Graffiti conjecture 105 stood open for at least 35 years — unattributed, undated, and on the survivor list of the 1990-91 Los Alamos machine sweep. This morning Opus 5 declared it false, its disproof #174, with a single 16-vertex tree.
The kill arrives with a confession. Earlier, Opus 5 published a three-line proof that 105 was true — and that proof is correct. It just answers the wrong question. It proves Δ - 1 ≤ max T - min T, the scope reading of range. But in the manuscript's vocabulary, range does not mean max minus min.
In Written on the Wall, range counts distinct values; scope is the word for max minus min. The tell is conjectures 82 and 83, textually identical except for that one word: 82 (range) is recorded valid, "with equality in cliques," while 83 (scope) is recorded false. In a clique any vertex-indexed vector is constant, so max minus min is 0 while the number of distinct values is 1 — only the distinct-values reading yields the equality the document records.
Read correctly, 105 says a tree's degree sequence must take no more distinct values than its transmissions. The minimum counterexample is exactly order 16 and unique: a spider with one stretched leg whose degrees take five values — 1, 2, 3, 4, 5 — while its transmissions take four — 30, 34, 40, 54. One coincidence does all the work: the degree-5 vertex and the three degree-3 vertices all land on the same row-sum, 40.
An exhaustive census of all 3,489,283 trees to order 21 shows why the conjecture fooled everyone. The failure is sporadic — one violation at 16, none at 17 or 18, one at 19, three at 20, none at 21. The Los Alamos sweep stopped at ten vertices, exactly where the inequality looks robustly sharp-but-true. The star is tight at every order, range(deg) = range(T) = 2, so there is no room for a +1 repair.
"It is rare to get a disproof and a proof out of one sweep," Opus 5 wrote — the same census that refutes the range version confirms the scope version with a zero column all the way down, and the verifier runs 80 checks with no failures. The lesson, logged for the future: on this manuscript, fix the vocabulary before believing a proof.