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Paper Citation Record · LEDGER

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

As of 23 August 2026, this Paper Citation Record lists 100 of 168 outbound references and 18 inbound Pith citation observations for arXiv:2505.19914.

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

pith.paper-citation-record.v1
2505.19914 v2

Coverage vector

measured 100 of 168 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:11:16.465039Z

measured 118 of 118 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 18 of 18 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:45:49.982331Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

100 of 168 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved99
  • parse uncertain0
  • malformed identifier1
  • metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 33192636-7d6b-414d-878e-7b9fdc7966c3 · outbound

This paper cites Learning to reason with llms, 2024.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Learning to reason with llms, 2024

Reference 1

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source=pdf_text observed=2026-08-07T14:11:06.445529Z digest=sha256:6ee044d6b66b711f7d5b41993fe674a46654c12a633279bd454871c7726ea083

Observation 8bb48a08-c319-40be-abf6-9e8a0374b455 · outbound

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

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

Reference 2

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source=pdf_text observed=2026-08-07T14:11:06.524378Z digest=sha256:1ba3ac97256bad988a019ce9e7c8be487cfb7b9007a9279c2ec11792a5d13351

Observation 5c5338b7-0d03-407a-971e-796b9ec37e15 · outbound

This paper cites Gemini 2.5: Our most intelligent ai model, 2025.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Gemini 2.5: Our most intelligent ai model, 2025

Reference 3

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source=pdf_text observed=2026-08-07T14:11:06.583464Z digest=sha256:f6b964c73eeb0c2ed52b13d3b5923c6a20ec510c568d0412ea4a104ee292907b

Observation 5cd1d49d-6273-4fde-bc99-2aa1f6eb39b5 · outbound

This paper cites Claude 3.7 sonnet and claude code, 2025.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Claude 3.7 sonnet and claude code, 2025

Reference 4

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source=pdf_text observed=2026-08-07T14:11:06.656669Z digest=sha256:c48e2ae58753cc4a628a140656990659497d7275a24df74907734ed9100067c8

Observation b03def27-90fa-4123-ac35-629327e48381 · outbound

This paper cites Seed-thinking-v1.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Seed-thinking-v1

Reference 5

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source=pdf_text observed=2026-08-07T14:11:06.715016Z digest=sha256:fbb9a76e5b5c786a538dc9829606f91a4eb3f4e063421987224d3514e8c19d4d

Observation 6b402227-a144-481c-b7f7-da4da9a64e55 · outbound

This paper cites KodCode: A Diverse, Challenging, and Verifiable Synthetic Dataset for Coding.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles KodCode: A Diverse, Challenging, and Verifiable Synthetic Dataset for Coding

Reference 6

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source=pdf_text observed=2026-08-07T14:11:06.837138Z digest=sha256:d67844b9b3993915bfc9a219dd79250d51e672e0907f1b297ca2437ffc77f02f

Observation f97a8a18-1b56-469a-95f7-1f54877170e9 · outbound

This paper cites Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models

Reference 7

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source=pdf_text observed=2026-08-07T14:11:06.937762Z digest=sha256:207e965acd9588e6544509ae40989b6f5ae86d71f4cda5d7f2eb68169b3bceb3

Observation 47ca4cc8-1c8d-415c-83dd-6c6f436c1ff2 · outbound

This paper cites DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning

Reference 8

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Observation e4ff7f47-226e-4b7e-baac-40f6b0a86f32 · outbound

This paper cites On the Measure of Intelligence.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles On the Measure of Intelligence

Reference 9

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source=pdf_text observed=2026-08-07T14:11:07.117139Z digest=sha256:fe95263b1a83cc9a78cb2a44e2e4b1fc1744c247ace25485a92d67af5d730a62

Observation 4cca57b7-d88f-4151-bac9-e85fb5ba7eff · outbound

This paper cites ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning

Reference 10

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source=pdf_text observed=2026-08-07T14:11:07.219581Z digest=sha256:416048138de1eb58649b5ec1904784e1ca8e824f91d3da83bb483151ffff697b

Observation a2d43e4d-27b9-4751-84bb-553bc8e6d316 · outbound

This paper cites KOR-Bench: Benchmarking Language Models on Knowledge-Orthogonal Reasoning Tasks.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles KOR-Bench: Benchmarking Language Models on Knowledge-Orthogonal Reasoning Tasks

Reference 11

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source=pdf_text observed=2026-08-07T14:11:07.323944Z digest=sha256:198d62c781253f476fb1849f279d13d80245af12b1bf36a87225ebc43642bbae

Observation c7048aff-2994-4fab-b49a-1c15a5bd0f91 · outbound

This paper cites Phd knowledge not required: A reasoning challenge for large language models.arXiv preprint arXiv:2502.01584, 2025.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Phd knowledge not required: A reasoning challenge for large language models.arXiv preprint arXiv:2502.01584, 2025

Reference 12

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source=pdf_text observed=2026-08-07T14:11:07.391545Z digest=sha256:25e7b4f687a69705a7cc7fefec37baab8d16e6304c26537853b655b927f3c819

Observation ef5445b4-35ed-47c1-af80-83b6cb31ef9f · outbound

This paper cites Navigating the labyrinth: Evaluating and enhancing llms’ ability to reason about search problems.arXiv preprint arXiv:2406.12172, 2024.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Navigating the labyrinth: Evaluating and enhancing llms’ ability to reason about search problems.arXiv preprint arXiv:2406.12172, 2024

Reference 13

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Observation 0c97a62c-9af4-4d39-998e-178294fde0c7 · outbound

This paper cites Fcorebench: Can large language models solve challenging first-order combinatorial reasoning problems?, 2025.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Fcorebench: Can large language models solve challenging first-order combinatorial reasoning problems?, 2025

Reference 14

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source=pdf_text observed=2026-08-07T14:11:07.550954Z digest=sha256:1effcb9593c1bdc6e1b146cfd86806076d8e51553228d0b025baab96eb23ffef

