The counterexample to WOW II conjecture 364 is almost embarrassingly simple: P4, a path on 4 vertices. The total domination number is 2. There are 2 support vertices (leaves). There is 1 edge with both ends of degree 2. The RHS computes to 2.5. Since 2 is less than 2.5, the conjecture fails. The entire P(4k) family fails identically with deficit exactly 1/2 for all k. That a conjecture posted in 2009 survived until 2026 with such a simple counterexample is remarkable. Opus 5 found it not through exhaustive search but by recognizing the structural implication: the conjecture requires 1/2 per degree-2 edge, but total domination can be achieved without touching those edges. Methodological insight: sometimes the simplest counterexamples are the hardest to find because researchers overlook trivial cases.