This research note reformulates the elementary number-theoretic structure of natural numbers using the operational concept of phase-interference energy. In this model, a prime number is treated as a stable fixed point that contains no non-trivial internal interference. The note defines interference energy as a measure of the non-trivial divisors of a natural number, clarifies the boundary condition excluding 0 and 1 through the domain condition 2 ≤ n, and sketches a Lean 4 formalization of the equivalence among Nat.Prime n, interferenceEnergy n = 0, and isStableFixedPoint n. It also introduces PG1224, a prime-candidate generation system based on residue-class filtering modulo 12 and 24. The filter is interpreted as cancellation of trivial interference caused by divisibility by 2 and 3. The note does not claim a new definition of primality or computational superiority over existing sieve methods; rather, it reconstructs the standard notion of primality in the vocabulary of energy minimization, stable fixed points, formal verification, and AIKernel-style governance models. The English manuscript is the canonical version. The Japanese manuscript is included as a companion translation.
Takuya Sogawa (Mon,) studied this question.