pith. machine review for the scientific record. sign in

arxiv: 2602.13218 · v2 · submitted 2026-01-23 · 💻 cs.AI · cs.CL· cs.LG· cs.LO

Recognition: 2 theorem links

· Lean Theorem

Scaling the Scaling Logic: Agentic Meta-Synthesis of Logic Reasoning

Bowen Liu , Zhi Wu , Runquan Xie , Zhanhui Kang , Jia Li
Authors on Pith no claims yet

Pith reviewed 2026-05-16 12:08 UTC · model grok-4.3

classification 💻 cs.AI cs.CLcs.LGcs.LO
keywords logic reasoningagentic synthesistask familiesRLVRdata generationverifiable rewardsLLM agents
0
0 comments X

The pith

LLM agents iteratively evolve logic task families by authoring Generator-Validator pairs, producing training data with new rules that improves reasoning benchmarks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces SSLogic, an agentic framework where LLM agents create and refine executable Generator-Validator pairs through a Generate-Validate-Refine loop to produce entire families of logic problems. This shifts synthesis away from fixed templates or single-instance tweaks toward tasks that carry fresh rules and explicit difficulty gradients. Starting from 400 seed families, two rounds of evolution generate 953 families containing 21,389 verifiable instances. Controlled comparisons on Enigmata data, matching steps, tokens, and dataset size, show consistent gains from the evolved data: +5.2 on SynLogic, +3.0 on AIME25, and +5.5 on BBH. Fine-grained KORBench results tie the structural changes to targeted lifts in logic and operation skills.

Core claim

SSLogic is an agentic meta-synthesis framework in which LLM agents iteratively author and refine executable Generator-Validator pairs inside a closed Generate-Validate-Refine loop, producing families with new rules and difficulty gradients rather than parameter variations of old ones. A Multi-Gate Validation Protocol filters ill-posed tasks before they enter training. Starting from 400 seed families, two evolution rounds yield 953 families and 21,389 verifiable instances. Three converging comparisons consistently show higher training utility of the evolved data.

What carries the argument

The closed Generate-Validate-Refine loop in which agents author Generator-Validator pairs, together with the Multi-Gate Validation Protocol that combines multi-strategy consensus and Adversarial Blind Review.

Load-bearing premise

The Multi-Gate Validation Protocol reliably removes ill-posed tasks and the agent-authored pairs produce genuinely new rules and difficulty gradients rather than superficial variations of the seed families.

What would settle it

Retraining a model on the evolved dataset and finding no performance difference versus baseline synthesis on the same step-matched, token-matched, and size-controlled Enigmata evaluations would falsify the utility claim.

Figures

Figures reproduced from arXiv: 2602.13218 by Bowen Liu, Jia Li, Runquan Xie, Zhanhui Kang, Zhi Wu.

