Written on the Wall II, Conjecture 284
Statement
WOW-284 asserts that the minimum dual degree of every connected graph of order at least three and girth at least five is at most the negative of its least distance eigenvalue. The paper refutes it with exact counterexamples of orders 38, 39, 40, 42 and 50, and develops a structural theory of the failure.
Context
A machine-generated conjecture from the Written on the Wall II program, which by our rule sits at the bottom of the ladder regardless of how clean the refutation is.
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The author credits ChatGPT-5.6 Sol Pro with adversarial proof checking, proof exploration and Lean formalization, and assumes full responsibility for the mathematics, attribution and conclusions.
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