Dark Matter as the Torsional Strain of a Discrete Chiral Vacuum: Deriving Galactic Halos, the Tully-Fisher Relation, and the a0 Acceleration Scale from Cosserat Elasticity

Standard cosmology requires the existence of invisible, collisionless Cold Dark Matter (CDM) to account for flat galactic rotation curves [1] and the gravitational lensing of galaxy clus- ters [2]. Despite decades of experimental searches, no such particle has been found. In the Selection-Stitch Model (SSM), the vacuum emerges as a Face-Centered Cubic (FCC, K = 12) tensor network with a fundamental lattice spacing on the order of the Planck scale (L∼lP) [5]. This letter proposes that Dark Matter is the macroscopic torsional strain of this discrete chiral vacuum. By modeling the vacuum limit as a Chiral Cosserat continuum, we show that baryonic matter—modeled as 1D topological braids (screw dislocations)—physically twists the tensor network. Computational simulations of the discrete K = 12 lattice explicitly confirm that these defects generate an effective dark mass halo Mhalo ∝r, geometrically guaranteeing flat rotation curves. By applying standard random-walk statistics to the topo- logical charges of the macroscopic baryonic gas, we derive the √Mb halo scaling necessary to recover the baryonic Tully-Fisher relation (v4 ∝Mb) [4]. Furthermore, we identify the struc- tural origin of the MOND acceleration scale (a0 = cH0/2π) [3] as the geometric boundary condition of this torsional field interacting with the cosmic horizon. Finally, we demonstrate that during galactic collisions (e.g., the Bullet Cluster), these torsional vacuum waves cross without electromagnetic friction, effectively reproducing the dynamics of collisionless dark matter.