When the Verifier Cannot Decide

Tracing Math-Verify Failures Through an RLVR Reward Pipeline

Yufeiyang Chen · preprint version of 3 November 2026

Current version: read the paper (PDF, 23 pages) · arXiv source package (main.tex, main.bbl, refs.bib; LaTeX source also in paper/main.tex) · validation record · reviewer guide · companion materials

This is a publicly available research manuscript. It has not been peer reviewed and has not been posted to arXiv; paper/SUBMISSION_CHECKLIST.md records the author's confirmations (licences, authorship, categories). Posting is not yet authorised. The companion archive contains code and evidence for inspection; it does not contain model weights, upstream datasets or the complete original raw-log archive.

Historical versions (kept unchanged, superseded): paper.pdf is the manuscript revised 12 October 2026 that this repository first published; earlier 3 November drafts are in paper/superseded/ and paper/reconstruction-from-pdf/. Cite or review the current version above.

Reproduction snapshot. The analysis code, result files and number checker used for the current manuscript are at commit da00bd6; later commits change only documentation, front matter and release notes (see paper/CHANGES.md). Some re-checks additionally read the author's input archive at the fixed commit e29d296 (branch author-inputs-20261103, not merged into main): the pre-correction main-run rows (recount of k = 1, u = 9,573), the heavy-input rows of the Linux scenes and the thesis-run records. That archive does not contain the reference-pass event files, so the reported u = 18 remains a historical report value; it has not been independently rebuilt from raw events. See audit/REPRODUCE.md.

Study

The study traces failure information from Math-Verify through a pinned verl reward wrapper, manager and batch aggregation. Controlled worker-failure tests reproduce a known sparse-metadata problem: the position of a failed row can determine whether its flag is lost or the batch raises an exception. The manuscript cites the related upstream proposals #6545 and #7151. Its contribution is the specific wrapper-to-consumer failure trace and the paired corpus and timeout/recovery measurements. The local aggregation prototype supplies 21 regression fixtures, not a new repair algorithm.

A pre-declared replay covers 93,733 stored mathematical responses. Longer checking limits recover one zero-to-one verdict and leave 18 responses undecided. A separate extension covers all 193,767 stored answers. Matched shared-pool tests and a fixed-source comparison distinguish the behavior of wrappers and execution settings.

These results are conditional on the fixed corpora and declared protocols. Longer checking is not mathematical ground truth. Controlled failure injections and shared-pool diagnostics do not measure failure rates in training, and no training benefit has been measured. The paper states the sampling assumptions, comparison units and limits of inference.

Inspect the evidence

Extract the companion archive into a fresh directory. From its root, run:

python3 -B experiments/check_artifacts.py --index package_manifest.json
python3 -B experiments/compare_runs.py

These commands inspect the distributed snapshot without installing packages or downloading data. The archive includes compact reports, derived score records, selected event traces, synthetic checks, exact upstream source revisions and a file manifest. Its README explains which records are included and which are omitted.

Replaying the measurements requires the documented dependencies, upstream sources and separately obtained datasets. The measured environment was macOS arm64 with CPython 3.12.8. A fresh installation and Linux have not been experimentally validated. Follow the archive's instructions in a fresh environment; do not overwrite retained original records or an existing measurement environment.

Public evidence clarification (3 November 2026)

The manuscript PDF and its reported measurements are unchanged. The companion now includes EVIDENCE_STATUS.md and a read-only, standard-library audit:

python3 -B experiments/audit_public_evidence.py

This independently counts the distributed default-pass derived records and checks recorded regression outcomes. It is not a new scoring experiment or an independent raw-event replication. The corrected main reference records and complete historical reanalysis inputs remain unavailable in the public package, so k=1 and u=18 are reported values, not independently reconstructed by this audit. The note also distinguishes reference-protocol unresolved rows from all library execution failures and lists the evidence still needed. No training benefit or fresh-machine replication has been added.

Evidence audit and revision (3 November 2026)

The audit adds, without changing the historical paper.pdf or the companion archive:

• audit/EVIDENCE_MAP.md: claim-to-evidence table and every check run.
• audit/GAPS.md: what still cannot be verified and the smallest input that would close each gap.
• audit/REPRODUCE.md: commands, environment and stored results.
• audit/upstream_chain/: real-function failure-chain tests and two patches for verl 0c4c3d4 (a port of the open upstream PR #7151, and a validation-accumulation fix).
• audit/experiments/e3_linux/: a new, pre-specified Linux replay of the labelled answer set.
• paper/: the author's original LaTeX source, revised (paper/CHANGES.md), with build notes, the compiled preprint and the arXiv source package; an earlier editable reconstruction from the public PDF is kept in paper/reconstruction-from-pdf/.
• audit/experiments/offline_policy/: the offline handling-policy comparison of §8.2 (synthetic failures on 72 human-labelled groups; a mechanism analysis, not a training result or a natural failure rate).
• audit/scripts/check_paper_numbers.py: checks manuscript numbers against their source files, with counter-tests.
• audit/THESIS_HANDOFF.md: items a dependent thesis must re-check.

New executions ran on Linux x86-64 (CPython 3.12.8); they are additional verification, not a replay of the historical macOS environment. Recounting the distributed derived records is not an independent reproduction from raw data. The author's pre-correction rows reproduce k = 1 and the uncorrected u = 9,573; the corrected u = 18 remains a report-only value.

Contribution and assistance

The author selected the research topic, research route and methods. AI agents provided substantial assistance with implementation, experiment execution, code analysis and manuscript drafting. The manuscript contains the full contribution and AI-use statement. Human answer labels in the supplementary analysis were supplied by the cited dataset authors.

Licences and fixed files

• Manuscript: CC BY 4.0 (confirmed by the author).
• Original companion code and synthetic fixtures: Apache-2.0; see LICENSE and NOTICE inside the archive.
• Original code, records and documentation under audit/: Apache-2.0; see audit/LICENSE and audit/NOTICE. The NOTICE lists the parts that keep third-party terms (verl code in the two patches, OpenR1 texts in the heavy-scene specs, the MIT human-label CSV); see audit/LICENSING_PLAN.md.
• Third-party sources and datasets retain their own licences and notices.

SHA-256 of the distributed files (historical paper.pdf and companion archive):

8efbb3471d23a8b5396bc1605fb5cf29d4769ee6e0214ede8e63e76f69c46811  paper.pdf
2aaf2113ebc11a5396dc17408a40534419bb14b70589de30a832c146a1381ae4  rewardfail-companion.zip