This paper introduces the Prime Move Operator, a minimal generative mechanism that produces irreversible distinction from undifferentiated unity. The operator consists of a five-stage cycle — Split, Tension, Failed Merge, Scar, Decay — that generates persistent residues which accumulate monotonically and drive continued evolution without external input. From four minimal axioms concerning the nature of nothing, unity, distinction, and residue, the paper derives four key properties: perfect erasure is logically impossible, the process cannot terminate internally once initiated, the structure is scale-invariant across hierarchical levels, and scar accumulation follows the Fibonacci recurrence converging asymptotically to the golden ratio φ ≈ 1.618. The five-stage structure is proven minimal. The framework extends Whiteheadian process ontology and resonates with Garfinkel’s ethnomethodology. Full formal proofs are provided in the companion mathematical paper (Paper 2).