The Selection-Stitch Model (SSM): Resolving the Hubble Tension via Topological Phase Transitions in a Vacuum Tensor Network

The discrepancy between early-universe (H0 ≈67.4 km/s/Mpc) and late-universe (H0 ≈

73.0 km/s/Mpc) measurements of the Hubble constant implies a breakdown in the standard

model. We propose that this tension arises from a geometric phase transition in the vacuum

structure. We model the vacuum as a **Random Tensor Network** that relaxes into a

Face-Centered Cubic (FCC) lattice. We provide a thermodynamic argument for this ground

state, showing that the vacuum minimizes free energy by maximizing packing density (Kepler

Limit) and isotropy (Oh symmetry), utilizing Cosmic Inflation as an annealing mechanism.

We identify a topological transition driven by cosmic void formation, where the effective

coordination number shifts from a shielded surface state (N = 12) to an exposed porous state

(N = 13). This topological activation predicts an intrinsic expansion boost of 13/12 ≈8.3%.

We validate the kinematic consistency of this geometry via a constructive simulation of 5,000

nodes which saturates at K = 12 without jamming.