RLVR versus SFT backtracking reproduction

This is a clean-room implementation of the directed-edge Markov model in Sections 3–4 of arXiv:2606.22938. It:

• solves expected hitting times from the Bellman linear system;
• differentiates that hitting time by an adjoint solve;
• executes signed-gradient RLVR dynamics at the paper’s full synthetic setting W=15, K=15, L=5;
• integrates the golden-path SFT and RLVR-trace-distillation cross-entropy dynamics;
• sweeps depth and edge multiplicity to test the inference-time separation;
• simulates the duplicate-state-avoiding search-agent accounting.

Run locally:

uv run reproduction/run_reproduction.py --output-dir outputs

The script is deterministic apart from the seeded search-agent Monte Carlo. It writes results.json plus three figures.