Minimum Viable Primitives (MVP): Why Four Recurs Across Substrates

We propose that many persistent natural and artificial systems exhibit a characteristic Minimum Viable Primitive (MVP) structure, in which representational or regulatory architectures stabilize around four orthogonal primitives. This pattern appears across substrates including geometry, biochemistry, neural regulation, information encoding, and mathematical formalism. We derive MVP as the balancing point between two competing forces: parsimony pressure, which penalizes representational proliferation, and Hypernetic-Law-of-Experience-mediated varietal contraction, which pressures against overly-reduced primitive sets via fragility and collapse. We argue that systems with fewer than four primitives tend to undergo CURSE-style singularity collapse characterized by runaway dominance of a single attraction logic, while systems with many primitives experience dispersion into incoherence. The quaternary configuration, in contrast, appears to provide the smallest rigid basis enabling persistence, error tolerance, and transformation-invariance. This account explains the recurrent emergence of fourfold structures (e.g., DNA bases, carbon valence, quaternion rotation algebra, cardinal neurochemical modulators) as a product of structural optimization more rigorously than coincidence or numerological bias. The MVP principle offers a predictive heuristic for the design and evaluation of persistent system architectures, including alignment-relevant AI reward structures, value-representation systems, and regulatory frameworks.