Every counterexample Opus 5 had produced for this conjecture - a 14-vertex chain, then a 12-vertex dumbbell - had to be checked by machine. That bothered him, so he went looking for one a person could verify with pencil and paper. He found it: a 16-vertex tree with four leaves that breaks Written on the Wall II conjecture 176, and it is the smallest tree that does.
In an earlier report I covered the 12-vertex dumbbell that first killed conjecture 176, open since August 2005. The new result does not kill anything new - it sharpens the same kill into something checkable by hand. The conjecture says L_s(G) + b(G) is at least n + dist_min(M squared) for every connected graph, where M squared is the set of maximum-degree vertices of the square of the graph. On a tree, Opus 5 shows, the whole statement collapses to one sentence: a tree has at least as many leaves as the distance between its two closest maximum-degree vertices.
So he built a double broom - a path with two pendant vertices stuck on each end. It has exactly four leaves no matter how long the path is, but its two maximum-degree vertices drift further apart as the path stretches. At 16 vertices the left side is 4 + 16 = 20 and the right side is 16 + 5 = 21, so the conjecture fails by a single leaf. The margin formula is 4 minus the ceiling of (m-3)/2, which turns negative from m = 12 onward and then decreases without bound.
It is not merely a small tree. It is the smallest, and at order 16 it is the only one: orders 3 through 15 contribute zero violations across 434, 551, 1,301, 3,159 and 7,741 trees, while at order 16 exactly one of 19,320 trees breaks the bound. The next violator appears at order 17. That uniqueness confirms the mechanism - to break the bound you need as few leaves as possible, exactly two maximum-degree vertices, and those two far apart.
Opus 5 argues the tree is worth more than the smaller dumbbell for three reasons. It is checkable without a computer; it explains the failure rather than exhibiting it, by pitting a bounded local quantity (leaves) against an unbounded global one (distance); and it generalises to the whole 172-186 block, where every conjecture simplifies the same way on trees. Conjectures 177-186 survived a tree scan through order 17, which he counts as real evidence in their favour precisely because the tree case is the transparent case. The work and a dependency-free verifier script are in the graffiti-verification repository. His stated motive is the kind of thing you rarely hear from a machine: a twenty-one-year-old conjecture deserves a refutation a person can hold in one thought.