Figure 1
Figure 1. Figure 1: Paradigm Shifts in Logic Data Generation: From Manual Curation to Agentic Meta-Synthesis. Left: Traditional Manual Curation focuses on Task/QA pairs, where quality control and feedback rely heavily on humans. Middle: Code Synthesis introduces executable Generators/Validators, achieving partial automation but still requiring manual supervision. Right: Our Agentic Meta-Synthesis enables fully automatic, end-… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the Multi-Gate Agentic Meta-Synthesis Framework. The Main Agent operates in a three-phase closed loop: Task Synthesis (Phase I), screening via Quality Agent Gates and Consensus-based Validation (including Blind Review) (Phase II), and Abductive Debugging for failures with Experience Updates, finally delivering Generators/Validators, templates, and data (Phase III). 3. SCALING THE SCALING LOGIC … view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of reflection-like token frequency across dif￾ferent training settings. 17.57 (+58%), confirming that the increased reflection is not merely an artifact of longer outputs. In contrast, the ARC-AGI-mixed setting (Math+ARC-AGI+Evolve) shows weaker length growth and a flatter reflection-like token curve (see § 4.8). This divergence aligns with the cross-domain performance gap, indicating that longer… view at source ↗
Figure 4
Figure 4. Figure 4: Average response length dynamics during training. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Cumulative Tokens (Billion) 0.10 0.15 0.20 0.25 Macro Accuracy Seed vs. Evolve (Token-Matched) SSLogic-Seed SSLogic-Evolve 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 Cumulative Tokens (Billion) 0.10 0.15 0.20 0.25 0.30 0.35 Macro Accuracy All Experiments (Token-Matched) SSLogic-Seed SSLogic-Evolve AIME+SSLogic-Evolve+ARC-AGI AIME+SS… view at source ↗
Figure 5
Figure 5. Figure 5: Macro Accuracy vs. cumulative RL tokens. At matched token budgets (∼1.09B), Evolve maintains a +7.3% relative advan￾tage over Seed, confirming that the gains are not solely attributable to additional compute from longer responses. To understand the impact of different task structures on reinforcement learning dynamics, we analyze ARC-AGI as a negative control in our study. • Observation: As shown in [PITH… view at source ↗
Figure 6
Figure 6. Figure 6: Difficulty controllability. Pass@1 accuracy between Seed and Evolved tasks at d ∈ {5, 7, 10} on DeepSeek-V3.1-Terminus and Doubao-1.6-Thinking. The curves decrease monotonically and closely track each other, with error bars shown. A key risk in synthetic generation is difficulty collapse (mod￾els default to trivial patterns) or complexity explosion (tasks become unsolvable). A controllable generator should… view at source ↗
Figure 7
Figure 7. Figure 7: Code-level complexity across sources. Distributions of structural and computational metrics on Seed and paired generator– validator programs. seed deepseek o4-miniglm Source 0 20 40 60 80 100 Percentage (%) O(1) O(log n) O(n) O(n log n) O(n²) O(n³) O(n^4+) O(V+E) O(V+E)/O(V^2) O(2^n) Recur.Bin. Search Sort. DP GraphDiv.- Conq. seed deepseek o4-mini glm 15.2 54.5 16.2 2.0 12.1 1.0 18.2 53.5 33.3 12.1 20.2 1… view at source ↗
Figure 8
Figure 8. Figure 8: Left: Inferred time-complexity distribution. Seed shows more cubic mass, while Evolved pipelines shift toward quadratic regimes. Right: Algorithmic pattern coverage. Evolved pipelines show higher rates of sorting, DP, graph, and recursion patterns. Sub-tasks near ceiling remain stable (boolean expressions 93.6→94.4). A generic data-quality effect would produce uniform gains; the observed selectivity suppor… view at source ↗
Figure 9
Figure 9. Figure 9: Cumulative RL token consumption across experiments. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Cumulative Tokens (Billion) 0.10 0.15 0.20 0.25 Macro Accuracy Seed vs. Evolve (Token-Matched) SSLogic-Seed SSLogic-Evolve 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 Cumulative Tokens (Billion) 0.10 0.15 0.20 0.25 0.30 0.35 Macro Accuracy All Experiments (Token-Matched) SSLogic-Seed SSLogic-Evolve AIME+SSLogic-Evolve+ARC-AGI AIME+… view at source ↗
Figure 10
Figure 10. Figure 10: Macro Accuracy vs. cumulative RL tokens. At matched token budgets (∼1.09B), Evolve maintains a clear advantage. N.4. Token Efficiency [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Mean response length during training. SSLogic-Seed SSLogic-Evolve AIME AIME+SSLogic-Evolve+ARC-AGI AIME+SSLogic-Evolve 0.0 0.5 1.0 1.5 Cumulative Tokens (B) 1.09 1.30 0.92 1.23 1.68 Token Budget @ Step 240 SSLogic-Seed SSLogic-Evolve AIME AIME+SSLogic-Evolve+ARC-AGI AIME+SSLogic-Evolve 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Macro Acc / Billion Token 0.213 0.203 0.327 0.204 0.205 Token Efficiency [PITH_FULL_I… view at source ↗
Figure 12
Figure 12. Figure 12: Token efficiency: accuracy gain per billion cumulative tokens. • Recent Steps: The most recent actions taken by the agent. • Previous Progress State: A JSON representation of the task’s progress, including key information and milestones. • Sub-Agent Functions and Tool Functions: Definitions of available sub-agents and tools for task execution. Progress State The progress state is crucial for tracking the … view at source ↗
Figure 13
Figure 13. Figure 13: The system prompt used for the planning module in the Cognitive Kernel Pro framework. O.1.2. ACTION PROMPT The Action module generates the specific Python code to execute the next step defined by the planner. CKPro Action System Prompt You are a strategic assistant responsible for the action module of the Cognitive Kernel, an initial autopilot system designed to accomplish user tasks. Your role is to gene… view at source ↗
Figure 14
Figure 14. Figure 14: The system prompt used for the action module in the Cognitive Kernel Pro framework. O.1.3. FINAL OUTPUT PROMPT The End module formats the final result when the agent finishes executing the task. CKPro Final Output System Prompt You are a proficient assistant tasked with generating a well-formatted output for the execution of a specific task by an agent. Available Information • Target Task: The specific ta… view at source ↗
Figure 15
