Paper Citation Record · LEDGER

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning

As of 9 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 7 inbound Pith citation observations for arXiv:2509.00125.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2509.00125 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T14:23:54.829237Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T03:33:43.695859Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-04T08:09:40.662689Z

Reference resolution

41 of 41 outbound references displayed

verified exact0
verified fuzzy16
unresolved25
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0fae64bf-bc87-4977-87d0-02d7f71eaf7e · outbound

This paper cites Learning to reason with llms, 2024.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Learning to reason with llms, 2024

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:52.012864Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9202f34b-3cb7-442f-97a4-4eab7dba5831 · outbound

This paper cites DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:52.044378Z

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Observation 4fd8135b-080c-4eec-bf07-a9e4ab3cbfe9 · outbound

This paper cites DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:52.097658Z

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Observation 34c9fb5e-b0bb-4a94-9879-00c3ce7d357a · outbound

This paper cites Qwen2.5 Technical Report.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Qwen2.5 Technical Report

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:52.153387Z

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Observation 82b20f8d-b312-4c59-b42d-59e511803bf2 · outbound

This paper cites Let’s verify step by step.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Let’s verify step by step

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:58.685654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fb93fe45-4a55-4b3c-8e64-3b59a4fb0a79 · outbound

This paper cites Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:52.252596Z

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Unavailable: canonical work link unavailable.

Observation 3703a958-d47e-45d0-92bb-5518f6b39972 · outbound

This paper cites Scalable best-of-n selection for large language models via self-certainty.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Scalable best-of-n selection for large language models via self-certainty

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:52.474556Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21250019-abda-44ec-8a32-2a4851ebe388 · outbound

This paper cites The impact of intrinsic rewards on exploration in Reinforcement Learning.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning The impact of intrinsic rewards on exploration in Reinforcement Learning

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:52.574469Z

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Unavailable: canonical work link unavailable.

Observation ea1186f2-c4dc-4e56-a502-2c850b501999 · outbound

This paper cites Thompson sampling: An asymptotically optimal finite-time analysis.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Thompson sampling: An asymptotically optimal finite-time analysis

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:58.434368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 71f55c8d-7cfa-4b66-b4e4-a509853d5451 · outbound

This paper cites Thompson sampling for contextual bandits with linear payoffs.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Thompson sampling for contextual bandits with linear payoffs

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:58.287010Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4060531c-1847-4585-b001-198f32c05dd6 · outbound

This paper cites Exploration-Exploitation in Constrained MDPs.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Exploration-Exploitation in Constrained MDPs

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:52.737271Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 822ae0fc-6db9-407b-be99-fa09a6948950 · outbound

This paper cites Why is posterior sampling better than optimism for reinforcement learning? In ICML, 2017.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Why is posterior sampling better than optimism for reinforcement learning? In ICML, 2017

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:58.007796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b1e214fe-a27f-4f1e-8e68-16d1520ea192 · outbound

This paper cites First return, then explore.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning First return, then explore

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:57.908440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5cfca35f-e4c9-4323-aab3-7ff3f6200c07 · outbound

This paper cites Automatic goal generation for reinforcement learning agents.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Automatic goal generation for reinforcement learning agents

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:57.672989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e0896c7a-5d24-49cc-99f5-bbf3454a21f9 · outbound

This paper cites MIT press Cambridge, 1998.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning MIT press Cambridge, 1998

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:52.986538Z

Source-reported events for the cited work

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Observation 4b22afa6-dbbf-4e5e-a976-d323cbf41029 · outbound

This paper cites Adaptiveε-greedy exploration in reinforcement learning based on value differences.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Adaptiveε-greedy exploration in reinforcement learning based on value differences

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:57.397962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation af537e40-7b37-47cf-8762-26f1ddde1bed · outbound

This paper cites # exploration: A study of count-based exploration for deep reinforcement learning.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning # exploration: A study of count-based exploration for deep reinforcement learning

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:57.233013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 625027fc-5657-457b-bc6a-a25ba0a7f7ea · outbound

This paper cites Deep exploration via bootstrapped dqn.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Deep exploration via bootstrapped dqn

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:57.077614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 47b9055b-4018-4590-9ea4-cd41539fb231 · outbound

This paper cites Curious model-building control systems.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Curious model-building control systems

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:56.843868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f64fc493-eefc-44ad-931a-d5febad69903 · outbound

This paper cites Curiosity-driven exploration by self-supervised prediction.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Curiosity-driven exploration by self-supervised prediction

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:56.624749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 071b3708-a6bb-4d24-9a98-dd9e66e6f994 · outbound

This paper cites Exploration by Random Network Distillation.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Exploration by Random Network Distillation

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:53.349740Z

Source-reported events for the cited work

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Observation b194bb3f-0f88-4cef-83ff-3c494a524657 · outbound

This paper cites Planning to explore via self-supervised world models.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Planning to explore via self-supervised world models

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:56.400136Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 954ec9c2-13a1-461f-8f5b-5848e91dbe33 · outbound

This paper cites Vime: Variational information maximizing exploration.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Vime: Variational information maximizing exploration

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:56.128094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b7cc4687-085e-40d0-bed4-45c222baf6b1 · outbound

This paper cites Diversity is all you need: Learning skills without a reward function.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Diversity is all you need: Learning skills without a reward function

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:55.855227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d57a21b2-6589-4b9f-a40b-01630ae61e98 · outbound

This paper cites Ttrl: Test-time reinforcement learning.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Ttrl: Test-time reinforcement learning

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:55.542844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9420cb17-f685-4dd4-a6d8-48a6600f33fa · outbound

This paper cites Learning to Reason without External Rewards.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Learning to Reason without External Rewards

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:53.726913Z

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Observation 747bd84f-aaff-4c49-8042-15dc9311dd0b · outbound

This paper cites Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:53.805378Z

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Observation 91c343ed-07cd-4656-85ed-de4239c3f1c1 · outbound

This paper cites The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:53.864174Z

Source-reported events for the cited work

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Observation 72352bc2-0201-46b3-9b37-71dd8e686483 · outbound

This paper cites One-shot Entropy Minimization.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning One-shot Entropy Minimization

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:53.913129Z

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Unavailable: canonical work link unavailable.

