Nonexistence of (243,121,60) difference sets in C3 × C9 × C9

A (v,k,λ) difference set in a finite group of order v is a k-element subset in which every nonidentity element occurs exactly λ times as an ordered difference. We prove, by exhaustive computation, that no $(243,121,60)$ difference set exists in C₃× C₉× C₉. This group-specific case appears as unresolved in the 1997 table of Vera López and García Sánchez and was singled out by Gordon in 2019 as the "Smallest Open Case." A multiplier-fixed translate has thirteen points in the subgroup of elements annihilated by three. Moment identities, singleton congruences, and legal affine normalizations reduce the problem to eight quotient multiplicity arrays, each with a complete ternary lifting tree. Integer difference-count searches exhaust these trees, with separate checks of decomposition completeness. Lean proves the multiplier reduction, normalization, lifting coverage, and pruning lemmas; its final nonexistence theorem is explicitly conditional on the externally established search assertions. Computer-assisted; not yet reviewed by experts. Produced by AI models under the author's direction.