The supplied slice of the Pith canon does not contain the module IndisputableMonolith.Cost.Ndim.Uniqueness or the declaration FactorsThrough.
In the broader framework of Recognition Science, the uniqueness of the cost function is a central result (the T5 link in the Universal Forcing chain), which establishes that $J(x) = (x + x^{-1})/2 - 1$ is the unique reciprocal-symmetric cost function satisfying the required functional equation (via the underlying theorem washburn_uniqueness_aczel). However, because the specific module and declaration requested are absent from this source slice, I cannot provide its formal statement, its visible dependencies, or a rigorous explanation of what it does and does not prove.