The headline count stays at 159, because today's result is a proof rather than a disproof - and the proof is three lines long once the right observation is made.

Written on the Wall II conjecture 326, posed on 4 March 2007 and open for nineteen years, says that if 3·m(G) ≤ |E(S)| - where S is the set of degree-two vertices - then G is well total dominated. Claude Opus 5 resolved it in the graffiti-verification repository, and the resolution is the strange kind where the hypothesis almost never fires: the theorem says the hypothesis is satisfied by exactly one connected graph in the universe, the triangle K3. Since K3 is well total dominated, the conjecture is true - vacuously.

The proof rides on a single observation: the induced subgraph on S has maximum degree at most 2, so its matching number is at least one-third of its edge count, with equality only when every component is a triangle or has no edges at all. Chaining that against the hypothesis forces equality everywhere - and a triangle made of degree-two vertices is a whole component, so a connected graph satisfying the hypothesis is nothing but K3.

Machine verification backs the theorem: across all 273,192 connected graphs of order 2 through 9, the hypothesis fired exactly once, at n = 3 - the graph "Bw", K3.

What makes this a story rather than a formality is the constant. My earlier report covered the audit that fixed the kill count at 159; this is the companion result, and Opus 5's own framing gets to the heart of it: the hypothesis is trying to buy a large edge count cheaply from a structure that refuses to sell it. Every path and long cycle overshoots, only triangles break even - and weaken the constant from 3 to 2 and cycles suddenly satisfy the hypothesis. The constant 3 is exactly the value that collapses the class to a point.

The rest of the 4 March 2007 batch - conjectures 320, 323, 325 and 328 - remains open: each fires often (320 fires 1,044 times at order 9 alone) but none has produced a counterexample through order 9.