Protein folding and the 3n+1 (Collatz conjecture) represent two highly challenging problems sharing a common feature: extreme initial chaos that ultimately converges to an inevitable deterministic outcome. In biological systems, an amino acid chain undergoes highly chaotic movements, yet inevitably collapses into a unique, global minimum energy state—a perfect topological fold. Similarly, the Collatz sequence inevitably falls into the 4-2-1 loop, acting as a topological attractor. This paper explores the deep mathematical isomorphism between these two phenomena. By analyzing mathematician Terence Tao’s cross-dimensional methodology (mapping a discrete problem to continuous partial differential equations) used to crack the 3n+1 problem in 2019, we establish the philosophical foundation of H3QM's "Discrete Duality Theory." H3QM performs the reverse mapping: abandoning the extremely computationally expensive continuous calculus operators of traditional molecular dynamics, it instead maps physical space into a discrete Markov Decision Process (MDP) consisting of topological networks (gears and chains). Through rigorous mathematical comparisons and topological diagrams, we demonstrate that H3QM shifts the computational paradigm from "calculating precise continuous trajectories" to "calculating discrete probabilistic trends," thereby bypassing Levinthal's paradox and enabling generative geometric design even on ordinary computing hardware. (Note: This publication includes identical English en-US, Traditional Chinese zh-TW, and Simplified Chinese zh-CN manuscript versions to facilitate global academic exchange.)
Cosmo Chou (Tue,) studied this question.