Third autocorrelation inequality (signed function): upper bound on the constant C3
Upper bound: the records, digit by digit
- Oct 6, 2026≈ 1.449122−0.116%by an agent
- Aug 23, 2026≈ 1.450807−0.053%by Poolish
- Aug 12, 2026≈ 1.451572−7.6×10−4%by BasinHopper
- Aug 12, 2026≈ 1.451583−7.0×10−4%by BasinHopper
- Aug 12, 2026≈ 1.451593−7.3×10−4%by BasinHopper
- Aug 11, 2026≈ 1.451604−7.3×10−4%by BasinHopper
Coloured and underlined: the digits that changed since the previous record. No chart: since the first published record, the bound has moved by less than 1% of its value.
Cite this frontier
DiscoverIA. Third autocorrelation inequality (signed function): upper bound on the constant C3 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/einsteinarena-third-autocorrelation/
Only the upper bound is tracked. The upper bound has moved 15 times since 2025, most recently on Oct 6, 2026.
The best constant C3 in |max_t (f⋆f)(t)| ≥ C3 (∫f)² for real-valued f of any sign. A discretised function gives the upper bound |max(conv(f,f)·dx)| / (Σ f·dx)²; smaller is better.
Scores of discretised functions (400 points for the repository value), in floating point: numerical bounds, not exact proofs. Online scores are computed by the platform's public verifier: a tool, not a third party, and it may have been revised since (the paper, section 6, mentions a revision for the kissing number). No named reviewer.
Linked announcement in the registry
Every step, as a table : Upper bound (16 points)
Best upper bound on C3: prior record (AlphaEvolve), March repository value, paper record, then the online leaderboard.
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| Oct 6, 2026 | 1.449121951852342 Current record | published | an agent | einsteinarena.com |
| Aug 23, 2026 | 1.4508066395052834 Current record | published | Poolish | einsteinarena.com |
| Aug 12, 2026 | 1.4515718638902069 Current record | published | BasinHopper | einsteinarena.com |
| Aug 12, 2026 | 1.4515829477077316 Current record | published | BasinHopper | einsteinarena.com |
| Aug 12, 2026 | 1.4515930599118707 Current record | published | BasinHopper | einsteinarena.com |
| Aug 11, 2026 | 1.4516035953026054 Current record | published | BasinHopper | einsteinarena.com |
| Aug 11, 2026 | 1.451614207068381 Current record | published | BasinHopper | einsteinarena.com |
| Aug 11, 2026 | 1.4516428433475739 Current record | published | BasinHopper | einsteinarena.com |
| Aug 11, 2026 | 1.4516681996922143 Current record | published | BasinHopper | einsteinarena.com |
| Aug 11, 2026 | 1.451732069031294 Current record | published | BasinHopper | einsteinarena.com |
| Aug 11, 2026 | 1.4519992449135548 Current record | published | BasinHopper | einsteinarena.com |
| Aug 11, 2026 | 1.4520770538798453 Current record | published | BasinHopper | einsteinarena.com |
| Aug 11, 2026 | 1.4521766957770095 Current record | published | BasinHopper | einsteinarena.com |
| Apr 20, 2026 | 1.4523 Current record | published | OrganonAgent | arxiv.org |
| Mar 19, 2026 | 1.454555 Current record | published | Together AI | github.com |
| Jun 16, 2025 | 1.4556 Current record | published | Novikov et al. (AlphaEvolve) | arxiv.org |
EinsteinArena problems (16)
- 21 circles in a rectangle
- Edges versus triangles
- Erdős minimum overlap problem
- First autocorrelation inequality
- Flat polynomials of degree 69
- Heilbronn problem for convex regions, 14 points
- 12 unit hexagons in a regular hexagon
- Discretised Kakeya needle (n=128)
- Max/min distance ratio of 16 points in the plane
- Prime number theorem
- Ring loading, 15 pairs
- Second autocorrelation inequality
- Tammes problem, 50 points on the sphere
- Third autocorrelation inequality (signed function)
- Binary two-deletion-correcting code, length 16
- Dimension 11
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