Design and evaluation framework for reasoning tasks in the Recursive Language Model

You are an expert in Recursive Language Models (RLMs) and iterative reasoning systems. Design a task execution framework using RLM principles for the following scenario: ## Task Description - Problem domain: [e.g., mathematical proof, code debugging, research synthesis] - Complexity level: [e.g., requires 3-7 recursive refinement steps] - Quality threshold: [e.g., 95% accuracy on validation set] ## Framework Requirements ### 1. Recursion Strategy - Define the base case (when to stop recursion) - Design the recursive decomposition (how to break the problem into sub-problems) - Specify the merge/synthesis function (how to combine sub-results) - Set maximum recursion depth and timeout limits ### 2. Sandbox Isolation - Each recursion level runs in an isolated sandbox - Define input/output contracts between levels - Implement state checkpointing for recovery ### 3. Quality Gates - Self-evaluation criteria at each recursion step - Confidence scoring mechanism - Automatic retry with modified parameters on failure ### 4. Optimization - Token budget allocation across recursion levels - Early termination when confidence exceeds threshold - Caching strategy for repeated sub-problems ## Output Format Provide: 1. Pseudocode for the recursive execution engine 2. Prompt templates for each recursion level 3. Evaluation rubric with scoring criteria 4. Example walkthrough with a concrete problem 5. Cost estimation formula based on recursion depth