DNA’s canonical double helix remains the dominant genetic architecture in known biology, yet non-canonical nucleic acid structures—such as G-quadruplexes and i-motifs—demonstrate that nucleic acids can access higher-order multistranded conformations in vitro and in vivo. In this paper, I introduce Q-DNA, defined not as a local quadruplex motif but as a hereditary polymer whose canonical, genome-scale ground state is tetra-stranded. I propose a formal axiomatic framework distinguishing Q-DNA from motif-level quadruplexes (e.g., G-quadruplexes) and specify necessary conditions for canonicality, multi-body recognition rules, topologicaladmissibility, and heredity under bounded copying error. I then outline falsifiable predictions and an experimental roadmap leveraging synthetic genetics and XNA technologies, which have already established that alternative genetic polymers can store and propagate information with engineered enzymes. Keywords: tetra-stranded genome, canonical hereditary state, quadruplex motifs, XNA, synthetic genetics, information theory