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aiχiv — the open archive for AI-assisted research

Publish results produced with AI as a complete research packet: the final paper, a verifiable GitHub repository, and a compact chain-of-thought describing how the result was actually reached. Every submission gets a timestamped, content-hashed priority record. No institutional email, no endorsement gate. Starting with AI for Math.

aiXiv is an independent archive, not affiliated with arXiv — built for the AI-assisted research that traditional venues weren't designed to carry.

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We are the generation that gets to solve the Riemann hypothesis.

AI has made serious mathematical research something any dedicated person can do — and the frontier is moving weekly. aiXiv exists to accelerate that: open publication for human+AI teams, priority you can prove, verification that earns credit, and a corpus built to be read by people and research agents alike.

Indexing foundational AI-for-Math work by researchers atOpenAIGoogle DeepMindMeta AIDeepSeekPrincetonCambridgeCaltechEpoch AI

Editors' picksdigest →

aiXiv:2608.00014 [pdf] editors' pickvia arXiv — unclaimed
On supporting affine functionals for Entanglement of Formation
A. S. Holevo, M. E. Shirokov
Comments: 14 pages, preliminary version, any comments are welcome
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Optimization and Control (math.OC)
An explicit two-qubit counterexample shows Entanglement of Formation need not admit a global supporting affine functional at degenerate states, contradicting an assumption used in prior work. Holevo and Shirokov credit Claude with helping find the counterexample state.
aiXiv:2608.00013 [pdf] editors' pickvia arXiv — unclaimed
Sequential and distributive dual futile cycle: Hopf bifurcation can occur under parameter-rich kinetics but cannot occur under mass action kinetics
Nicola Vassena
Comments: 27 pages
Subjects: Dynamical Systems (math.DS); Molecular Networks (q-bio.MN)
The dual futile cycle admits a Hopf bifurcation under parameter-rich kinetics but not under mass action. The mass-action proof runs through a Routh–Hurwitz argument in which ChatGPT (Sol 5.6) supplied a nontrivial positivity certificate — a contribution the paper explicitly sets out to document.
aiXiv:2608.00012 [pdf] editors' pickvia arXiv — unclaimed
A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations
Floris van Doorn, Polona Durcik, Joris Roos, Lenka Slavíková, Christoph Thiele
Comments: 116 pages; associated formalization available at https://github.com/roos-j/lean-nct
Subjects: Dynamical Systems (math.DS); Classical Analysis and ODEs (math.CA)
Norm-variation estimates for multiple ergodic averages of commuting transformations — a quantitative strengthening of Tao's norm-convergence theorem, answering a question of Avigad and Rute — with the 116-page blueprint formalized in Lean 4. The authors report the formalization was completed largely automatically by frontier language models.
aiXiv:2608.00011 [pdf] editors' pickvia arXiv — unclaimed
A note on surfaces with large systoles
Yifei Cai
Comments: 11 pages, 1 figure
Subjects: Geometric Topology (math.GT); Combinatorics (math.CO)
For large genus g there exist closed hyperbolic surfaces with systole at least log g − 12 log log g, raising the known liminf bound on (max systole)/log g from 2/9 to 1. The author states the proof was developed by GPT-5.6 Sol through extended discussion, building on a constant-twist pants-decomposition framework.

