No-Go Theorem Requires Modification: An Additional Constant Term $C$ and Its Laurent Series Structure in f(R) gravity

No-go theorems often assert that certain solutions or configurations in gravitational and field-theoretic models cannot exist under a prescribed set of assumptions~\cite{NoGoClassic}. However, recent analyses using a \emph{modified} Robson-Villari-Biancalana (RVB) approach~\cite{RobWilcz1,BanKul1,BanKul2} indicate the presence of an additional integration constant, $C$, that may appear in topological or horizon-based integrals (notably through expansions in Laurent series). This subtle term invalidates the usual dismissal of boundary or horizon contributions and demands a revised understanding of no-go arguments. In this work, we demonstrate how $C$ can be revealed through careful Laurent expansions about the horizon and discuss why ignoring this term undermines the classical no-go statement. We illustrate these ideas with examples in $f(R)$ gravity~\cite{fR-Review1,fR-Review2,fR-Review3}, emphasizing how familiar no-go theorems must be updated to accommodate the extra freedom that $C$ provides.