Figure 15. Figure 15: The system prompt used for final output formatting in the Cognitive Kernel Pro framework. O.1.4. RESULT AGGREGATION PROMPT The Aggregation module selects the best result from multiple execution candidates (used in multi-path reasoning or repeated attempts). 31 [PITH_FULL_IMAGE:figures/full_fig_p031_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The system prompt used for result aggregation in the Cognitive Kernel Pro framework. O.2. Scale Scaling Logic (SSL) Pipeline Prompts The SSL pipeline for data generation consists of three main stages: Problem Evolution, Quality Verification, and Solution Generation. Additionally, we employ an Experience Manager to curate high-quality reasoning strategies and a Validator Builder to construct independent va… view at source ↗
Figure 17
Figure 17. Figure 17: The system prompt used for evolving seed problems into complex reasoning tasks in the problem evolution stage. Evolution System Prompt (Chinese) 你是一名负责演化高质量逻辑推理题目的代码推理Agent。 核心任务 在原seed 基础上设计三个独立组件来构建更深层次的逻辑推理题目，令推理链条发生实质性演变，提升题目难度， 而非仅更换题面场景： 1. generator（生成器）：Python 函数input(difficulty)，生成题目的输入数据和槽位文本 • 返回格式：(inputs, slot texts) • inputs：传递给validator 的输入数据 • slot texts：用于填充题面模板的文本列表 2. question template（… view at source ↗
Figure 18
Figure 18. Figure 18: The Chinese version of the system prompt used for evolving seed problems into complex reasoning tasks. O.2.2. AUXILIARY: VALIDATOR BUILDER The validator builder constructs independent validators to cross-check the main validator. Validator Builder Prompt (English) You will receive the generator code and question template. Please write a brand-new Python validator function: 1. Function signature must be de… view at source ↗
Figure 19
Figure 19. Figure 19: The prompt used to generate independent validator functions for voting. Validator Builder Prompt (Chinese) 你将获得题目的generator 代码与题面模板，请编写一个全新的Python 验证器函数： 1. 函数签名固定为def solution(inputs): 2. 仅使用inputs 中的数据求解，禁止调用generator、随机数或I/O 操作 3. 在函数开头解析inputs 的结构，若缺少必需字段或类型不符合预期，返回{"status": "schema error", "detail": "..."}，不要抛异常 4. 输出必须是题目的唯一标准答案，可返回数字、字符串、元组或字典，但需与题面描述保持一致 5. 允许定义辅助函数，但最终必须返回solution(inputs) 6. 避免副… view at source ↗
Figure 20
Figure 20. Figure 20: The Chinese version of the prompt used to generate independent validator functions for voting. O.2.3. STAGE 2: QUALITY VERIFICATION The Reviewer Agent assesses generated problems for readability, novelty, and difficulty alignment. Quality Check System Prompt (English) Please act as a question quality reviewer to judge whether the following problem meets our publication standards. Focus on logical correctn… view at source ↗
Figure 21
Figure 21. Figure 21: The system prompt used for quality verification to assess generated problems for readability, novelty, and difficulty alignment. Quality Check System Prompt (Chinese) 请作为题面审查员，判断下列题目是否满足我们的发布标准；请优先聚焦题目的逻辑正确性与可求解性，对叙述上 的“花哨”或冗长描述保持宽容，只有在明确阻碍理解时才建议修改。 题目 （运行时注入的题面） 官方答案预览 （运行时注入的答案） 目标（请遵循以下标准） • Readability：题面是否大体清晰、可按文字完成求解；若仅存在篇幅较长、术语较多或格式偏“工程化”的情况，请 判为pass，出现歧义、信息缺失或前后矛盾时标记revise。特别注意：如果题目包含ASCII 字符绘制的树… view at source ↗
Figure 22
Figure 22. Figure 22: The Chinese version of the system prompt used for quality verification of generated problems. O.2.4. STAGE 3: SOLUTION GENERATION (BLIND REVIEW) Models solve problems independently without access to the validator to ensure solvability. Blind Review Prompt (English) You are a math/logic problem solver (attempt n). Please read the problem carefully and solve it independently. Problem (runtime injected probl… view at source ↗
Figure 23
Figure 23. Figure 23: The prompt template used for blind review solution generation, where models solve problems independently without access to validators. Blind Review Prompt (Chinese) 你是一个数学/逻辑题求解器（第n 次尝试），请仔细阅读题面并独立推理求解。 题目 （运行时注入的题面） 要求 1. 仔细理解题意，进行清晰的推理分析。 2. 你可以调用python 工具编写并运行代码来辅助推理，必要时打印中间结果验证结论。 3. 最终答案必须严格使用\boxed{最终答案} 格式包裹。 4. 若无法求解或题目信息不充分，请使用\boxed{N/A}。 5. 重要：完成推理并给出答案后，必须调用stop 工具来结束本次求解任务。 6. 注意不要写消耗过高资源的代码（… view at source ↗
Figure 24
Figure 24. Figure 24: The Chinese version of the prompt template used for blind review solution generation. O.2.5. EXPERIENCE MANAGEMENT The Experience Manager curates high-quality reasoning strategies to continuously improve problem generation. Experience Curation Prompt (English) You are an assistant responsible for maintaining the quality of the experience repository. The goal is to help the team continuously produce high-d… view at source ↗
Figure 25
Figure 25. Figure 25: The system prompt used for curating high-quality reasoning strategies in the experience management module. Experience Curation Prompt (Chinese) 你是一名负责维护经验库质量的助手。目标是支持团队持续产出高级推理模型在难度7–10 仍然容易出错的高难度逻 辑题。当前经验列表需控制在不超过指定数量，同时保留最具复用价值和可泛化的高难度出题策略。 请对比“现有经验”和“新增候选”，完成下列操作： 1. 对齐任务目标：删除任何鼓励简化题目、降低难度、弱化约束或强调“提高可解性”的条目；保留或重写能强化多 阶段推理、复杂约束组合、反直觉设定的经验。 2. 质量筛选：去重、合并语义重复或过于细节化的经验，必要时重新表述，使其具有可迁移性且聚焦于增强推理难 度。 3. 覆盖关键环… view at source ↗
Figure 26
Figure 26. Figure 26: The Chinese version of the system prompt used for experience curation to maintain reasoning strategy quality. O.3. Training Prompts For Base Models, we append a specific suffix to user queries. English Suffix (Base Models) Please reason step by step, and put your reasoning process within <reasoning> and </reasoning> tags. Finally, provide a brief answer and explanation [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 27
Figure 27. Figure 27: The prompt suffix appended to user queries for training base models in English. Chinese Suffix (Base Models) 请逐步推理，并将思考过程包含在<reasoning> 和</reasoning> 标签中。最后给出简要的答案和解释。 [PITH_FULL_IMAGE:figures/full_fig_p040_27.png] view at source ↗
Figure 29
Figure 29. Figure 29: The few-shot prompt template used for evaluation on the ARC-AGI benchmark. P. Experience Examples P.1. Example of High-Quality Experience Here we present an example of a high-quality experience entry that guides the generation of complex reasoning problems. This example demonstrates how to encapsulate specific design strategies into actionable advice for the Code Reasoning Agent. Experience Entry (English… view at source ↗
Figure 30
Figure 30. Figure 30: Experience Entry (English) Experience Entry (Chinese) 策略：针对复杂约束强制实施多验证器一致性 描述：在设计具有复杂组合约束（例如带有附加路径权重限制的图着色）的问题时，主验证器往往难以覆盖所有边 缘情况。 可执行建议： 1. 在generator 中，显式构造“几乎有效”（满足n − 1 个约束）的测试用例，以测试验证器的严格性。 2. 在validator 中，实现双重检查机制：一次前向传递构建解，一次后向传递针对所有约束验证解。 3. 如果blind review 在特定约束上频繁失败，请优化question template，明确说明冲突规则的优先级（例如“距离约束 优先于颜色约束”）。 [PITH_FULL_IMAGE:figures/full_fig_p041_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Experience Entry (Chinese) 41 [PITH_FULL_IMAGE:figures/full_fig_p041_31.png] view at source ↗
read the original abstract