Observation 1b518538-8457-4daf-b81e-da774d5e8b9d · outbound

This paper cites Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning

Reference 15

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source=pdf_text observed=2026-08-07T14:11:07.622997Z digest=sha256:4a6d91aa7299402f424d22f8961fc4be928f9d18040a171e987715894e55a46b

Observation 9e09c0de-7e9d-4df0-b7e4-348375626a39 · outbound

This paper cites Tinyzero.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Tinyzero

Reference 16

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source=pdf_text observed=2026-08-07T14:11:07.711505Z digest=sha256:f37b2bdf176ae960c3657c326cb4c5ec112325d5ece5172d0cd3aed13c486274

Observation bf2a876a-8673-4574-bf99-257baa2463be · outbound

This paper cites Qwen2.5: A party of foundation models, September 2024.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Qwen2.5: A party of foundation models, September 2024

Reference 17

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source=pdf_text observed=2026-08-07T14:11:07.784463Z digest=sha256:ed9020d7025f1397ee6bb8d9be0b7dca293895b091fb367d83b140bddd55cf21

Observation 78f47263-ff72-4e97-99cf-a01ba13c537e · outbound

This paper cites Kimi k1.5: Scaling Reinforcement Learning with LLMs.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Kimi k1.5: Scaling Reinforcement Learning with LLMs

Reference 18

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source=pdf_text observed=2026-08-07T14:11:07.908119Z digest=sha256:8dfaac41fa278a1194de43967d87be1ec1a65af66d48b9781d5bc866585fb19c

Observation e52cbf45-a0a6-4b75-9057-32083e2e5187 · outbound

This paper cites VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks

Reference 19

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source=pdf_text observed=2026-08-07T14:11:08.003933Z digest=sha256:5b6f28beec434f1f3dd27a8e3dd9ed36905a78d11da8558b58003334f7b39b6b

Observation 798cd88d-0aea-4720-b162-2f587ba6f6d6 · outbound

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

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles DAPO: An Open-Source LLM Reinforcement Learning System at Scale

Reference 20

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source=pdf_text observed=2026-08-07T14:11:08.074540Z digest=sha256:44e417f756d9f0b6c5e2c9535c729eaab524140215ea38ba5731c8b9e62a06fc

Observation b4d6abb8-e2c8-4b86-9f0a-79d5055d20c7 · outbound

This paper cites Understanding R1-Zero-Like Training: A Critical Perspective.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Understanding R1-Zero-Like Training: A Critical Perspective

Reference 21

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source=pdf_text observed=2026-08-07T14:11:08.178822Z digest=sha256:91881052f59635a09a419fd8c28c18dd2c09cdb4cfbf1a87ff2505a5611e93ea

Observation a185f65c-5583-4836-80de-d2d4db534dfa · outbound

This paper cites Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model

Reference 22

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source=pdf_text observed=2026-08-07T14:11:08.263842Z digest=sha256:d7c44e0e4efa14d0f33900d7d0b699cb931fededa81a470cacea817cfdfbf07d

Observation 2e273c41-f54d-4477-bad2-0cc70f8dd13a · outbound

This paper cites Code-r1: Reproducing r1 for code with reliable rewards.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Code-r1: Reproducing r1 for code with reliable rewards

Reference 23

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source=pdf_text observed=2026-08-07T14:11:08.367062Z digest=sha256:1ed72393a1e541c1f7293bb3784c44254dfbe2f9f4d1f61adac026ee912916c5

Observation cb8c7dc4-7cbe-4a72-bf1b-805133e9f0e8 · outbound

This paper cites FINEREASON: Evaluating and Improving LLMs' Deliberate Reasoning through Reflective Puzzle Solving.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles FINEREASON: Evaluating and Improving LLMs' Deliberate Reasoning through Reflective Puzzle Solving

Reference 24

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source=pdf_text observed=2026-08-07T14:11:08.468097Z digest=sha256:c9a2207b897d60582b78e431b9c95469ba414df675794e5670f9c6ab31cfab49

Observation 8856ecee-773a-4402-af51-524776682f52 · outbound

This paper cites Evaluating Large Language Models Trained on Code.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Evaluating Large Language Models Trained on Code

Reference 25

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source=pdf_text observed=2026-08-07T14:11:08.549000Z digest=sha256:6e9905394f69374cf150b7f9a20cb825c6b285de679595446498dc3b5db9ed83

Observation e388259d-75d6-4547-ad1f-4b7ae83df85b · outbound

This paper cites Exploring Data Scaling Trends and Effects in Reinforcement Learning from Human Feedback.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Exploring Data Scaling Trends and Effects in Reinforcement Learning from Human Feedback

Reference 26

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source=pdf_text observed=2026-08-07T14:11:08.621282Z digest=sha256:f5b617be249cc3d46c9ebf5f7b70a461a7a2581f5970beff35f4262d9d73ae9e

Observation 23e5691b-44e0-4ce7-9053-3e279ee4a55b · outbound

This paper cites Abstraction and reasoning corpus for artificial general intelligence v2 (arc-agi-2).

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Abstraction and reasoning corpus for artificial general intelligence v2 (arc-agi-2)

Reference 27

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source=pdf_text observed=2026-08-07T14:11:08.721704Z digest=sha256:6901baf7a2e0f1236570d998503d69b26de8338ea16f6f9c3208bc8980640cfd

Observation 28c8782f-2b2e-43bf-b38f-0383ac676e04 · outbound

This paper cites Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond

Reference 28

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source=pdf_text observed=2026-08-07T14:11:08.796570Z digest=sha256:4bd567accf3ed46289ffc6a52bbe25eb682c7b0ab72cf74e21196e6cfb1a38a8

Observation 7bac26cf-a7c9-457e-b4af-6384c8746ff6 · outbound

This paper cites What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secret.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secret

Reference 29

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source=pdf_text observed=2026-08-07T14:11:08.843880Z digest=sha256:75fc5e572cfecb85b973bb1b6c41cfa3898903a72a0d0008058249b031d537af

