Hyperbolic surfaces with large systoles in every large genus
For every sufficiently large genus there is a closed hyperbolic surface whose systole is at least log g minus 12 log log g, raising the known asymptotic constant from 2/9 to 1.
- Lab
- Independent
- Model
- GPT-5.6 Sol
- Field
- Mathematics
- Date
- 2026-08-27
- Human collaborators
- Yifei Cai
Sources
Original work
Independent commentary
What was found
For every sufficiently large genus g the note constructs a closed hyperbolic surface with systole at least log g minus 12 log log g, which gives a lower bound of 1 for the limit inferior of the maximum systole over genus-g surfaces divided by log g, improving the previously known bound of 2/9. It continues the author's earlier work on the diameter of finite covers, using the same constant-twist pants decomposition framework applied to systoles instead.
Novelty check
The improvement is stated against a specific numerical baseline, the previously known bound of 2/9 for the same limit inferior, so the delta is explicit. The note names its own predecessor, arXiv:2608.12887, and reuses that framework, which makes clear what is new here as against what was already built. No stronger bound appears in the cited literature or in the vibemathed record.
Caveats and known objections
A short preprint, unrefereed, not formalized, with no independent check on record, and vibemathed records the resolution as partial. Autonomy is graded ai-led on the paper's declaration on the use of AI, which credits the model with the proof but the framework to the author: starting from the constant-twist pants decomposition approach described in the note, GPT-5.6 Sol developed the first complete proof of the main theorem through an extended discussion with the author.
Also recorded at
vibemathedlarge-systoles-in-every-sufficiently-large-genus
Nothing mechanically. It is a parallel listing of the same result, carrying its own verification label rather than an independent check.
Nobody outside the lab has checked this yet.
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Entry history (1 event)
- AddedEntered the registry graded Author verified and AI-led.
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Graded author verified for verification and ai-led for autonomy. What these mean.
Cite this entry
whataifound.org. (2026). Hyperbolic surfaces with large systoles in every large genus. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-08-27-large-systolesBibTeX
@misc{whataifound-independent-2026-systoles,
title = {Hyperbolic surfaces with large systoles in every large genus},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Independent. Verification: Author verified. Autonomy: AI-led.},
url = {https://whataifound.org/finding/2026-08-27-large-systoles}
}