Bounded Geometric Phase Transition in Finite Causal Posets with Exact Entropy

We construct a 7-family poset ensemble and compute exact linear extension counts for N = 10–44 elements to study action-weighted competition between Lorentzian-like geometric structures and Kleitman–Rothschild (KR) high-entropy posets. Under a decomposable action combining neutral and geometric penalty terms, the critical geometric coupling γ_c remains O(1) across all tested sizes — the first finite-size evidence of a bounded phase transition threshold in this setting. Systematic ablation identifies a minimal backbone of two constraints: global layer-shape balance and dimensional scale consistency, the latter replaceable by a non-target-anchored variant with γ_c preserved.