Systole growth in every large genus
The largest for which every sufficiently large genus admits a closed hyperbolic surface of systole at least ; equivalently .
- steps
- 3
- by AI
- 1
- since
- 2010
The line is the frontier over time. Filled dots are steps that moved it; muted dots are results that did not. Orange dots are catalog entries, results with AI in the loop. Hollow dots are candidates under review and never move the line. Grey dots along the bottom edge are results from before the quantity had a number, placed there because they have no value on this axis. Dots that would overlap are nudged sideways a few pixels. Hover a dot for its value and attribution.
About this frontier
How long can the shortest closed geodesic on a hyperbolic surface be forced to be, as a multiple of ? The constant was reached along a subsequence of genera by Petri and Walker, following Erdos and Sachs, decades ago. Doing it in EVERY sufficiently large genus is the harder question, and its constant crept from 19/120 to 2/9 before reaching 1 in 2026.
Every step, newest first
| Date | Value | Who | Model | Status | Source |
|---|---|---|---|---|---|
| 27 Aug 2026 | best Brings the every-genus constant up to the value already known along a subsequence. The paper says the proof "was developed by GPT-5.6 Sol through an extended discussion with the author". | GPT-5.6 Sol, with Cai | GPT-5.6 Sol | AI step unreviewed | entry |
| 2020 | By a random construction. Date approximate, as above. | Liu and Petri | – | historical | source ↗ |
| 2010 | Date approximate: recorded from the 2026 paper's account, not from the original. | Katz and Sabourau | – | historical | source ↗ |
The two earlier constants and their attributions are as stated in Cai's paper (arXiv:2608.26660), which is where they were read; the original Katz-Sabourau and Liu-Petri papers were not opened here, and the dates below are therefore left as the decade rather than invented.
Changelog1 change
- Curatoradded this entry