What problem does it solve? Broken or ambiguous competitive programming problems waste downstream effort on test generation, reviews, and editorials. This Skill acts as a quality gate that solves a problem draft first, proving solvability before any further pipeline work proceeds. ## Core Features & Use Cases - Solvability Gate: Outputs a structured solution.json with a success verdict or a SOLVABILITY_FAILURE with a specific, actionable failure reason that routes the draft back for revision. - Verified Reference Solution: Produces language-agnostic pseudocode, step-by-step time and space complexity derivations, and a formal correctness proof using one of five techniques (loop invariant, exchange argument, induction, monotonicity, greedy stays ahead). - Adversarial Support Artifacts: Generates a brute-force solution for cross-verification and a list of common wrong approaches with concrete counterexamples for test design. - Use Case: Given a problem_draft.json describing a binary-search-on-answer task with N up to 10^5, verify the constraints match the required O(N log N) complexity, prove correctness via monotonicity, and flag any sample-statement contradictions before tests are written. ## Quick Start Verify the solvability of the problem in problem_draft.json and produce a reference solution with a correctness proof and complexity analysis.