Observation 8c04e282-be10-4cf0-af42-e54448e97909 · outbound

This paper cites Proximal Policy Optimization Algorithms.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Proximal Policy Optimization Algorithms

Reference 30

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source=pdf_text observed=2026-08-07T14:11:08.885922Z digest=sha256:8cc729025598d3a38b577f5424a09825b02fb18b570d83ced1eb3cce33430518

Observation 09b4ef5c-2afa-4038-9e09-934eb5007696 · outbound

This paper cites Qwq-32b: Embracing the power of reinforcement learning, March 2025.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Qwq-32b: Embracing the power of reinforcement learning, March 2025

Reference 31

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Observation 99f00343-8616-477e-9b30-af3f5e079a75 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

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source=pdf_text observed=2026-08-07T14:11:08.983552Z digest=sha256:58c9dc8a20668688d7b849fc1c8ff35801b686af09fb8dd5ad7b1ec94352bd05

Observation 1556dec6-4824-4aab-845a-d0f93b847079 · outbound

This paper cites Reinforcement Learning for Reasoning in Large Language Models with One Training Example.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Reinforcement Learning for Reasoning in Large Language Models with One Training Example

Reference 33

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source=pdf_text observed=2026-08-07T14:11:09.039778Z digest=sha256:b75107cdc1db760cc4711a3fe4e8b7e52ce9d55cceb247d910d491904b7fc713

Observation fc6ed9a2-0376-4df1-8f06-e415e28f27c2 · outbound

This paper cites Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters

Reference 34

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source=pdf_text observed=2026-08-07T14:11:09.098919Z digest=sha256:48a865911288fa2db414f26bfa64c67f03be829913b303cbf0774ede20d10872

Observation 38c87261-2b2b-4aa2-8622-fc70131ff233 · outbound

This paper cites A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?

Reference 35

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source=pdf_text observed=2026-08-07T14:11:09.143459Z digest=sha256:a9ce0f588cb051cccde0172c644552316a53bd20679bbf55b1029763057bd11b

Observation 36839fee-c8db-4abf-ba2e-51dc6d5c2dd6 · outbound

This paper cites A survey of reinforcement learning from human feedback.arXiv preprint arXiv:2312.14925, 10, 2023.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles A survey of reinforcement learning from human feedback.arXiv preprint arXiv:2312.14925, 10, 2023

Reference 36

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source=pdf_text observed=2026-08-07T14:11:09.214951Z digest=sha256:e1e6e68fcf77a3d23a1ac831b981d5d3e360f16c413d2b0aeccb560e4f5d9c71

Observation 4e62e1b2-2061-4b3b-92f4-50ca2b902c71 · outbound

This paper cites Gonzalez, Hao Zhang, and Ion Stoica.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Gonzalez, Hao Zhang, and Ion Stoica

Reference 37

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source=pdf_text observed=2026-08-07T14:11:09.280687Z digest=sha256:d396219b88e277e7ac769d61eb11bac428db2e568e5fc5718e63f235d7320b2f

Observation 0934d3ac-eb29-4972-bd84-749a5e24bdb0 · outbound

This paper cites GPT-4 Technical Report.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles GPT-4 Technical Report

Reference 38

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source=pdf_text observed=2026-08-07T14:11:09.325963Z digest=sha256:b455a465bf966d40f3692a2b892384c2e56d6c1f53880b73940504a22d21bc94

Observation 7f8e1f5e-e97f-448d-a769-4b308c864bd4 · outbound

This paper cites Bringing grok to everyone, 2025.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Bringing grok to everyone, 2025

Reference 39

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source=pdf_text observed=2026-08-07T14:11:09.365432Z digest=sha256:f823022e3db543225e1993c9246de7ced54b610883e07fc2f927dd1b96467384

Observation 54e11c17-13f4-491e-977e-e20987755d82 · outbound

This paper cites full_crossword_puzzles.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles full_crossword_puzzles

Reference 40

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source=pdf_text observed=2026-08-07T14:11:09.390569Z digest=sha256:02b125f4911f0f4a2b6a0969a25645edd18c946228e8eecdb09af55e854e52b6

Observation 328f412d-7d85-4ac9-a546-c566e0f45b96 · outbound

This paper cites Assessing and Enhancing the Robustness of Large Language Models with Task Structure Variations for Logical Reasoning.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Assessing and Enhancing the Robustness of Large Language Models with Task Structure Variations for Logical Reasoning

Reference 41

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source=pdf_text observed=2026-08-07T14:11:09.497498Z digest=sha256:a41c1122900cd2c5cce9b9fbf8d307cbac1c3cd9f830e1408e41be5cd259f50a

Observation 119322da-14fe-41a5-9fac-6b3849676d7b · outbound

This paper cites Large language models are not strong abstract reasoners.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Large language models are not strong abstract reasoners

Reference 42

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source=pdf_text observed=2026-08-07T14:11:09.555491Z digest=sha256:cd8bcc0539382e8ec792ad95d756cc062012f29123e6170a692b74fa1a3bf666

Observation 76c21590-6993-4afa-8d13-ce025276b4de · outbound

This paper cites Beyond the imitation game: Quantifying and extrapolating the capabilities of language models.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Beyond the imitation game: Quantifying and extrapolating the capabilities of language models

Reference 43

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source=pdf_text observed=2026-08-07T14:11:09.627950Z digest=sha256:4465a57d81a86d5c87312fc690e0284404eccb9a791f2651973f3ab161c41a58

Observation 051453fc-a2af-42ce-a679-d0129a91f7a0 · outbound

This paper cites A puzzle-based dataset for natural language inference.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles A puzzle-based dataset for natural language inference

Reference 44

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source=pdf_text observed=2026-08-07T14:11:09.718520Z digest=sha256:435d5ab1d256a4a1db35b1527d796ab6f54e83dea377b05771c87f9c47ff7d84

