Failure of Rockafellar's Sum Conjecture via an Explicit Non-(FPV) Operator

RESUMO

Building on a construction of Weifeng Yang, we present a simplified counterexample to Rockafellar's sum conjecture on $c_0(\N_0\times\N)$. The central observation is geometric: the domain of a maximally monotone operator can have a nonconvex norm closure. In our example, this gives a short proof that the operator is not of type (FPV), which in turn implies the failure of the sum conjecture. We define an explicit operator using geometric series and provide a detailed proof of its maximal monotonicity. The example was developed with assistance from GPT-6 Astra. The purpose is to simplify and explain the construction, not to claim an independent counterexample mechanism.