Primality as a Structural Invariant in Balanced Numeral Systems

Primality as a Structural Invariant in Balanced Numeral Systems Abstract. Primality of odd integers is decidable via deterministic, representation-theoretic propertiesin balanced numeral systems—without arithmetic computation, iteration, or probabilistic checks. Themethod reveals length-dependent structural invariants that deterministically separate primes fromcomposites, in time constant relative to digit length. Empirically complete across all odd integers andscalable to arbitrary magnitude, the separation is invariant to the choice of the odd radix—resolutionremains constant, only representation length changes. This approach is inherently suitable for hardware-native validation, post-quantum cryptography, and billion-scale metadata integrity. The work establishesa new paradigm: primality is not a computational problem, but a read-only property of numeral structure.