Pith Number

pith:YIPXLBFK

pith:2026:YIPXLBFKIR64FLKSD77A5MQPXS

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Controllable and Verifiable Process Data Synthesis for Process Reward Models

Lucien Wang, Yinghui Chi

A synthesis method builds controllable process supervision data by injecting template-aware errors into symbolic reasoning chains, recomputing trajectories, and translating them to natural language for training process reward models.

arxiv:2605.02395 v2 · 2026-05-04 · cs.AI

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\usepackage{pith}
\pithnumber{YIPXLBFKIR64FLKSD77A5MQPXS}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Experiments show that the synthesized data improve Best-of-8 reranking on logical reasoning benchmarks and transfer to mathematical reasoning. Step-level evaluation further shows that first-error localization remains substantially more challenging than overall step classification.

C2weakest assumption

The assumption that template-aware errors injected into symbolic chains and then recomputed produce trajectories whose error patterns and consistency properties transfer meaningfully to natural-language reasoning processes used in real PRM training.

C3one line summary

A controllable synthesis method creates prefix-invalid yet trajectory-consistent process supervision data for training and evaluating process reward models by injecting verifiable errors into symbolic reasoning chains.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-06-05T01:14:39.903081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c21f7584aa447dc2ad521ffe0eb20fbcb742473a92848b82c03b10aea0fb069d

Aliases

arxiv: 2605.02395 · arxiv_version: 2605.02395v2 · doi: 10.48550/arxiv.2605.02395 · pith_short_12: YIPXLBFKIR64 · pith_short_16: YIPXLBFKIR64FLKS · pith_short_8: YIPXLBFK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YIPXLBFKIR64FLKSD77A5MQPXS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c21f7584aa447dc2ad521ffe0eb20fbcb742473a92848b82c03b10aea0fb069d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f4f310104438fccb75c5a90592ba01100485f452c56fb76290f326fd8fed9c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-05-04T09:36:57Z",
    "title_canon_sha256": "c149d2cbea3f31883b2110a96f47abfdbf165eee56ece73506d976a1e1b3bc08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02395",
    "kind": "arxiv",
    "version": 2
  }
}