Constraint, Stability, and Intrinsic Selection in Mode-Resolved Matter Systems

This work presents extended results from the Matter Resolution Test (MRC) program, focusing on Tests MRC-02, MRC-03, and MRC-04. These tests investigate the structural conditions under which discrete, persistent mode configurations emerge from an initially continuous mode basis under constraint.

Building on prior results demonstrating threshold-mediated reduction in effective degrees of freedom, the present study examines three mechanisms: constraint-driven spectral deformation, recursive stability selection, and intrinsic spectral gap-based selection. The analysis evaluates how constraint and stability processes influence mode orthogonality, eigenvalue structure, and persistence.

Results show that constraint alone produces continuous spectral deformation without intrinsic discrete mode selection. Recursive stability selection yields a reduced orthogonal basis that remains invariant under iteration, while intrinsic spectral gap selection collapses the system to a single dominant mode. These findings indicate that multi-mode persistence requires externally defined stabilization mechanisms rather than arising intrinsically from spectral structure.

The results support a structural interpretation in which persistent configurations correspond to constraint-stabilized subsets of modes that remain resolvable under bounded resolution conditions. Full methodological and implementation details are restricted pending further development.