The Galactic Halo as a Metric Depletion Zone: A Lattice Solution to the Dark Matter Problem

Title: The Galactic Halo as a Metric Depletion Zone: A Lattice Solution to the Dark Matter Problem Abstract: The observed flat rotation curves of spiral galaxies imply a gravitational potential significantly stronger than what visible baryonic mass can generate. Standard cosmology attributes this discrepancy to "Dark Matter," a hypothetical non-baryonic particle that has eluded detection for decades. We propose that this "missing mass" is not a particle, but a geometric artifact of a discrete, information-processing vacuum. Building on the UIT-81 Framework, we hypothesize that the vacuum density (rho_{vac}) is a dynamic variable: systems of high computational complexity (Active Nodes) consume lattice cycles, creating a local depletion in the vacuum structure. We derive a modified force law based on the hydrostatic pressure gradient of this depleted lattice, demonstrating that a logarithmic saturation profile naturally reproduces flat rotation curves (v= const) without fitting parameters. Furthermore, this framework resolves the Bullet Cluster anomaly by decoupling gravity from inertial mass. We demonstrate that the gravitational halo follows the computationally active galaxies ("Active Nodes") rather than the passive bulk gas, effectively eliminating the need for invisible particles. Key Contributions: Geometric Unification: Unifies Dark Energy (Vacuum Injection) and Dark Matter (Vacuum Depletion) under a single thermodynamic principle regarding node density. The Lattice Force Law: Derives the Unified Force Equation, F{total} = F{Newton} + F{attice}, where the lattice term acts as a hydrostatic pressure gradient. Flat Rotation Curves: Mathematically recovers the 1/r force law required for constant orbital velocities using a logarithmic vacuum depletion profile. Bullet Cluster Resolution: Reinterprets the separation of lensing and gas as a result of "Vacuum Viscosity" and the specific interaction of active computational nodes (stars/black holes) versus passive mass (gas). Keywords: Discrete Symplectic Lattice, Dark Matter, Modified Gravity, Galactic Rotation Curves, Bullet Cluster, Vacuum Depletion, UIT-81 Framework, Quantum Gravity,.Emergent Spacetime