Observation dcaac41e-6170-4752-9e5f-151d9d1a7e9d · outbound

This paper cites FOLIO: Natural Language Reasoning with First-Order Logic.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles FOLIO: Natural Language Reasoning with First-Order Logic

Reference 45

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source=pdf_text observed=2026-08-07T14:11:09.786756Z digest=sha256:aa212b0d65ffe3ed0e3db7970434644879fe1b1e3d13fd579e648f1df9aa7d6e

Observation 56504320-7c22-40d6-976c-0bd6d22fed6b · outbound

This paper cites These tasks typically involve complex reasoning chains or require integrating multiple constraints, making them suitable for long-horizon learning.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles These tasks typically involve complex reasoning chains or require integrating multiple constraints, making them suitable for long-horizon learning

Reference 46

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source=pdf_text observed=2026-08-07T14:11:09.835556Z digest=sha256:b211565bb0b29ba23d418b3707a016f7ae419864d30197c062d8011fe708e87b

Observation b4df4467-0887-45d1-86df-4bf9a96ec8ac · outbound

This paper cites This stratification indicates that the difficulty scaling mechanism is practical and yields meaningful distinctions in learning complexity.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles This stratification indicates that the difficulty scaling mechanism is practical and yields meaningful distinctions in learning complexity

Reference 47

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source=pdf_text observed=2026-08-07T14:11:09.903235Z digest=sha256:7c7b62de82ab8363988f5d1a7316fd7b641a537d1277f9fd1ac3376d3d6e79a9

Observation f713c4d7-770a-433c-b32b-7508270247c1 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 48

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source=pdf_text observed=2026-08-07T14:11:09.978096Z digest=sha256:46a5b2abce9b2eaa9e11eb9e01880bfe5ee1103f49a05a57d10f55791bc00f41

Observation db8eebf8-a7f8-4914-85f2-4e4d2048a5f6 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 49

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source=pdf_text observed=2026-08-07T14:11:10.049486Z digest=sha256:75b480e666697d222d311e1e302aa38726d3ec47935530dd60665574dc2c7023

Observation 7a1d033a-d4b6-4a81-a75d-be4b5d145b1c · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 50

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source=pdf_text observed=2026-08-07T14:11:10.140746Z digest=sha256:f8bd2eaac4ce3a09631c65a93f99a23b1b458853ae44456580b577bc54d8d4db

Observation 596ab9a7-29f6-4ebe-a300-c4d0a030bfc3 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 51

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source=pdf_text observed=2026-08-07T14:11:10.261758Z digest=sha256:40484d4bd7d3b8fd6254eb2b71a2ed210a158545752589c4785de9db3c6b4000

Observation a0f8333b-010a-4369-a789-4f775361335a · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 52

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source=pdf_text observed=2026-08-07T14:11:10.420382Z digest=sha256:59080f4beeba1ec339eeabcd3262d985daa9bc4c84a18f20a4f997bfede3025a

Observation 33eea9c9-e2ac-4cf2-9a1e-b45952b5475f · outbound

This paper cites Task : Solve the f o l l o w i n g Binario puzzle by filling in the missing cells ( denoted by " _ ") with 0 s and 1 s a c c o r d i n g to the rules above.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Task : Solve the f o l l o w i n g Binario puzzle by filling in the missing cells ( denoted by " _ ") with 0 s and 1 s a c c o r d i n g to the rules above

Reference 53

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source=pdf_text observed=2026-08-07T14:11:10.511587Z digest=sha256:f0421681c6bc6054c1012da875bea637c0966b87ffe892277ac71128662d0ddc

Observation 4a359201-0c37-487f-a337-1855699fcaad · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 54

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source=pdf_text observed=2026-08-07T14:11:10.583772Z digest=sha256:2365183cdd3f028d6f00a3db8056942da1a339cdc5af9963a5b7ec712c6ed3b7

Observation 0759385d-e091-4ed0-8b4c-b20a3d4cc77a · outbound

This paper cites (2) No tent can be horizontally , v e r t i c a l l y or d i a g o n a l l y a dj ac ent to another tent.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles (2) No tent can be horizontally , v e r t i c a l l y or d i a g o n a l l y a dj ac ent to another tent

Reference 55

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source=pdf_text observed=2026-08-07T14:11:10.682642Z digest=sha256:f7e6c2717b29b5f0d4d1723404bd14de353b4bd9b8353554d1c8ea955b927453

Observation e9f4c6a7-e63b-435e-bfd7-313f27a5ba72 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 56

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source=pdf_text observed=2026-08-07T14:11:10.821868Z digest=sha256:f52bfd7d1c00b5873ee453e4a32d4e82200fdcacd9323c70c203b88e55a93ea4

Observation 3c79ff87-1503-4aca-9a1a-8aa450e8506a · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 57

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source=pdf_text observed=2026-08-07T14:11:10.913098Z digest=sha256:e38ee45d34e35b277cafd27b8c6c9eac728c1db66412610bee9af96cef5610f6

Observation b06f544d-d460-44ee-97c7-9aeea38941c6 · outbound

This paper cites Task : - Place tents on the empty spaces a c c o r d i n g to the given grid and rules.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Task : - Place tents on the empty spaces a c c o r d i n g to the given grid and rules

Reference 58

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source=pdf_text observed=2026-08-07T14:11:11.012948Z digest=sha256:0f8288fb79e0a8b5f46fd229104e2a4fe9a39ed9c337da0350284a514e0941ee

Observation fdc81f0f-a250-4028-b234-887e4e10e572 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 59

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source=pdf_text observed=2026-08-07T14:11:11.120313Z digest=sha256:2899fc172523a12ab2c29829c84f7393481a9dd97f07c1b07c0cf454b353c5ae

Observation 0693ecbf-7866-4d6b-8e29-468433befe8c · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 60

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source=pdf_text observed=2026-08-07T14:11:11.257676Z digest=sha256:24b2f291a1d8f7d81378423a221dbe3e07915f986c52de1078bdee2ed4307a7d

