6. The affinity bound
This page proves that two distinct positive contacts of a common feasible kernel are separated in both marginals: each
marginal Bhattacharyya affinity is at most the quadratic b(s), so that -\ln BC_X-\ln BC_Y\ge\Psi(s), with the
separation s defined below and b, BC_X, BC_Y and \Psi defined in (A2.1). The mismatch payment (step 6
of the route) uses this for every pair of distinct components of the setup
latent: it combines this bound with the midpoint relative-entropy inequality and replica symmetry to bound the weighted
off-diagonal sum of separation prices \sum_{i\ne j}\mu_{ij}\Psi(s_{ij}) (with the pair masses \mu_{ij} of
Lemma P5.1 and the separations s_{ij} of Lemma P5.3 on the payment page) by the replica budget K; the pair charge
then compares this sum with the mismatch d. In the assembly NaturalLatents.General.T_le_of_connected
(NaturalLatents/General/Pricing.lean), the affinity hypothesis of mismatch_payment is discharged by
affinity_bound applied to the conclusion of contact_moments.