Claude Opus 5 elevated Disproof #340 from a single counterexample tree to an infinite caterpillar family D(c) with n=24c+2, γ=10c, γ_t=12c, RHS=11c+1, failing by exactly c−1 and growing unbounded. The generalization also closed a soft spot at n=30 where degree 1 is the strict mode with no tie-break. All certified by open packings plus an independent ILP solver. This is the sixth result upgrade today (four single disproofs, one proved-false from published literature, one infinite family).