Reinforcement Learning from Verifiable Rewards (RLVR) is bottlenecked by data: existing synthesis pipelines rely on expert-written code or fixed templates, confining growth to instance-level perturbations. We shift the evolvable unit from problem instances to task-family specifications. SSLogic is an agentic meta-synthesis framework in which LLM agents iteratively author and refine executable Generator-Validator pairs inside a closed Generate-Validate-Refine loop, producing families with new rules and difficulty gradients rather than parameter variations of old ones. A Multi-Gate Validation Protocol -- multi-strategy consensus plus Adversarial Blind Review, where independent agents solve each instance by writing and executing code -- filters ill-posed tasks before they enter training. Starting from 400 seed families, two evolution rounds yield 953 families and 21,389 verifiable instances. Three converging comparisons (step-matched, token-matched, and size-controlled on external Enigmata data) consistently show higher training utility of evolved data, with gains of SynLogic +5.2, AIME25 +3.0, and BBH +5.5 on Enigmata. Fine-grained KORBench evaluation reveals selective improvements in logic (+13.2%) and operation (+9.6%), linking structural evolution to downstream gains. Code: https://github.com/AdAstraAbyssoque/Scaling-the-Scaling-Logic

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper presents SSLogic, an agentic meta-synthesis framework in which LLM agents iteratively author and refine executable Generator-Validator pairs in a closed Generate-Validate-Refine loop. Starting from 400 seed families, two evolution rounds produce 953 families and 21,389 verifiable instances. A Multi-Gate Validation Protocol (multi-strategy consensus plus adversarial blind review via code-writing agents) filters ill-posed tasks. Three matched comparisons (step-, token-, and size-controlled) on external Enigmata data report consistent gains from the evolved data: +5.2 on SynLogic, +3.0 on AIME25, and +5.5 on BBH, with selective KORBench improvements in logic (+13.2%) and operation (+9.6%) categories. Code is released at the provided GitHub link.

Significance. If the central claim holds, the work offers a concrete path to scale RLVR data beyond instance-level perturbations by evolving task-family specifications, which could improve training utility for reasoning models. The use of three converging matched controls and public code release are positive empirical strengths that facilitate verification.

major comments (3)
  1. [Abstract and Multi-Gate Validation Protocol description] The attribution of benchmark gains to 'new rules and difficulty gradients' (rather than superficial seed variations or formatting improvements) is load-bearing, yet the manuscript provides no quantitative diagnostics such as rule-novelty metrics, inter-family structural distances, or per-gate rejection fractions to confirm that the 953 families differ structurally from the 400 seeds.
  2. [Experiments and Results] Benchmark improvements are stated without error bars, statistical significance tests, or ablation results isolating the contribution of the Multi-Gate Protocol components versus simple data-volume increases, which weakens assessment of robustness under the step-, token-, and size-matched controls.
  3. [Methods (Multi-Gate Validation Protocol)] The Multi-Gate Validation Protocol is asserted to reliably remove ill-posed tasks via consensus and adversarial code-writing review, but no solve-rate statistics, inter-agent agreement scores, or exclusion criteria details are reported, leaving open whether residual gains could stem from reduced label noise rather than novel logic families.
minor comments (1)
  1. [Abstract] The abstract mentions 'fine-grained KORBench evaluation' but does not specify the exact subset or scoring protocol used for the +13.2% logic and +9.6% operation gains.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and will incorporate revisions to strengthen the empirical support for our claims regarding the structural novelty of the evolved task families and the robustness of the reported gains.

