probability steering**
+- Designing **prompting, inference, or sampling strategies**
+- Thinking about CoT, ToT, ReAct from a **theoretical / information-theoretic** angle
+
+This is **not**:
+- a benchmark paper
+- a performance hack
+- a production recipe
+
+It is a **conceptual tool**.
+
+---
+
+## How to use this work
+
+You are encouraged to:
+- Reuse the mathematical framing
+- Adapt the notation to your own context
+- Extend it with:
+  - Bayesian inference
+  - filtering / particle methods
+  - causal or SCM analysis
+  - empirical validation
+
+If you find it useful:
+- **Please credit or shout out the author** (Kevin T.N)
+- You do **not** need permission
+- You **should** adapt and update it to your own framing
+
+This work is intentionally open and unfinished.
+
+---
+
+## Citation / Attribution (informal)
+
+If you reference this idea in writing or discussion, a simple attribution is enough:
+
+> “Based on a probabilistic interpretation of Chain-of-Thought as sequential conditional distribution constriction by Kevin T.N.”
+
+Formal citation is optional.
+
+---
+
+## License
+
+This project is released under the **MIT License**.
+
+You are free to:
+- use
+- copy
+- modify
+- merge
+- publish
+- distribute
+- sublicense
+
+with **no warranty**, as long as the license notice is included.
+
+---
+
+## MIT License
+
+MIT License
+
+Copyright (c) 2026 Kevin T.N
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.