We introduce \textbf{Prism}, a framework for structural symmetry diagnosis in complex networks. Given a graph Laplacian
L and a duality operator
P (a symmetric involution), Prism computes the \emph{duality defect}
δ(L,P)=∥LP−PL∥F/∥L∥F -- a scalar measuring how far the network deviates from structural self-consistency. When
P encodes the network's true symmetry,
δ starts near zero and rises monotonically as structure degrades; an arbitrary
P gives noise. We prove that the optimal
L′ satisfying
[L′,P]=0 is given by a closed-form block-diagonal projection, and provide an unsupervised alternating optimization that learns
P from the graph's own Fiedler vector. Experiments on synthetic networks show the true-
P defect is
3.38× more sensitive to structural degradation than an index-reversal baseline and more sensitive than modularity. On Zachary's Karate Club with edge noise, Prism achieves
94.5% community detection accuracy at
5% noise versus
76.6% for the raw Laplacian baseline. Applied to live S&P~500 data (2026-05-17), Prism detects rising structural stress (defect
0.43→0.73 over 90 days) while surface correlations remain low -- a signal invisible to correlation-based methods. In a historical backtest spanning five major stress events (2011--2020), the duality defect exhibits a consistent pattern: it reaches elevated levels \emph{before} the correlation spike that accompanies each crisis, and sustains high readings during periods of structural fragility that conventional metrics classify as calm. The duality defect is a first-principles structural admissibility condition, requiring no training data and computable in milliseconds.