New Advances in Machine-Verified Mathematical Proofs
kevrussell · x · 2026-07-11
This post highlights a new mathematical result: the upper bounds for the number of points in the dual kissing configuration problem for R¹¹ and R¹² cannot exceed 820 and 1,228, respectively.
The author emphasizes two key aspects of this approach:
- It provides tighter bounds in these dimensions compared to the "halving upper bound."
- The same pipeline can exactly reproduce classic sharp values, such as 120 for E₈ and 12 for D₄.
Technically, it utilizes a Delsarte linear programming method based on "completely rational exact arithmetic":
- Uses rational multipliers
- Employs Sturm root-counting over ℚ for root counting
- The certification path avoids floating-point numbers entirely
The author also provides a way to reproduce the experiments: clone the repository and run make verify. The verifier can reconstruct the theorem from raw coefficients in seconds. The post notes this is the fifth machine-verified note in the series and includes a DOI.
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