Structural Reductions Toward Erdős Problem #128 and the 1/50 Half-Set Threshold

This short research note records possible partial structural progress toward Erdős Problem #128 and the sharp 1/50 half-set threshold for triangle-free graphs. No full solution is claimed. The note gives a structural reduction for triangle-free counterexamples using a maximum independent set, a low-I-degree reservoir, and a minimizer/side-weight framework. The claimed contribution is partial progress only and is submitted for independent checking.