The mechanical properties of a hereditary polymer constrain its capacity for replication, transcription, and segregation. Duplex DNA occupies a well-characterized elastic regime described by the worm-like chain (WLC) and its twistable extensions. Here, I develop a unified theoretical and experimental framework for the mechanics of Q-DNA, a canonical tetra-stranded hereditary polymer, and show that such a system necessarily defines a distinct elastic regime. I introduce a generalized worm-like chain model (Q-WLC) incorporating multi-strand bending, torsion, and inter-strand coupling modes, derive experimentally observable response functions, and propose concrete single-molecule assays capable of validating or falsifying the model. This work establishes mechanics as a decisive feasibility axis for tetra-stranded heredity. Keywords: Q-DNA, tetra-stranded genome, worm-like chain, twistable WLC, single-molecule force spectroscopy, torsional stiffness