# Reasoning Core: A Scalable RL Environment for LLM Symbolic Reasoning

arXiv: https://arxiv.org/abs/2509.18083 · HTML: https://mlsanity.com/paper/2509.18083/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 27 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 20 of 20)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Leveraging Procedural Generation to Benchmark Reinforcement Learning](https://mlsanity.com/paper/1912.01588/) (2019)
- [Dynabench: Rethinking Benchmarking in NLP](https://mlsanity.com/paper/2104.14337/) (2021)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Will we run out of data? Limits of LLM scaling based on human-generated data](https://mlsanity.com/paper/2211.04325/) (2022)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [The Leaderboard Illusion](https://mlsanity.com/paper/2504.20879/) (2025)
- [AutoLogi: Automated Generation of Logic Puzzles for Evaluating Reasoning Abilities of Large Language Models](https://mlsanity.com/paper/2502.16906/) (2025)
- [Sudoku-Bench: Evaluating creative reasoning with Sudoku variants](https://mlsanity.com/paper/2505.16135/) (2025)
- [Logic Haystacks: Probing LLMs Long-Context Logical Reasoning (Without Easily Identifiable Unrelated Padding)](https://mlsanity.com/paper/2502.17169/) (2025)
- [Attention Overflow: Language Model Input Blur during Long-Context Missing Items Recommendation](https://mlsanity.com/paper/2407.13481/) (2024)
- [Saturation-Driven Dataset Generation for LLM Mathematical Reasoning in the TPTP Ecosystem](https://mlsanity.com/paper/2509.06809/) (2025)

## Built on by (most cited first, 5 of 5)

- [Golden Goose: A Simple Trick to Synthesize Unlimited RLVR Tasks from Unverifiable Internet Text](https://mlsanity.com/paper/2601.22975/) (2026)
- [Agentic Environment Engineering for Large Language Models: A Survey of Environment Modeling, Synthesis, Evaluation, and Application](https://mlsanity.com/paper/2606.12191/) (2026)
- [Breaking the Solver Bottleneck: Training Task Generators at the Learnable Frontier](https://mlsanity.com/paper/2606.18284/) (2026)
- [Structured In-context Environment Scaling for Large Language Model Reasoning](https://mlsanity.com/paper/2509.23330/) (2025)
- [MagicBeanStalk: Escaping the RLVR Zero Advantage Trap with Recursive Data Synthesis](https://mlsanity.com/paper/2610.12659/) (2026)

## Abstract (arXiv)

We introduce Reasoning Core, a new scalable environment for Reinforcement Learning with Verifiable Rewards (RLVR), designed to advance foundational symbolic reasoning in Large Language Models (LLMs). Unlike existing benchmarks that focus on games or isolated puzzles, Reasoning Core procedurally generates problems across core formal domains, including PDDL planning, first-order logic, context-free grammar parsing, causal reasoning, and system equation solving. The environment is built on key design principles of high-generality problem distributions, verification via external tools, and continuous difficulty control, which together provide a virtually infinite supply of novel training instances. Initial zero-shot evaluations with frontier LLMs confirm the difficulty of Reasoning Core's tasks, positioning it as a promising resource to improve the reasoning capabilities of future models.