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The conjecture is made based on a plausible, but not rigorous argument, suggesting that the unknot probability for a randomly generated self-avoiding polygon of N≫1 edges has only logarithmic, and not power law corrections to the known leading exponential law: Punknot(N)∼exp−N/N0+o(lnN) with N0 being referred to as the random knotting length. This conjecture is consistent with the numerical result of 2010 by Baiesi, Orlandini, and Stella.

Scaling Conjecture Regarding the Number of Unknots among Polygons of N≫1 Edges