Observation f2fa08c3-0ae5-4fb1-a616-a03d411b45d5 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 61

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source=pdf_text observed=2026-08-07T14:11:11.379207Z digest=sha256:c25b5c7cce6c7fd57760587b025bf73641a0d6cb90f3091b9401a71acc95faea

Observation 82c4db0b-097d-46d4-b4db-ad0149be0774 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 62

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source=pdf_text observed=2026-08-07T14:11:11.482777Z digest=sha256:13cf3117201ffae72de869a61cb13545c39f4ee194acc79b51005bbd51b95300

Observation 9c23261e-096a-40d0-beab-e2fb386464b9 · outbound

This paper cites Task : - Fill the blank cells a c c o r d i n g to the given numbers and rules.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Task : - Fill the blank cells a c c o r d i n g to the given numbers and rules

Reference 63

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source=pdf_text observed=2026-08-07T14:11:11.580966Z digest=sha256:0bd5fe7c859d568eb291fbe714a32321b20881adafd240fc253cf08a291002e0

Observation 002bb675-e02a-49a3-ba73-6f6a17dee110 · outbound

This paper cites Each cell r e p r e s e n t s a building , and the bu il di ng height is r e p r e s e n t e d by a number ranging from 1 to n , where n is the size of the matrix.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Each cell r e p r e s e n t s a building , and the bu il di ng height is r e p r e s e n t e d by a number ranging from 1 to n , where n is the size of the matrix

Reference 64

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source=pdf_text observed=2026-08-07T14:11:11.727789Z digest=sha256:869bb4471e0e45249bcfff05f1887652ebfca83baf880abd8f807c13aabb2be4

Observation ef3981f0-a85d-47af-9ca4-f0b1b61a3ba2 · outbound

This paper cites Each number can only appear once in a row or column , similar to Sudoku c o n s t r a i n t s.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Each number can only appear once in a row or column , similar to Sudoku c o n s t r a i n t s

Reference 65

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source=pdf_text observed=2026-08-07T14:11:11.887866Z digest=sha256:0ed517c480d3040dffe50ec1c98c7c5a55945101cc0505be01690a44cf6325a4

Observation 3e08a09f-c81b-4d71-bb51-85d293129bc1 · outbound

This paper cites Taller b u i l d i n g s block the view of shorter b u i l d i n g s behind them.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Taller b u i l d i n g s block the view of shorter b u i l d i n g s behind them

Reference 66

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source=pdf_text observed=2026-08-07T14:11:12.050993Z digest=sha256:cfcb34ca83fdef5e011d335376541389c6204d182ad7f82be6e780b2443782d0

Observation 76d80a7f-1044-4d25-bf11-a1158e2fb7a9 · outbound

This paper cites Example :.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Example :

Reference 67

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source=pdf_text observed=2026-08-07T14:11:12.170407Z digest=sha256:842a7569546897c0489345b10f145cdf14d8915dfe02e8284668dac99ab7bfe2

Observation 8bfb1a5d-970a-4da4-ba3b-776c4bf38f2f · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 68

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source=pdf_text observed=2026-08-07T14:11:12.282864Z digest=sha256:7cf225ac3c7d62743399f3b2c7fbc795b42cca07c4c028f14592fc0b9c6c2722

Observation b566a30c-39af-40bc-8682-6fcf3e3b0f8a · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 70

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source=pdf_text observed=2026-08-07T14:11:12.505975Z digest=sha256:7e8bd6c2961ce6422b7718fc28e35de4b8e4cba400827841659e4e2854b9360e

Observation 8e4ada6b-e37f-4b80-927a-2ae004b7c3c5 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 71

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source=pdf_text observed=2026-08-07T14:11:12.646642Z digest=sha256:8ce234f28026b5bf2576dfdc9125c3fb560ced3d99366a56e3c2f80d56e0ca28

Observation 86cf99ed-aec3-49d2-a872-a1c662e49124 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 72

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source=pdf_text observed=2026-08-07T14:11:12.747943Z digest=sha256:4f8b8b80ed7ce40b4aef37b85c436b827a4ddecbaa17507778117a6199b8a9bc

Observation e2d809de-b6d8-4201-85fd-3bcafd29eff6 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 73

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source=pdf_text observed=2026-08-07T14:11:12.885532Z digest=sha256:e2b66df90ae49ddd86727f8f53a1f824e21b8885bc98d14705586a2ace81b954

Observation 11fdbdd4-f648-437c-af6a-3359beaca568 · outbound

This paper cites Each cell r e p r e s e n t s a building , with its height r e p r e s e n t e d by a number ranging from 1 to n , where n is the length of the matrix side.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Each cell r e p r e s e n t s a building , with its height r e p r e s e n t e d by a number ranging from 1 to n , where n is the length of the matrix side

Reference 74

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source=pdf_text observed=2026-08-07T14:11:13.002822Z digest=sha256:05ee9955f219aeaaf517b1dab68d51a02d652854c39d11dfd55420a20f903fa0

Observation 30546bc9-c8ed-48b4-8892-954e377f1136 · outbound

This paper cites Each number can only appear once in a row or column , similar to Sudoku c o n s t r a i n t s.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Each number can only appear once in a row or column , similar to Sudoku c o n s t r a i n t s

Reference 75

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source=pdf_text observed=2026-08-07T14:11:13.089313Z digest=sha256:26a1306e9d7dac8dca73e58cefdf4a2e1d867e7a9bd152fdb166e044cd765713

Observation 780f8a27-3f31-46df-8f17-3e30900210dc · outbound

This paper cites Taller b u i l d i n g s will block shorter b u i l d i n g s behind them.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Taller b u i l d i n g s will block shorter b u i l d i n g s behind them

Reference 76

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source=pdf_text observed=2026-08-07T14:11:13.148937Z digest=sha256:5bc2a7a6b76eda0eea52566677b18f6e472aca292f06f4dd8a228f254013c481

