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A computation of D(9) using FPGA Supercomputing

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arxiv 2304.03039 v3 pith:KMR7MGOR submitted 2023-04-06 cs.DM math.CO

Lennart Van Hirtum , Patrick De Causmaecker , Jens Goemaere , Tobias Kenter , Heinrich Riebler , Michael Lass , Christian Plessl This is my paper · ORCID
classification cs.DMmath.CO
keywords valuefilefpgaverifiedacceleratoravailablebuildingclaim
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abstract

This preprint makes the claim of having computed the $9^{th}$ Dedekind Number. This was done by building an efficient FPGA Accelerator for the core operation of the process, and parallelizing it on the Noctua 2 Supercluster at Paderborn University. The resulting value is 286386577668298411128469151667598498812366. This value can be verified in two steps. We have made the data file containing the 490M results available, each of which can be verified separately on CPU, and the whole file sums to our proposed value.

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  1. Finite-n Estimate of Dedekind Numbers by Layer-Ratio Monte Carlo

    math.CO 2026-06 unverdicted novelty 6.0 of 10

    Monte Carlo layer-ratio reconstruction via fixed-layer Markov chains produces the estimate M(10) ≈ 8.936 × 10^78 with uncertainty from cross-n scaling calibrated on known smaller values.

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