For two nonreducible planar graphs the computed dimension of a Khovanov-Robert foam invariant exactly matches the Tait number; for the dodecahedral graph the computation leaves dimensions 58 or 60, with evidence pointing to 58.
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Computer Bounds for Kronheimer-Mrowka Foam Evaluation
For two nonreducible planar graphs the computed dimension of a Khovanov-Robert foam invariant exactly matches the Tait number; for the dodecahedral graph the computation leaves dimensions 58 or 60, with evidence pointing to 58.