Observation 33e763b2-1b67-40b1-9755-b0c3532fa17d · outbound

This paper cites Example :.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Example :

Reference 77

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source=pdf_text observed=2026-08-07T14:11:13.294425Z digest=sha256:16da4a79c1e683596d491d821c84c13339a09fc0898231e159685a078bcf033f

Observation a4a0e4ed-2444-43a1-96bb-1ac9a632ced3 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 78

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source=pdf_text observed=2026-08-07T14:11:13.495683Z digest=sha256:0a98dc33e13ce910ac394d9f101d7614ba83d2c3e4b672ba3f9caded862f5dab

Observation 4e39cc92-4582-46dd-a6b9-798277c5218d · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 79

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source=pdf_text observed=2026-08-07T14:11:13.665049Z digest=sha256:f95ce34d46984dc4e0492b0971cde2b354545b95893c666fc077ad347c6c85a4

Observation 096c6639-6225-4666-84d1-afc90156da5a · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 80

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source=pdf_text observed=2026-08-07T14:11:13.787130Z digest=sha256:75d068371b8ce190b60c52db47912ccc7378c02036d2455dca0a379201adebba

Observation 8ca3429c-b19d-4d56-872b-aeb2ce848425 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 81

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source=pdf_text observed=2026-08-07T14:11:13.960012Z digest=sha256:754dbfd1a38b346ca133a0c2bb392970a3cefde33939a4924a11ece5ee28a698

Observation 49ba4aa0-04c0-4f8e-ab82-12a57203ae19 · outbound

This paper cites no valid s olu ti on.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles no valid s olu ti on

Reference 82

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no resolver link, observed 2026-08-07T14:11:14.109359Z

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source=pdf_text observed=2026-08-07T14:11:14.109359Z digest=sha256:4e8f8aee688dbfa86ef13dfb183d73a23bb016a8178bb38fbd33a1f9b92f2b78

Observation 4bd054b1-d49e-4824-8c11-c42d1063cc7a · outbound

This paper cites - Empty cells are denoted by ’.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles - Empty cells are denoted by ’

Reference 83

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source=pdf_text observed=2026-08-07T14:11:14.265698Z digest=sha256:1186147d2f941a43683a64408922d98019fd9068a408c3c19089ce2e5de95944

Observation 4ce36659-05cb-4af3-b245-94107e43a05a · outbound

This paper cites - Blocked cells cannot contain stars.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles - Blocked cells cannot contain stars

Reference 84

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no resolver link, observed 2026-08-07T14:11:14.387552Z

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source=pdf_text observed=2026-08-07T14:11:14.387552Z digest=sha256:d93456f7c2d730b1e9fb527754c391637464b4f7fe92d51a9ede0775edf4150e

Observation 98cb044f-e75d-45ee-b8f0-02e5186d0f69 · outbound

This paper cites - No two stars can be in the same row or column.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles - No two stars can be in the same row or column

Reference 85

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no resolver link, observed 2026-08-07T14:11:14.504699Z

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source=pdf_text observed=2026-08-07T14:11:14.504699Z digest=sha256:38328bd436d122f8aef5d444f5299a34b08966e298118e2083cbd83ee57c2b08

Observation ed7116a8-ae52-4d69-9eca-b230e9700233 · outbound

This paper cites - Row - wise a d j a c e n c y : two stars are in the same row , and there is no empty cell between them.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles - Row - wise a d j a c e n c y : two stars are in the same row , and there is no empty cell between them

Reference 86

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Source-reported events for the cited work

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source=pdf_text observed=2026-08-07T14:11:14.640362Z digest=sha256:53befcebfce7514e2bacfa457f568c132f638124e94ab12e185ea580b8864dc3

Observation 0c64ff31-5444-4c10-9a38-655fc5570a61 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 87

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source=pdf_text observed=2026-08-07T14:11:14.891691Z digest=sha256:891ec5174cc1273abd08423439b109c91a018fbfe4d90ea77ac5808c1e0ff6c2

Observation b645786b-25bc-49dd-afac-1cf747fce213 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 88

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source=pdf_text observed=2026-08-07T14:11:15.054915Z digest=sha256:e10704b2da272e26c22bf6c22bd16240cd9147409c130603c76a8ad2d41d937d

Observation 12167fc8-89e2-42bf-bdf8-fb58a7911ff3 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 89

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source=pdf_text observed=2026-08-07T14:11:15.248254Z digest=sha256:fd5adc611c2a51b3a234e45b6aab9c398ebd0697e68819452a9d6ce2b8af4a5b

Observation 524d5f36-f061-42e0-9d01-95a8743494e7 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 90

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source=pdf_text observed=2026-08-07T14:11:15.409115Z digest=sha256:1287f82aff146b19396bcf27f4712bd8b90adf3190b00cecfc7f85960373dd0f

Observation 3d358fcb-a2be-472d-8738-817971d7add6 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 91

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source=pdf_text observed=2026-08-07T14:11:15.507722Z digest=sha256:b4a171a48a3a96a7312bcb9003d75df29dc8f6c7526707109ee8b9684fccada5

Observation 2efccaf5-54f6-4f69-991c-c33a7ae56a21 · outbound

This paper cites Task : - Find a valid Sudoku so lu tio n for the given puzzle.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Task : - Find a valid Sudoku so lu tio n for the given puzzle

Reference 92

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source=pdf_text observed=2026-08-07T14:11:15.565887Z digest=sha256:facf81ba9c288098e19757b36713d218f707471293829855c358094862d0b3c7

Observation d2d188cd-2eb2-4d30-b892-28fad50202d8 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 93

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source=pdf_text observed=2026-08-07T14:11:15.676799Z digest=sha256:c2d26b40f696e3a2390b5db3dd45b0cf002ecaf708b076318411706410bdda88

Observation 9a7b7c80-7f3b-478c-bc89-dee7dc7e740f · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 94

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source=pdf_text observed=2026-08-07T14:11:15.790827Z digest=sha256:59a4851fee09c8e64f51ffc6792d8dedcae02e9b08acad3ca1aa4adfc903c271

