A computer-assisted package verifies the case of 14 runners by checking 111 prime gates and includes code for an audit.
The work presents a computer-assisted proof of the 14-runner case of the Lonely Runner Conjecture. Its verification checks 111 prime-based cases, called gates, and reports no surviving configurations that would contradict the conjecture.
The accompanying archive contains per-gate certificates, hashes, logs, C++ source code, orchestration scripts and a Python audit script. Running the audit script is reported to recheck all 111 gates and confirm that the verification is complete.
The package certifies that the relevant set is empty for 111 prime gates whose combined logarithmic measure is greater than 681.5292. This exceeds the stated finite-checking threshold, which is below 670.3498, by more than 11.17; the margin remains after removing any one gate.
For each gate, the computation generates the required candidate families, applies exact filters, and reduces them to two persistent multiplicative orbits. An exact branch-and-bound search then eliminates the remaining 713 fibers at level 14, finding zero improper survivors. The included audit script is reported to reverify all 111 gates, with all checks passing and the proof marked complete.
The result addresses the 14-runner case of a conjecture about whether, among runners moving at constant but possibly different speeds around a track, each runner must at some time be sufficiently far from all the others. It extends the reported computer-assisted verification to thirteen moving runners, while also making the computational record available for checking through certificates, logs and source code.
This is a computer-assisted mathematical proof presented as a preprint, rather than a peer-reviewed journal article. The claim depends on the stated finite-checking framework and on exact computations across the 111 gates. The archive includes an audit script using only Python's standard library, but peer review may identify errors or lead to changes in the manuscript or verification package.
arXiv (Cornell University) · 2026 · DOI: 10.5281/zenodo.22066771
Authors: J Allikvere
A new open-source pipeline uses an existing AI system to segment far more of very large Earth-observation images without training data or manual threshold tuning. Across seven scenes, it increased coverage to 91–98% and joined objects split across image tiles.
A survey of human-AI collaboration argues that more capable AI systems do not automatically produce reliable partnerships. It identifies human-centered design, governance and attention to high-stakes uses as central to making these systems trustworthy and beneficial.
Deep-learning tools for predicting RNA splicing can rely on genomic clues unrelated to splicing and miss important effects of RNA structure, a study finds. These weaknesses were linked to systematic errors, especially when the tools evaluated sequences that differed from those used for training.
