# Source audit

Paper: “Provable Benefits of RLVR over SFT for Reasoning Models: Learning to Backtrack Efficiently.”

- OpenReview: https://openreview.net/forum?id=P3Mnh7mF5a
- ar5iv HTML: https://ar5iv.labs.arxiv.org/html/2606.22938
- native arXiv HTML: https://arxiv.org/html/2606.22938
- arXiv abstract: https://arxiv.org/abs/2606.22938

Retrieved 2026-08-02T21:25:02Z. The Hugging Face paper API and markdown page returned HTTP 404, so ar5iv was used first and native arXiv HTML as the cross-check.

```text
062be411b3806eaeb00210fad3eae84cdd4184720785617cf692ac8ed7275609  ar5iv_2606.22938.html
cf881567846718959e1c5bd12385381893a45fb20dbfc8e010aef9390a7e76ff  arxiv_2606.22938.html
```

Claim anchors:

1. Theorem 2 and Appendix A: shortest-path SFT row support and gradient flow.
2. Theorem 3 and Appendix B: sign policy-gradient flow.
3. Theorem 4 and Appendix C: inference-time recurrence and separation.
4. Corollary 1 and its proof: rejected generations under directed-state duplicate avoidance count as work.
5. Theorem 5 and Appendix D: row-wise CE on RLVR-induced transition pairs. Figure 3 sets `W=15,K=15,L=5`, sign-GD learning rate `0.01`, and reports `4WK=900`.

No official code repository is linked by the paper or its arXiv source. The implementation is clean-room and links its public ID-keyed mirror at https://github.com/MachineLearning-Nerd/P3Mnh7mF5a.