7. The replica budget
This page bounds the replica budget K of a finite latent: draw two labels L_1,L_2 independently from the
posterior at the same cell, and let K be the total information that L_2 carries about the two coordinates given L_1.
With the budgets M, B defined in (Q3.1) and K and the two nonnegative remainders C, N defined in
(Q3.3), the page proves the exact identity K=2M+B-C-2N, and hence K\le2M+B. The later mismatch-payment argument
(step 6 of the route) compares a weighted sum of component separation
prices (\Psi(s) of the affinity page) with K, and this inequality converts that comparison into the budgets M and B. In
the assembly NaturalLatents.General.T_le_of_connected (NaturalLatents/General/Pricing.lean), replica_budget is
passed to mismatch_payment as its replica hypothesis. The Lean statement is the inequality only.