These bounds are conditional, not guarantees for arbitrary schedules. Let n>=1 be the number of original bits, M the number of factor-variable occurrences, and b a bound with M<=bn. Assume the schedules give groups of size at most 2n/r and maximum label multiplicity h with hD<=2M. If the exceptional basis fraction is at most epsilon, the auxiliary matrix has c<=epsilonD rows. Splitting all h copies among r groups then gives rhc<=rhepsilonD<=2repsilonM<=2repsilonbn rows. Choosing epsilon=tau/(rb) gives at most 2taun rows. The manuscript has a separate incidence-balancing lemma and parameter choices to supply these assumptions; their proofs are not established by this calculation.