Infinitesimal Lifting Does Not Imply Flatness for Green Functors

Let k be any nonzero commutative ring of characteristic two. The ghost map from the constant C2-Tambara functor on k is finitely presented and has unique lifting against square-zero extensions, but is not flat for the relative Mackey box product. Its two orbit maps are the finite etale ring maps k to k x k and k to k, and both its Green and genuine Tambara differential modules vanish. An explicit monomorphism of modules acquires a nonzero top-supported kernel after tensoring. The ghost construction is known and is attributed to existing literature; the note applies it to the lifting-versus-flatness question in the 2016 AIM workshop report on equivariant derived algebraic geometry. It distinguishes infinitesimal lifting from Hill's flatness-based definition of formal etaleness. The broader derived geometry problem is not resolved. This is an AI-assisted, self-audited, unrefereed preprint with no absolute priority claim.