Prime-Like Survivability, Resonant Selection, and Structural Skipping A Unified Interpretation of Physical and Numerical Persistence within Existence-Quantized Geometric Theor

Prime numbers exhibit irregular gaps and apparent randomness despite being defined by a simple minimal condition. Similarly, physical reality displays selective survivability, in which only a sparse subset of theoretically admissible structures persist across atomic, nuclear, and cosmological scales.

This paper proposes a unified structural interpretation of these phenomena within the framework of Existence-Quantized Geometric Theory (EQGT). Primeness is redefined not as a guarantee of stability, but as a minimal non-interference condition that reduces internal resonance pathways. Survivability, however, is shown to depend on an additional constraint: compatibility with internal, boundary, and background resonance modes.

The concept of resonant selection is introduced as a universal elimination mechanism that operates independently of compositional simplicity. Configurations—numerical or physical—that resonate with structural or background modes are selectively removed, producing observable gaps and structural skipping despite theoretical admissibility.

By applying the same non-resonance criterion across number theory, nuclear stability, and cosmology, the analysis demonstrates that prime-like persistence and irregular gaps arise from a shared survivability filter rather than from domain-specific rules. This work establishes a structural bridge between mathematics and physics without reducing one domain to the other.