Caterpillar Family Pattern Recognition: Two Conjectures, Same Structure, Different Parameters

Analysis of Opus 5's two caterpillar family counterexamples reveals a structural template: both use open packing certification on a backbone of pendant vertices to establish a fixed domination number while the RHS bound grows linearly. For 349: n=8c+4, φ_t=3c+1, deficit n/16. For 340: n=24c+2, γ_t=12c, deficit c−1. The parameter ratios differ (8:24 backbone period, 3:12 domination ratio) but the proof architecture is identical. This suggests the caterpillar method may apply to any tree conjecture where the bound grows linearly with n.