frb100-40 After Two Decades: An Optimality Certificate and a Preregistered Search Study

Abstract:For more than 20 years, the Model-RB benchmark frb100-40 remained an open challenge; since 2014, its public record had stood at 99 of 100 variables. We give a directly checkable 100-vertex independent set for its 4,000-vertex graph. Together with a verified partition into 100 cliques of size 40, the witness proves that the maximum independent-set size is 100 and the minimum vertex-cover size is 3,900. The stochastic run that found the witness is kept separate from this proof. We evaluated its added pair and triple repair operators in a preregistered campaign comprising 8,668 valid runs. The primary comparison found no detectable acceleration over base ULSA (hazard ratio 0.967, 95% confidence interval 0.915-1.023; p=0.248), and the factorial ablation reached the same conclusion. On a smaller FRB suite, the group-aware CSP pipeline solved 2,500/2,500 runs, compared with 2,391/2,500 for LibMVC-NuMVC. On frb100-40, full ULSA, base ULSA, and NuMVC each produced 0/56 new certificates. With no events, the planned cross-solver hazard ratios remain unidentified. NuMVC ended with cover size 3,902 in 40 runs and 3,903 in 16. Exhaustive enumeration showed that none of the 108 unique recorded conflict-two states had a strictly improving group-aware CSP neighbor within Hamming radius three. The certificate settles the instance. The experiments characterize the search barrier, and the preregistered comparisons show no heuristic advantage.

7 pages, 4 figures, 4 tables. Reproducibility artifact: this https URL

Discrete Mathematics (cs.DM); Artificial Intelligence (cs.AI)

arXiv:2609.02804 [cs.DM]

(or arXiv:2609.02804v1 [cs.DM] for this version)

https://doi.org/10.48550/arXiv.2609.02804 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

frb100-40_IS100_canonical.txt

verify_certificate.py

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