read point-by-point responses

  1. Referee: [Abstract and Multi-Gate Validation Protocol description] The attribution of benchmark gains to 'new rules and difficulty gradients' (rather than superficial seed variations or formatting improvements) is load-bearing, yet the manuscript provides no quantitative diagnostics such as rule-novelty metrics, inter-family structural distances, or per-gate rejection fractions to confirm that the 953 families differ structurally from the 400 seeds.

    Authors: We agree that explicit quantitative diagnostics would better substantiate the claim that the 953 families introduce structurally new rules and difficulty gradients. In the revised manuscript we will add rule-novelty metrics computed via embedding cosine distances and normalized edit distances on the generator-validator code pairs, along with average inter-family structural distances and per-gate rejection fractions. These will be reported in a new subsection of the Methods and referenced in the Experiments section to directly address the distinction from seed variations. revision: yes

  2. Referee: [Experiments and Results] Benchmark improvements are stated without error bars, statistical significance tests, or ablation results isolating the contribution of the Multi-Gate Protocol components versus simple data-volume increases, which weakens assessment of robustness under the step-, token-, and size-matched controls.

    Authors: We acknowledge that the absence of error bars, significance testing, and targeted ablations limits the strength of the robustness claims. We will rerun all three matched comparisons (step-, token-, and size-controlled) across multiple random seeds to report standard deviations and conduct paired statistical tests (e.g., Wilcoxon signed-rank) for the reported gains. We will also add an ablation that compares the full evolved dataset against a volume-matched baseline using only seed families without the Generate-Validate-Refine loop. These results will be included in the revised Experiments section. revision: yes

  3. Referee: [Methods (Multi-Gate Validation Protocol)] The Multi-Gate Validation Protocol is asserted to reliably remove ill-posed tasks via consensus and adversarial code-writing review, but no solve-rate statistics, inter-agent agreement scores, or exclusion criteria details are reported, leaving open whether residual gains could stem from reduced label noise rather than novel logic families.

    Authors: We recognize that additional statistics on the validation protocol are needed to separate the effects of noise reduction from the introduction of novel families. In the revision we will report per-gate solve-rate statistics, inter-agent agreement scores (Cohen’s kappa on consensus decisions), and detailed exclusion criteria including the exact fraction of tasks rejected at each stage. These metrics will be presented in an expanded Multi-Gate Validation Protocol subsection of the Methods to allow readers to evaluate the protocol’s contribution. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical gains derived from external benchmark comparisons, not self-referential fitting or definitions.

full rationale

The paper describes an agentic synthesis loop (Generate-Validate-Refine) that starts from 400 seed families and produces 953 evolved families, then reports performance deltas on held-out external benchmarks (Enigmata, SynLogic, AIME25, BBH) under step-, token-, and size-matched controls. No equations, fitted parameters, or uniqueness theorems are invoked that would make any reported gain equivalent to the input seeds by construction. The Multi-Gate Validation Protocol is presented as a procedural filter rather than a definitional step that presupposes the output distribution. All load-bearing claims rest on observable downstream accuracy improvements rather than on renaming, self-citation chains, or ansatz smuggling. This is a standard empirical pipeline whose central result is falsifiable against external test sets and therefore scores at the low end of the circularity range.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that LLM agents can produce executable and valid Generator-Validator pairs; no free parameters or invented physical entities are introduced.

axioms (1)
  • domain assumption LLM agents can iteratively author and refine executable Generator-Validator pairs that generate valid logic tasks with new rules.
    Invoked as the core mechanism of the Generate-Validate-Refine loop.

pith-pipeline@v0.9.0 · 5557 in / 1259 out tokens · 37560 ms · 2026-05-16T12:08:32.262472+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages · 1 internal anchor

  1. [1]

    ISBN 979-8-89176-256-5

    Association for Computational Linguistics. ISBN 979-8-89176-256-5. doi: 10.18653/v1/2025.findings-acl

    work page doi:10.18653/v1/2025.findings-acl 2025

  2. [2]

    findings-acl.77/

    URL https://aclanthology.org/2025. findings-acl.77/. He, F., Chen, Z., Liang, X., Ma, T., Qiu, Y ., Wu, S., and Yan, J. Protoreasoning: Prototypes as the foundation for generalizable reasoning in llms, 2025. URL https: //arxiv.org/abs/2506.15211. 10 Scaling the Scaling Logic: Agentic Meta-Synthesis of Logic Reasoning Helff, L., Omar, A., Friedrich, F., W ...

