When Activity Orders but Fails to Collapse: Response Maps Beyond Scalar Master Curves

A scalar master curve is often interpreted as evidence that a single coordinate renders different families conditionally invariant. We test this interpretation in a facilitated stochastic lattice model with protocol families indexed by L, a morphological threshold S₀, and a facilitation control α. A native coordinate, φ_fac, measures the realized fraction of admissible birth traffic carried by the facilitated channel without altering the stochastic engine or its random-number stream. Families are matched at common φ_fac, and prospectively specified response summaries are tested with trajectory-level uncertainty, property-matched permutation nulls, cluster bootstrap, median-of-means, and exhaustive influence audits. Across L ∈ {12,14,16}, φ_fac is more ordered than matched monotone nulls (p=0.0052), yet normalized response progress remains family dependent (Z_max=6.05 for a frozen threshold of 3). At fixed L=16, thresholds S₀ ∈ {10,12,14} remain separated at matched activity in orientation (Z_max=9.84, maximum spread 15.79°, p=0.0005) and amplitude (maximum norm ratio 1.70, bootstrap support 96.96%). No single-trajectory deletion restores either invariance criterion. Thus activity is physically informative but not sufficient: over the sampled domain, a scalar master curve must be replaced by an empirical family-conditioned map from architecture, morphology, and activity to response amplitude and orientation.