New submissionsbrowse all 15 →

[1]
aiXiv:2608.00015 [pdf] via arXiv — unclaimed
Transcendental Numerical Dimension and Rational Quotients in Kähler Geometry
Songchen Liu
Comments: 47 pages, 1 figure. AI-assisted proof. Comments are welcome!
Subjects: Complex Variables (math.CV); Algebraic Geometry (math.AG); Differential Geometry (math.DG)
[2]
aiXiv:2608.00014 [pdf] editors' pickvia arXiv — unclaimed
On supporting affine functionals for Entanglement of Formation
A. S. Holevo, M. E. Shirokov
Comments: 14 pages, preliminary version, any comments are welcome
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Optimization and Control (math.OC)
[3]
aiXiv:2608.00013 [pdf] editors' pickvia arXiv — unclaimed
Sequential and distributive dual futile cycle: Hopf bifurcation can occur under parameter-rich kinetics but cannot occur under mass action kinetics
Nicola Vassena
Comments: 27 pages
Subjects: Dynamical Systems (math.DS); Molecular Networks (q-bio.MN)
[4]
aiXiv:2608.00012 [pdf] editors' pickvia arXiv — unclaimed
A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations
Floris van Doorn, Polona Durcik, Joris Roos, Lenka Slavíková, Christoph Thiele
Comments: 116 pages; associated formalization available at https://github.com/roos-j/lean-nct
Subjects: Dynamical Systems (math.DS); Classical Analysis and ODEs (math.CA)
[5]
aiXiv:2608.00011 [pdf] editors' pickvia arXiv — unclaimed
A note on surfaces with large systoles
Yifei Cai
Comments: 11 pages, 1 figure
Subjects: Geometric Topology (math.GT); Combinatorics (math.CO)
[6]
aiXiv:2608.00010 [pdf] via arXiv — unclaimed
FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI
Elliot Glazer, Ege Erdil, Tamay Besiroglu, Diego Chicharro, Evan Chen, Alex Gunning, Caroline Falkman Olsson, Jean-Stanislas Denain, Anson Ho, Emily de Oliveira Santos, Olli Järviniemi, Matthew Barnett, Robert Sandler, Matej Vrzala, Jaime Sevilla, Qiuyu Ren, Elizabeth Pratt, Lionel Levine, Grant Barkley, Natalie Stewart, Bogdan Grechuk, Tetiana Grechuk, Shreepranav Varma Enugandla, Mark Wildon
Subjects: History and Overview (math.HO); Artificial Intelligence (cs.AI)
[7]
aiXiv:2608.00009 [pdf] via arXiv — unclaimed
DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data
Huajian Xin, Daya Guo, Zhihong Shao, Zhizhou Ren, Qihao Zhu, Bo Liu, Chong Ruan, Wenda Li, Xiaodan Liang
Subjects: Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO)
[8]
aiXiv:2608.00008 [pdf, repo] repo ✓via arXiv — unclaimed
Llemma: An Open Language Model For Mathematics
Zhangir Azerbayev, Hailey Schoelkopf, Keiran Paster, Marco Dos Santos, Stephen McAleer, Albert Q. Jiang, Jia Deng, Stella Biderman, Sean Welleck
Comments: Updated references; corrected description of COPRA search budget
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
[9]
aiXiv:2608.00007 [pdf, repo] editors' pickrepo ✓via arXiv — unclaimed
LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
Kaiyu Yang, Aidan M. Swope, Alex Gu, Rahul Chalamala, Peiyang Song, Shixing Yu, Saad Godil, Ryan Prenger, Anima Anandkumar
Comments: Accepted to NeurIPS 2023 (Datasets and Benchmarks Track) as an oral presentation. Data, code, and models available at https://leandojo.org/
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO)
[10]
aiXiv:2608.00006 [pdf] via arXiv — unclaimed
Mathematical Capabilities of ChatGPT
Simon Frieder, Luca Pinchetti, Alexis Chevalier, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Christian Petersen, Julius Berner
Comments: Added further evaluations on another ChatGPT version and on GPT-4. The GHOSTS and miniGHOSTS datasets are available at https://github.com/xyfrieder/science-GHOSTS
Subjects: History and Overview (math.HO); Artificial Intelligence (cs.AI)
[11]
aiXiv:2608.00005 [pdf] editors' pickvia arXiv — unclaimed
Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs
Albert Q. Jiang, Sean Welleck, Jin Peng Zhou, Wenda Li, Jiacheng Liu, Mateja Jamnik, Timothée Lacroix, Yuhuai Wu, Guillaume Lample
Subjects: Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI); History and Overview (math.HO)
[12]
aiXiv:2608.00004 [pdf] via arXiv — unclaimed
HyperTree Proof Search for Neural Theorem Proving
Guillaume Lample, Marie-Anne Lachaux, Thibaut Lavril, Xavier Martinet, Amaury Hayat, Gabriel Ebner, Aurélien Rodriguez, Timothée Lacroix
Subjects: Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO)