The Vortex Markov Chains of the Prime Lattice

This paper formalises two memoryless arithmetic processes—the Prime Gap State Machine and the Collatz odd backbone—as exact Markov chains on the six vortex residues {1,2,4,5,7,8} (mod 9) defined by the Prime Lattice Coherence Theorem (PLCT). The chains arise directly from the PLCT’s zone structure and its core theorems. For the Collatz process, the transition matrix is derived analytically from the Hard‑Wall Theorem and the geometric distribution of the 2‑adic valuation. Its unique stationary di