We exhibit a finite, explicit obstruction to parameter-stable extension in strongly regular graphs. Using the Paley graph on 13 vertices as an explicit witness, we show that while a strongly regular graph with parameters (13, 6, 2, 3) exists, no strongly regular graph with parameters (14, 6, 2, 3) can exist, as the standard feasibility identity fails. The obstruction is purely arithmetic, finite, and fully checkable, demonstrating that parameter-stable extension heuristics fail even in highly regular algebraic settings.
Bailey et al. (Sat,) studied this question.