We investigate the microscopic origin of the effective Brane Tension previously identified as a mechanism for galactic confinement Frisina, Zenodo 2026, Paper XI. We propose that the phenomenology attributed to "Dark Matter" is not a particle effect, but an emergent thermodynamic force arising from the Entanglement Entropy between our Brane and a parallel Shadow Brane. Using the Ryu-Takayanagi formula in an AdS5 Bulk geometry, we calculate the area of the minimal surface anchoring a galactic region to the bulk. We demonstrate that the variation of this entanglement entropy under spatial deformation gives rise to an Entropic Force. Crucially, we prove mathematically that for a dual-brane geometry, the minimal surface topology transitions from a dome (Newtonian regime) to a flux tube (Confinement regime) at large scales, creating a potential that scales linearly with distance (V proportional to r). This reproduces exactly the Linear Tension term postulated in modified virial dynamics studies. This confirms the ER=EPR conjecture on a cosmological scale: the "invisible elastic tether" holding galaxies together is the quantum entanglement weaving the spacetime fabric between the two branes. Dark Matter is reinterpreted as the energy cost of stretching the information links of the vacuum.
Giovanni Frisina (Thu,) studied this question.