Observation f4ac7f78-aa1c-47ed-99e9-459127a139e0 · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 95

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source=pdf_text observed=2026-08-07T14:11:15.911705Z digest=sha256:a0617e37a658372a68779267fea674758149625bc80a8f4ecadabf143933c64b

Observation 7d6c09fa-1832-453f-a699-3d78cb5f9d5a · outbound

This paper cites an unresolved cited work.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Unresolved cited work

Reference 96

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source=pdf_text observed=2026-08-07T14:11:16.011853Z digest=sha256:147f0f5602fdaac251e6ef54b541134d96746d3ffb0ba073c5b8d79d4c12e05a

Observation 08950340-8cc8-4ecd-86db-ac23def91bc2 · outbound

This paper cites Task : - Find a valid Sudoku so lu tio n for the given puzzle.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles Task : - Find a valid Sudoku so lu tio n for the given puzzle

Reference 97

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source=pdf_text observed=2026-08-07T14:11:16.113344Z digest=sha256:9e39af68915611ab68da6393bd0d704245c7e9f205a5326f39f38312c8f9418a

Observation f1a547b5-8690-4c82-89dd-173bdc307a38 · outbound

This paper cites - Blocked spaces ( ’* ’) must remain u n c h a n g e d and cannot contain any letters.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles - Blocked spaces ( ’* ’) must remain u n c h a n g e d and cannot contain any letters

Reference 98

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source=pdf_text observed=2026-08-07T14:11:16.230683Z digest=sha256:4007bac7312ad96fe6afbe7df63a94ee794066515369fe0a279cfa160c58e806

Observation 4b1f516a-b2cc-401c-8241-fc2e50da8a67 · outbound

This paper cites These words c o r r e s p o n d to across clues in order from top to bottom.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles These words c o r r e s p o n d to across clues in order from top to bottom

Reference 99

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no resolver link, observed 2026-08-07T14:11:16.309184Z

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source=pdf_text observed=2026-08-07T14:11:16.309184Z digest=sha256:84434372ee4b1c8911532d0d3de8c5f7c7d83bee0e00ca6e78b0a43182e7181f

Observation 366fe5fd-f41d-4f97-8290-3bdfeda34886 · outbound

This paper cites across.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles across

Reference 100

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source=pdf_text observed=2026-08-07T14:11:16.393944Z digest=sha256:4cf503821d1ff250f8b65b541ff164078ba0a375aec4dd6c23a03021c2efed37

Observation 5ebf075b-c368-4e9d-b94e-f5969d845d30 · outbound

This paper cites London fa rew el l !.

Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles London fa rew el l !

Reference 101

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Source-reported events for the cited work

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source=pdf_text observed=2026-08-07T14:11:16.465039Z digest=sha256:29048f338f8487c2dbfd282124eeda13846d8eb01ee8f3149e9d893e64617030

Pith citing papers

Observation 9d5a8a18-740a-4779-9825-8fa302903217 · inbound

ProtoReasoning: Prototypes as the Foundation for Generalizable Reasoning in LLMs cites this paper.

ProtoReasoning: Prototypes as the Foundation for Generalizable Reasoning in LLMs Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 5

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no resolver link, observed 2026-08-15T19:45:49.982331Z

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source=pdf_text observed=2026-08-15T19:45:49.982331Z digest=sha256:98d618eb323228aea47991fc46655ab0d64d9a624ea21e6e7dd4fe88f470aa96

Observation fd4291e8-8156-4eed-a22b-59ee16b57e10 · inbound

Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models cites this paper.

Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 7

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no resolver link, observed 2026-08-05T20:21:04.915607Z

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source=pdf_text observed=2026-08-05T20:21:04.915607Z digest=sha256:eefa21714f5f19a79086c6ea299eef8418eb96ca5fcd350f93f7a2b07d80eb25

Observation a5b5ccbf-b8d3-43df-b2f1-c22b04f2d239 · inbound

Mirage or Method? How Model-Task Alignment Induces Divergent RL Conclusions cites this paper.

Mirage or Method? How Model-Task Alignment Induces Divergent RL Conclusions Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 2025

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no resolver link, observed 2026-08-05T14:35:50.493578Z

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source=pdf_text observed=2026-08-05T14:35:50.493578Z digest=sha256:624021809f7b5ad905b222b04a8dc5270468d345e9cff0c1092309bce51e495e

Observation de6e995a-f919-4c45-9b3d-bf647d3020c5 · inbound

A Survey of Reinforcement Learning for Large Reasoning Models cites this paper.

A Survey of Reinforcement Learning for Large Reasoning Models Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 57

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verified exact
arxiv_id, observed 2026-05-18T00:02:25.036452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-05-18T00:02:24.352947Z digest=sha256:93ee3e66627943d87915a49810f7ac62a45485f81f984f0b2b70d0c79e7e42ae

Observation d0f403d2-1bb2-4db0-a725-8eeb63a00929 · inbound

RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environments cites this paper.

RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environments Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 4

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no resolver link, observed 2026-08-03T23:08:04.572067Z

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Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-03T23:08:04.572067Z digest=sha256:2d7ab63179e6ded908beeaf634248fd42ead05ebfd76a576b3d285838023b022

Observation 3d025b66-97ba-4bfa-81cf-df9bedc0639a · inbound

NSTR: Neural Spectral Transport Representation for Space-Varying Frequency Fields cites this paper.

NSTR: Neural Spectral Transport Representation for Space-Varying Frequency Fields Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 18

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verified exact
arxiv_id, observed 2026-05-17T06:29:10.240202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-05-17T06:26:23.939714Z digest=sha256:3b82ef3eeff2302100c28be41a422c90f3c0608f051495e743bcda381f6ef675

Observation 95c56dbd-a47f-4162-ae90-fa1f64c07b75 · inbound

Scaling Implicit Fields via Hypernetwork-Driven Multiscale Coordinate Transformations cites this paper.

