Recursive Stabilization of Persistent Modes Under Constraint

This work presents MRC-05, an extension of the Matter Resolution Test (MRC) program, addressing the mechanism responsible for persistent multi-mode structure under constraint. Previous tests established that constraint reshapes spectral accessibility without producing intrinsic discrete selection, that recursive filtering yields reduced orthogonal mode sets, and that intrinsic spectral structure alone collapses to a single dominant mode.

The present study introduces recursive stabilization as the necessary condition for sustained multi-mode persistence. Stabilization is defined as the invariance of a mode basis under repeated projection, filtering, and reconstruction within a constrained system. The analysis evaluates convergence behavior, orthogonality preservation, and eigenvalue stability under iterative re-resolution.

Results demonstrate that persistence is not a consequence of spectral structure alone, but requires closure under recursive stabilization. Mode sets that satisfy this condition converge to stable orthogonal configurations, while non-stabilized configurations exhibit orthogonality degradation and spectral decay. The findings establish stabilization as the mechanism linking constraint-defined accessibility to persistent structure.

These results establish stabilization as the critical mechanism linking constraint-defined accessibility to persistent structure, completing the core mechanism of the Matter Resolution framework. Further tests will examine resolution limits, observability conditions, and stability boundaries of the resulting configurations.