Deriving Flat Rotation Curves and the Hubble Tension from a Phyllotactic Vacuum Lattice

Paper XI: The Elastic Halo - Deriving Flat Rotation Curves and the Hubble Tension from a Phyllotactic Vacuum Lattice Author: Bijan Pedram Description: Standard cosmological models currently treat Dark Energy and Dark Matter as unrelated phenomena: one acting as a repulsive field driving cosmic acceleration, and the other as an invisible massive particle required for galactic stability. In the UIT-81 Framework, we unify these distinct observations as conjugate phases of a single geometric substrate. By applying the Golden Equivalence Principle—which dictates the conservation of geometric stress—we demonstrate that the vacuum undergoes a thermodynamic phase transition from an Entropic Liquid (Expansion/Dark Energy) to a Stiffened Solid (Contraction/Dark Matter) in the presence of baryonic mass. We analytically derive the "Dark Matter Halo" not as a cloud of hidden particles, but as a region of High Lattice Stiffness required to balance the local reduction in entropy. This geometric framework naturally resolves three major crises in modern physics: Galactic Rotation Curves: It reproduces the flat velocity profiles observed in spiral galaxies (Tully-Fisher Relation) via a stiffness field that decays linearly with distance. The Hubble Tension: It explains the discrepancy between local and global expansion rates as a geometric shear effect caused by the Local Void. The Neutron Lifetime Anomaly: It identifies the 1% discrepancy in neutron decay experiments as a signature of Dark Matter production, predicting a specific topological decay channel. This paper offers a falsifiable alternative to the particle dark matter hypothesis, unifying the dark sector through the geometry of the vacuum itself.