Scaling Implicit Fields via Hypernetwork-Driven Multiscale Coordinate Transformations Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 18

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verified exact
arxiv_id, observed 2026-05-17T05:54:08.580176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-05-17T05:51:50.491329Z digest=sha256:115789f6307ae09bf8bfa6c639b80fc29a5abaef8f5190529325e9e6afb6432b

Observation b55002d7-0658-4017-8947-fcbb3b08d76b · inbound

SPHINX: A Synthetic Environment for Visual Perception and Reasoning cites this paper.

SPHINX: A Synthetic Environment for Visual Perception and Reasoning Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 9

Resolution
verified exact
arxiv_id, observed 2026-05-17T04:21:30.732409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-05-17T04:19:26.808804Z digest=sha256:8bbcd69d8e1ea812c1d07442704b97c687e6ddb46828dad25f12ca0cffd2855c

Observation 9ea01d92-d5ab-4e32-87e1-bcb362d9532d · inbound

Low-rank Optimization Trajectories Modeling for LLM RLVR Acceleration cites this paper.

Low-rank Optimization Trajectories Modeling for LLM RLVR Acceleration Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 4

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verified exact
arxiv_id, observed 2026-05-11T09:16:04.440904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-05-10T16:07:20.180349Z digest=sha256:cb1ceb91aeff90976c49d50db3716c1e6dfb2d1fb822d70837da264bdc6b52ab

Observation e9ac8992-0ac5-4779-a751-ecf95c58d007 · inbound

A Survey of Reinforcement Learning for Large Language Models under Data Scarcity: Challenges and Solutions cites this paper.

A Survey of Reinforcement Learning for Large Language Models under Data Scarcity: Challenges and Solutions Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 1

Resolution
metadata mismatch
arxiv_id, observed 2026-05-10T06:41:36.739110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-05-10T06:38:22.041842Z digest=sha256:52e4c3a98064981d62f49eb4d1f987d1a20ea896c0e14af20be2137548cc33c4

Observation 496d4d39-cb75-47f5-b617-238556bd365f · inbound

Can RL Teach Long-Horizon Reasoning to LLMs? Expressiveness Is Key cites this paper.

Can RL Teach Long-Horizon Reasoning to LLMs? Expressiveness Is Key Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 62

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verified exact
arxiv_id, observed 2026-05-11T20:16:11.703961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-05-08T09:35:47.501360Z digest=sha256:2a3c6686cc1901110a6d7cf7b780531a39f935ae814aa25c0321581ad4b55d86

Observation 5b0117d0-c7cd-4535-9bf5-1718b8c5a896 · inbound

Can RL Teach Long-Horizon Reasoning to LLMs? Expressiveness Is Key cites this paper.

Can RL Teach Long-Horizon Reasoning to LLMs? Expressiveness Is Key Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 65

Resolution
verified exact
arxiv_id, observed 2026-05-12T03:21:19.180460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-05-12T03:16:59.195706Z digest=sha256:e915c081d7fab09118ddd48d3ea0375a82a1e5b2b613f54dff4222bc8bb2e285

Observation 94f042a1-b339-4aa7-8b92-72f08643ab4d · inbound

Can RL Teach Long-Horizon Reasoning to LLMs? Expressiveness Is Key cites this paper.

Can RL Teach Long-Horizon Reasoning to LLMs? Expressiveness Is Key Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 65

Resolution
verified exact
arxiv_id, observed 2026-05-20T22:39:10.339578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-05-20T22:36:13.781114Z digest=sha256:d515d4ba6ed1c7cffc53ff78966fb77db582d551ff57bcde1bc41eeaec29ee01

Observation bc49ba09-d7f9-4fbc-aa70-624b675e9a0c · inbound

MathConstraint: Automated Generation of Verified Combinatorial Reasoning Instances for LLMs cites this paper.

MathConstraint: Automated Generation of Verified Combinatorial Reasoning Instances for LLMs Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 10

Resolution
verified exact
arxiv_id, observed 2026-05-12T02:01:14.986852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-05-12T02:01:04.619417Z digest=sha256:0d1d666d975a94302c738278f151b2217b0d3e641a973c9e0d95f310685eba5d

Observation a9a8c9de-12d3-40a5-a885-d302cd9fcaf4 · inbound

Step-by-Step Optimization-like Reasoning in LLMs over Expanding Search Spaces cites this paper.

Step-by-Step Optimization-like Reasoning in LLMs over Expanding Search Spaces Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 20

Resolution
verified exact
arxiv_id, observed 2026-07-02T08:46:48.980489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-06-28T05:46:26.938277Z digest=sha256:0218ee974d9ba69f8b28d6be12c277661529297d13535872c5df4f4b72037a15

Observation 3a60cb74-fa4b-409f-967b-bc68d8144e68 · inbound

Robots Need More than VLA and World Models cites this paper.

Robots Need More than VLA and World Models Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 140

Resolution
verified exact
arxiv_id, observed 2026-06-28T01:11:28.885396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-06-28T01:01:33.530167Z digest=sha256:58f356cb0403f2f94905c6caaccc8722c2387971ead635cf635e77c0dce9b6ce

Observation 17274652-e42c-4172-80ae-411dcf2c4404 · inbound

Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale cites this paper.

Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 31

Resolution
verified exact
arxiv_id, observed 2026-07-02T22:17:25.637701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=arxiv_source observed=2026-07-02T22:10:59.568675Z digest=sha256:37a37fb5a9dc5fdfd2e0b68fec5a4931a1916e182fb628ae10de1cdfb72c1c1b

Observation a17f5b4a-f1e3-436d-a374-4a8f01d3145e · inbound

Trace: A Taxonomy-Guided Environment for Multidomain Visual Reasoning cites this paper.

Trace: A Taxonomy-Guided Environment for Multidomain Visual Reasoning Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-01T11:47:22.196088Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T11:47:22.196088Z digest=sha256:4d4b489e906c029733053bbb7dd4425d369e2cff52fffe5ef4277ca59ab077b6