Lean 4 formalization of the non-factorization countermodels for a boundary-screening premise in causal-set presentations — companion code to 'Exact finite-size corrections for spacelike-volume estimators in causal diamonds'

Lean 4 formalization (bare core, no Mathlib; toolchain leanprover/lean4:v4.33.1) of the finite countermodels that establish the independence result used in Section 5 of the companion paper. The companion paper studies a boundary counting law for causal sets sprinkled into finite causal diamonds, and states the extra premise any gravity-style reading of that law requires: that presentations of a region factor through its boundary layer. This deposit proves, at kernel-checked grade, that the factorized premise does not follow from the twenty-condition axiom core it would extend: two finite countermodels satisfy all core conditions and agree on everything the boundary layer determines, while a coupling readout differs between them — the readout factors through neither the screened interface (FGB1.scr_not_factors) nor the padded incidence interface (FGB1.inc_not_factors), and factors through the channel interface (FGB1.chan_factors). The headline theorems depend only on the standard logical axioms propext and Quot.sound; there is no sorry and no native_decide. Build with `lake build` in src/.