jkdkr2439/exchange-invariant-technique

EIT Proof Framework

Exchange–Invariant Technique (EIT)
A structured reasoning framework for inequality proofs and invariant-based arguments.

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Overview

This repository contains a concise methodological note on the Exchange–Invariant Technique (EIT) —
a structured way to reason about inequalities and optimization problems using symmetry, exchange arguments, and invariant analysis.

⚠️ This work does not claim a new mathematical theorem or a novel proof method.

EIT is a formalized reasoning template that reorganizes well-known techniques (exchange arguments, invariants, symmetry) into a reusable analytical framework.

The primary goal is clarity, pedagogy, and transferability, not novelty.

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What This Is

• A reasoning framework for:
  • Inequality proofs
  • Symmetry-based arguments
  • Invariant-driven transformations
• A proof structuring tool
• A thinking scaffold useful for:
  • Students
  • Educators
  • AI reasoning systems
  • Formal proof decomposition

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What This Is NOT

• ❌ Not a new inequality theorem
• ❌ Not a replacement for classical methods
• ❌ Not claiming mathematical originality beyond organization and exposition

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Core Idea (Informal)

Many inequality and optimization problems can be analyzed by:

1. Identifying exchangeable variables
2. Applying local swaps that preserve constraints
3. Tracking invariants under these exchanges
4. Showing monotonic improvement or convergence to an extremal configuration

EIT makes this logic explicit and repeatable.

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Contents

• EIT.pdf
  The main document describing:
  • Conceptual structure of EIT
  • Formal reasoning steps
  • Worked examples
  • Limitations and scope

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Intended Use Cases

• Mathematical education
• Proof strategy learning
• Competitive programming reasoning
• Symbolic reasoning research
• Training data for AI systems learning proof patterns

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Citation

If you use or reference this framework, please cite as:

Kevin T.N.,
Exchange–Invariant Technique (EIT): A Proof Structuring Framework, 2026.

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License

MIT License — free to use, adapt, and redistribute with attribution.

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Author Note

This repository treats reasoning structure itself as the object of study.
The value lies not in new results, but in making implicit proof logic explicit and reusable.