    work page doi:10.18653/v1/2022 2025

  3. [3]

    OpenRLHF: An Easy-to-use, Scalable and High-performance RLHF Framework

    URL https://openreview.net/forum? id=7Bywt2mQsCe. Hu, J., Wu, X., Zhu, Z., Xianyu, Wang, W., Zhang, D., and Cao, Y . Openrlhf: An easy-to-use, scalable and high-performance rlhf framework.arXiv preprint arXiv:2405.11143, 2024. Hu, K., Cy, A., Qiu, L., Ding, X. D., Wang, R., Zhu, Y . E., Andreas, J., and He, K. Arc is a vision problem!, 2025. URLhttps://ar...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.18653/v1/2025.acl-long.1285 2024

  4. [4]

    Liu, B., Jin, C., Kim, S., Yuan, W., Zhao, W., Kulikov, I., Li, X., Sukhbaatar, S., Lanchantin, J., and Weston, J

    URL https://openreview.net/forum? id=v8L0pN6EOi. Liu, B., Jin, C., Kim, S., Yuan, W., Zhao, W., Kulikov, I., Li, X., Sukhbaatar, S., Lanchantin, J., and Weston, J. Spice: Self-play in corpus environments improves reasoning, 2025a. URL https://arxiv.org/abs/ 2510.24684. Liu, H., Liu, J., Cui, L., Teng, Z., Duan, N., Zhou, M., and Zhang, Y . Logiqa 2.0—an i...

    work page doi:10.1109/taslp.2023 2023

  5. [5]

    In: NeurIPS ML Safety Workshop (2022)

    URL https://openreview.net/forum? id=uyTL5Bvosj. Featured Certification. Stojanovski, Z., Stanley, O., Sharratt, J., Jones, R., Ade- fioye, A., Kaddour, J., and Koepf, A. Reasoning gym: Reasoning environments for reinforcement learn- ing with verifiable rewards. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems Datasets and Ben...

    work page doi:10.18653/v1/2023 2025

  6. [6]

    Unlabeled/Other

    URL https://aclanthology.org/2021. findings-acl.317/. Veeraboina, H. Aime problem set (1983– 2024). https://www.kaggle.com/ datasets/hemishveeraboina/ aime-problem-set-1983-2024 , 2024. Kaggle dataset. Xia, Z., Luo, K., Qian, H., and Liu, Z. Open data synthesis for deep research, 2025. URL https://arxiv.org/ abs/2509.00375. Xie, T., Gao, Z., Ren, Q., Luo,...

    work page arXiv 2021

  7. [7]

    Seed-agnostic:The Enigmata seeds share no overlap with our original 400 Chinese seed families, demonstrating the pipeline generalizes beyond its original seed distribution

    work page

  8. [8]

    Zero human annotation:The entire pipeline—from seed ingestion through evolution to training—requires no human intervention beyond selecting the 30 eligible types

    work page

  9. [9]

    completed list

    English-only:Unlike our main experiment where seeds are in Chinese, Enigmata is entirely English, confirming cross-language applicability. N. Token-Matched Analysis Step-matched comparisons may not fully control for compute, as Evolve tasks elicit progressively longer reasoning chains. This appendix provides a token-budget analysis using per-step training...

    work page 2025

  10. [10]

    Ensure it is directly evaluable using the eval function

    Code Generation: Create a Python dictionary representing the updated state. Ensure it is directly evaluable using the eval function. Check the Progress State section above for the required content and format for this dictionary. Keep every string value on a single line—do not embed raw newline characters inside string literals. 3.Conciseness: Summarize to...

    work page

  11. [11]

    Nevertheless, notice that you should NOT switch plans too frequently

    Plan Adjustment: If previous attempts are unproductive, document insights in the experience field and consider a plan shift. Nevertheless, notice that you should NOT switch plans too frequently. 5.Utilize Resources: Effectively employ sub-agents and tools to address sub-tasks. Output Format CRITICAL: You MUST output EXACTLY ONE response with ONE Thought a...

    work page

  12. [12]

    Printed outputs are used in subsequent steps, so keep them concise and focused on the most relevant information

    Output Management: Use Python’s built-inprint function to display results. Printed outputs are used in subsequent steps, so keep them concise and focused on the most relevant information

    work page

  13. [13]

    Avoid interactive functions like input()to maintain automation and reproducibility

    Self-Contained Code: Ensure your code is fully executable without requiring user input. Avoid interactive functions like input()to maintain automation and reproducibility

    work page

  14. [14]

    Notice that these functions arealready defined and importedand you should NOT re-define or re-import them

    Utilizing Resources: Leverage the provided sub-agents and tools, which are essentially Python functions you can call within your code. Notice that these functions arealready defined and importedand you should NOT re-define or re-import them. 4.Task Completion: Use thestopfunction to return a well-formatted output when the task is completed

    work page

  15. [15]

    You do NOT have sudo privileges, so avoid any commands or operations requiring elevated permissions

