A problem-solving tool inspired by Claude Shannon's systematic and iterative approach to complex problems.

This tool helps break down problems using Shannon's methodology of problem definition, mathematical modeling, validation, and practical implementation.

When to use this tool:

• Complex system analysis

• Information processing problems

• Engineering design challenges

• Problems requiring theoretical frameworks

• Optimization problems

• Systems requiring practical implementation

• Problems that need iterative refinement

• Cases where experimental validation complements theory

Key features:

• Systematic progression through problem definition → constraints → modeling → validation → implementation

• Support for revising earlier steps as understanding evolves

• Ability to mark steps for re-examination with new information

• Experimental validation alongside formal proofs

• Explicit tracking of assumptions and dependencies

• Confidence levels for each step

• Rich feedback and validation results

Parameters explained:

• thoughtType: Type of thinking step (PROBLEM_DEFINITION, CONSTRAINTS, MODEL, PROOF, IMPLEMENTATION)

• uncertainty: Confidence level in the current thought (0-1)

• dependencies: Which previous thoughts this builds upon

• assumptions: Explicit listing of assumptions made

• isRevision: Whether this revises an earlier thought

• revisesThought: Which thought is being revised

• recheckStep: For marking steps that need re-examination

• proofElements: For formal validation steps

• experimentalElements: For empirical validation

• implementationNotes: For practical application steps

The tool supports an iterative approach:

1. Define the problem's fundamental elements (revisable as understanding grows)

2. Identify system constraints and limitations (can be rechecked with new information)

3. Develop mathematical/theoretical models

4. Validate through proofs and/or experimental testing

5. Design and test practical implementations

Each thought can build on, revise, or re-examine previous steps, creating a flexible yet rigorous problem-solving framework.