Observation f2e1034f-eb4b-4ef7-9838-69608525c0c4 · outbound

This paper cites Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:53.993294Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d8e9ecb-8f18-4653-b893-fc7ccde05aad · outbound

This paper cites First Return, Entropy-Eliciting Explore.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning First Return, Entropy-Eliciting Explore

Reference 32

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Observation f036f048-214b-4d9e-8a89-9046536ab732 · outbound

This paper cites Reasoning with Exploration: An Entropy Perspective.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Reasoning with Exploration: An Entropy Perspective

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:54.165008Z

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Observation 77947edf-38ea-4181-93e3-f094562744d5 · outbound

This paper cites Process Reinforcement through Implicit Rewards.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Process Reinforcement through Implicit Rewards

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:54.263620Z

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Observation c944a4df-f17b-4859-8da6-eafd9de83834 · outbound

This paper cites Free Process Rewards without Process Labels.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Free Process Rewards without Process Labels

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:54.346422Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6ace7843-b82d-4429-a83c-473e3d336d9d · outbound

This paper cites HybridFlow: A Flexible and Efficient RLHF Framework.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning HybridFlow: A Flexible and Efficient RLHF Framework

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:54.429131Z

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Observation 1e3a05f2-725d-472a-89fd-6cf0e83dd2eb · outbound

This paper cites DAPO: An Open-Source LLM Reinforcement Learning System at Scale.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning DAPO: An Open-Source LLM Reinforcement Learning System at Scale

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:54.506644Z

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Observation 7bcc21ec-a01b-4b73-b936-4c3833198956 · outbound

This paper cites Measuring Mathematical Problem Solving With the MATH Dataset.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Measuring Mathematical Problem Solving With the MATH Dataset

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:54.563362Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a84f266-0bad-4488-ae18-149dd2857216 · outbound

This paper cites The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:54.656234Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f7d0dc9-5dd4-47be-8d47-40168e4891c3 · outbound

This paper cites Curriculum learning.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Curriculum learning

Reference 40

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ab1850b-1883-4ced-b777-0144ee09d814 · outbound

This paper cites Efficient memory management for large language model serving with pagedattention.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Efficient memory management for large language model serving with pagedattention

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-05T14:23:54.804613Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3480521a-824d-43ae-a716-80da712b82e7 · outbound

This paper cites Math-Verify: Math Verification Library.https://github.com/huggingface/math-verify, 2025.

Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning Math-Verify: Math Verification Library.https://github.com/huggingface/math-verify, 2025

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:23:55.242466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

Observation ccf703d3-489a-4cbe-adaf-5d000ca5b6bf · inbound

rePIRL: Learn PRM with Inverse RL for LLM Reasoning cites this paper.

rePIRL: Learn PRM with Inverse RL for LLM Reasoning Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-21T13:14:10.971468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 09b23c32-fb30-4c1a-a096-9dbebe7a4b2b · inbound

rePIRL: Learn PRM with Inverse RL for LLM Reasoning cites this paper.

rePIRL: Learn PRM with Inverse RL for LLM Reasoning Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T03:33:43.695859Z

Source-reported events for the cited work

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Observation 5c05e544-ae55-45ef-b807-6a1da0229726 · inbound

HTPO: Towards Exploration-Exploitation Balanced Policy Optimization via Hierarchical Token-level Objective Control cites this paper.

HTPO: Towards Exploration-Exploitation Balanced Policy Optimization via Hierarchical Token-level Objective Control Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-12T00:51:14.596330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f4f5a4c4-890c-4235-bb9b-38ae12da4741 · inbound

Epistemic Uncertainty for Test-Time Discovery cites this paper.

Epistemic Uncertainty for Test-Time Discovery Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-13T01:57:06.044731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation efaff5c3-2482-45f9-8ded-02939fa1f10b · inbound

From Reasoning Traces to Reusable Modules: Understanding Compositional Generalization in Language Model Reasoning cites this paper.

From Reasoning Traces to Reusable Modules: Understanding Compositional Generalization in Language Model Reasoning Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning

Reference 147

Resolution: verified exact; arxiv_id, observed 2026-07-03T20:38:56.101152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 09d9d026-81c7-47ef-bb80-983a28743583 · inbound

Formalizing Task-Space Complexity for Zero-Shot Generalization cites this paper.

Formalizing Task-Space Complexity for Zero-Shot Generalization Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning

Reference 69

Resolution: verified exact; arxiv_id, observed 2026-07-04T03:59:32.894403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7648875b-3f7a-4c46-af90-34ae6c91614b · inbound

Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning cites this paper.

Modularized Reinforcement Learning on LLMs: From MDP Creation to Exploration and Learning Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning

Reference 102

Resolution: verified exact; arxiv_id, observed 2026-07-04T08:09:40.664145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.