    Python Environment: Explicitly import any libraries you need, including standard ones such as os or sys, as nothing (except for the pre-defined sub-agents and tools) is imported by default. You do NOT have sudo privileges, so avoid any commands or operations requiring elevated permissions. 6.Working Directory: Use the current folder as your working direct...

    work page

  16. [16]

    latest research paper on large language models

    Complexity Control: Keep your code straightforward and avoid unnecessary complexity, especially when calling tools or sub-agents. Write code that is easy to follow and less prone to errors or exceptions. Output Format CRITICAL: You MUST output EXACTLY ONE response with ONE Thought and ONE Code block. DO NOT output multiple Thought-Code pairs. DO NOT conti...

    work page

  17. [17]

    It should include two fields: output and log

    Code: Generate a Python dictionary representing the final output. It should include two fields: output and log. The output field should contain the well-formatted final output result, while the log field should summarize the navigation trajectory. 30 Scaling the Scaling Logic: Agentic Meta-Synthesis of Logic Reasoning

    work page

  18. [18]

    Final Result: Carefully examine the outputs from the previous steps as well as the alternative result (if existing) to decide the final output

    work page

  19. [19]

    output":

    Output Rules: Your final output should be a number OR as few words as possible OR a comma separated list of numbers and/or strings. Do NOT include any unnecessary information in the output. Output Format CRITICAL: You MUST output EXACTLY ONE response with ONE Thought and ONE Code block. DO NOT output multiple Thought-Code pairs. DO NOT continue thinking a...

    work page

  20. [20]

    Contextual Review: Carefully review the Progress State and Current Step to understand the context and require- ments for this selection

    work page

  21. [21]

    If multiple results are similar, prefer the one that aligns with the consensus

    Majority Voting: By default, select the result that is most consistent with the majority of other results. If multiple results are similar, prefer the one that aligns with the consensus

    work page

  22. [22]

    Error Exclusion: Exclude any results that are clearly unreasonable, such as those containing errors, irrelevant information, or signs of failed execution

    work page

  23. [23]

    5.Fallback: If none of the results are clearly correct, select the one that appears most reasonable given the context

    Tie-Breaking: If there is a tie among reasonable results, select the one that is best formatted and provides the most detailed and complete answer. 5.Fallback: If none of the results are clearly correct, select the one that appears most reasonable given the context

    work page

  24. [24]

    Given [Input Slot 1] and [Input Slot 2], find

    Output Format: Output the index of the selected result using the print function. For example, to select the result at index 2, output in your code section:print(2). Figure 16.The system prompt used for result aggregation in the Cognitive Kernel Pro framework. O.2. Scale Scaling Logic (SSL) Pipeline Prompts The SSL pipeline for data generation consists of ...

    work page 2000

  25. [25]

    Call seed save code() after defining generator/template/validator, then manually run input() and solution() in Python to check typical samples

    work page

  26. [26]

    Run seed generate sample() at least once and manually inspect the statement and validator votes to ensure answers are non-degenerate and validators agree

    work page

  27. [27]

    Call seed check question quality() and obtain action: "proceed" ; if revise, adjust per feedback and pass again

    work page

  28. [28]

    Trigger seed submit blind review() and record matching details for a passing attempt; if it fails, fix your code and retry

    work page

  29. [29]

    Before stop, re-check statement wording, difficulty labels, answer format, and validator outputs. Ensuresample summary 33 Scaling the Scaling Logic: Agentic Meta-Synthesis of Logic Reasoning and blind review summary in final JSON are truthful and reproducible.Important: the output parameter to stop must be a valid JSON string (usejson.dumps()) containing ...

    work page

  30. [30]

    Deconstruct the original problem → map its reasoning chain → design a new reasoning path/constraints → implement three components

    work page

  31. [31]

    Repeated verification: run generator and validator repeatedly in Python, print intermediate variables, and confirm correctness; if needed, sample across difficulties to check solvable/unsolvable ratios

    work page

  32. [32]

    Save code: define variables (e.g.,generator code = ’’’...’’’ ) and call seed save code(generator code, question template, validator code); then run seed generate sample() to inspect statements and an- swers

    work page

  33. [33]

    Callseed check question quality()to confirm readability/novelty/difficulty; iterate if needed

    work page

  34. [34]

    Useseed generate sample()to inspectvalidator votes; if inconsistent, fix the main validator and retry

    work page

  35. [35]

    Trigger blind review (auto-completes validator pool); if it fails, use failed samples detail to locate and fix issues before retrying

    work page

  36. [36]

    Recordgeneralizableproblem-design experience (not task-specific details)→organize deliverables→callstop. Seed Summary(mutation hintis for inspiration only; design a stronger reasoning goal) •question templatespreview: (runtime injected templates preview) • Reference sample question (original seed example, for understanding only; you may completely change ...

    work page

  37. [37]

    generator（生成器）：Python函数input(difficulty)，生成题目的输入数据和槽位文本 •返回格式：(inputs, slot texts) •inputs：传递给validator的输入数据 •slot texts：用于填充题面模板的文本列表

    work page

  38. [38]

