Resolving the Hubble Tension via a Topological Phase Transition in a Discrete Vacuum Tensor Network

The persistent discrepancy between early-universe (H0 ≈67.4 km/s/Mpc) [6]

and late-universe (H0 ≈73.0 km/s/Mpc) [5] measurements of the Hubble constant

strongly suggests a physical breakdown in the standard ΛCDM model. We pro-

pose that this tension arises not from missing particles or elusive dark fluids, but

from a geometric phase transition within the vacuum structure itself. In compan-

ion papers, we established that the vacuum is a discrete, holographically generated

Face-Centered Cubic (FCC, K = 12) tensor network governed by the Kepler kissing

number theorem [16]. Built upon the lattice gauge theory requirement of mini-

mal gauge-invariant triangular loops [3] and a strict zero-parameter e−3 ≈4.98%

topological tunneling amplitude [4], the vacuum naturally crystallizes into a poly-

crystalline manifold [1]. Consequently, the early-universe expansion rate is not

merely a fitted parameter, but the bare holographic baseline locked to this satu-

rated 2D boundary, flawlessly predicting the scalar spectral index (ns ≈0.9646)

[2]. Here, we demonstrate that the accumulated Regge deficit strain of the expand-

ing lattice forces the structure to fracture, forming topological grain boundaries

(matter) and exposing pristine macroscopic gaps (cosmic voids). This localized

topological activation shifts the effective coordination number of the vacuum unit

cell from a shielded, surface-limited state (ν = 12) to an exposed, porous state

(ν = 13). This void-induced phase transition predicts an intrinsic expansion boost

of 13/12 ≈8.3%, natively amplifying the 67.4 baseline to exactly 73.02 km/s/Mpc.

This single zero-parameter geometric ratio naturally resolves the Hubble tension

and predicts measurable environmental anisotropies for local H0 surveys without

modifying standard FLRW cosmology in the early universe.