Published December 6, 2025 | Version v1

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Description

We propose a comprehensive resolution to the Vacuum Catastrophe and the Hubble Tension

by modeling the quantum vacuum not as a continuous manifold, but as a Supersolid Active Ne-

matic Lattice governed by strict hydrodynamic and topological stability limits. The core of the

theory is the identification of a dimensionless Geometric Tension (∆Φ ≈ 0.258%) arising from

an irreducible conflict between the Michell Hydrodynamic Limit (Φcrit = 1/7) and the topolog-

ical matter packing requirement (Φvoid). This tension is the source term for Dark Energy. We

rigorously derive the Maximum Incompressibility Anchor (ΞMAX ≈ 8.3275) by showing its in-

verse relationship to the cube root of the Geometric Tension (ΞMAX ∝ (∆Φ)−1/3). This anchor

dictates the maximum collapse ratio of the lattice and provides a definitive, falsifiable predic-

tion: the existence of Gravitational Wave Echoes (S-waves) propagating at vs ≈ 36, 000 km/s,

searchable in current astrophysical data.

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