A new architectural audit of Excalidraw utilized linear algebra to detect 'Logic Echoes' in the popular React application. The analysis, conducted using the react-state-basis tool in its v0.3.1 release, identified critical state management inefficiencies. The audit highlighted a perfect collinearity in the theme engine, where appTheme and editorTheme mirrored each other, creating redundant data vectors.

Additionally, telemetry detected 'Sequential Sync Leaks,' causing unnecessary double-reconciliation cycles in high-performance rendering. The tool achieved this via a 'Ghost' implementation using a Babel AST transformer and Vite Proxy, requiring zero code changes. Following the audit, a Pull Request was submitted to Excalidraw, refactoring the logic into a Pure Projection using useSyncExternalStore.

This resolved the vector redundancy, restoring linear independence and optimizing theme transitions. The methodology moves frontend auditing from simple syntax analysis to scientific signal processing, offering developers a forensic view into architectural debt. This advancement provides a Basis for solving complex state synchronization issues in large-scale React ecosystems.