Evaluations of LLM personas via psychometric questionnaires typically rely on aggregate scores, discarding within-instance correlation structure. We test whether this geometric structure is intrinsic or frame-dependent. Constructing within-instance correlation matrices from IPIP-50 responses, we analyze geometry on SPD manifolds under manipulated question orderings in GPT-4o simulating American and Chinese-American personas. We find that persona expression comprises two dissociable components: aggregated features (Big Five scores) degrade under randomization (21% drop) but are frame-robust; geometric features (SPD manifold) collapse under frame misalignment (42% drop) but recover substantially (to 84%) under shared frames, surpassing aggregated features (76%). This collapse-recovery pattern reveals that persona geometry is not intrinsic but a frame-dependent coordination pattern encoding information invisible to aggregation. Our findings establish a dual-nature framework for LLM personas, frame-dependent geometry versus frame-robust aggregates, necessitating frame-aware evaluation and challenging static trait conceptions.