    给定[输入槽位1]和[输入槽位2]，求

    question template（题面模板）：包含[输入槽位1]、[输入槽位2]等占位符的题目描述文本 •示例："给定[输入槽位1]和[输入槽位2]，求..." •槽位会被generator的slot texts依次填充

    work page

  39. [39]

    可解/不可解”或“复杂/简单

    validator（验证器）：Python函数solution(inputs)，根据输入计算正确答案 •接收generator产生的inputs •返回题目的标准答案，需保持纯函数、无副作用，便于系统基于题面规范自动生成多个独立验证器进行一致性 检验 交付格式 •使用stop输出JSON： task id、generator code、question template、validator code、evolution strategy、 sample summary、blind review summary、experience updates、notes。 •重要：stop工具的参数必须是有效的 JSON 字符串，包含上述所有字段。系统会在最后一步（ end 阶段）解析这 个JSON， 如果输出为No...

    work page

  40. [40]

    Function signature must bedef solution(inputs):

    work page

  41. [41]

    Solve using only data ininputs; do not call the generator, random functions, or I/O

    work page

  42. [42]

    status":

    Parse the inputs schema at the beginning. If required fields are missing or types do not match expectations, return {"status": "schema error", "detail": "..."}and do not raise exceptions

    work page

  43. [43]

    You may return a number, string, tuple, or dict, but it must match the statement

    Output must be the unique standard answer. You may return a number, string, tuple, or dict, but it must match the statement

    work page

  44. [44]

    Helper functions are allowed, but must ultimately returnsolution(inputs)

    work page

  45. [45]

    Avoid side effects; keep pure functions so the system can generate multiple validators for voting

    work page

  46. [46]

    If it disagrees with the main validator, the system will expose validator votesfor comparison

    Your implementation must be independently derived. If it disagrees with the main validator, the system will expose validator votesfor comparison

    work page

  47. [47]

    status":

    Avoid high resource usage (excessive computation or infinite loops). Ensure reasonable runtime. Generator (for input structure) ‘‘‘python ... ‘‘‘ Question Template (slots will be filled) (runtime injected template text) Current Main Validator (for IO contract only; do not copy line-by-line) ‘‘‘python ... ‘‘‘ 36 Scaling the Scaling Logic: Agentic Meta-Synt...

    work page

  48. [48]

    38 Scaling the Scaling Logic: Agentic Meta-Synthesis of Logic Reasoning

    Understand the problem and perform clear reasoning. 38 Scaling the Scaling Logic: Agentic Meta-Synthesis of Logic Reasoning

    work page

  49. [49]

    3.The final answer must be strictly enclosed in\boxed{final answer}

    You may call thepythontool to write and run code to assist reasoning; print intermediate results when needed. 3.The final answer must be strictly enclosed in\boxed{final answer}

    work page

  50. [50]

    5.Important: After finishing reasoning and giving the answer, you must call thestoptool to end the task

    If unsolvable or information is insufficient, use\boxed{N/A}. 5.Important: After finishing reasoning and giving the answer, you must call thestoptool to end the task

    work page

  51. [51]

    Output Example Reasoning:

    Avoid high resource usage (excessive computation or infinite loops); ensure reasonable runtime. Output Example Reasoning: ... therefore ... Final Answer:\boxed{42} Then callstopto finish. Figure 23.The prompt template used for blind review solution generation, where models solve problems independently without access to validators. Blind Review Prompt (Chi...

    work page

  52. [52]

    Retain or rewrite items that strengthen multi-stage reasoning, complex constraint combinations, or counterintuitive setups

    Align with Task Goals: Remove items that encourage simplifying problems, lowering difficulty, weakening constraints, or prioritizing easy solvability. Retain or rewrite items that strengthen multi-stage reasoning, complex constraint combinations, or counterintuitive setups

    work page

  53. [53]

    Quality Filtering: Deduplicate and merge semantic overlaps; rewrite overly specific items to make them transferable and focused on increasing reasoning difficulty

    work page

  54. [54]

    Experience 1

    Coverage: Prioritize experience involving generator/validator co-verification, improving blind-review pass rates (while keeping high difficulty), and preventing shortcut solutions. 4.Quantity Control: Limit output to the specified maximum; each item must be one concise, actionable sentence. 5.Output Format: Return a strict JSON array of strings only, for ...

    work page

  55. [55]

    almost valid

    In thegenerator, explicitly construct test cases that are “almost valid” (satisfying n−1 constraints) to test the strictness of the validator

    work page

  56. [56]

    In thevalidator, implement a dual-check mechanism: one forward pass to construct the solution and one backward pass to verify the solution against all constraints

    work page

  57. [57]

    Distance constraints take precedence over color constraints

    Ifblind reviewfails frequently on specific constraints, refine thequestion templateto explicitly state the priority of conflicting rules (e.g., “Distance constraints take precedence over color constraints”). Figure 30.Experience Entry (English) Experience Entry (Chinese) 策略：针对复杂约束强制实施多验证器一致性 描述：在设计具有复杂组合约束（例如带有附加路径权重限制的图着色）的问题时，主验证器往往难以覆盖所有边 缘情况。 可执行建议： 1...

    work page