The ACORN Cosmology Suite: A Unified Geometric Solution to Dark Matter, Dark Energy, Black Holes, and the Big Bang

The ACORN Cosmology Pentapoly (2025) presents a unified geometric framework in which all physical phenomena arise from the finite curvature structure of a smooth, compact 5D manifold. The observable 4D universe is interpreted as a projection (or slicing) of this higher-dimensional geometry, and all particles, fields, forces, constants, and cosmological phenomena emerge as different sectors of its curvature spectrum. Across five papers, the Pentapoly develops: • Paper I — A finite-curvature reformulation of electromagnetism, inertia, and rest mass through the mass-partition relation and the 5D projection metric. • Paper II — A 5D extension of General Relativity, yielding the unified Einstein–Maxwell system as a 4D projection of the higher-dimensional geometry. • Paper III — Curvature quantisation across the proton–Planck boundary, generating the discrete curvature modes that correspond to the spectrum of elementary particles. • Paper IV — ACORN (A Curvature–Origin Reality Network), which identifies electromagnetic inertia, charge, and quantum-like behaviour as 5D curvature oscillations and projection effects. • Paper V — The cosmological completion of the framework: the Big Bang is shown to be a projection singularity (a caustic) rather than a physical beginning. Cosmic expansion arises from the motion of the 4D hypersurface through 5D rather than from metric creation, dark energy fluids, or inflation. Dark matter emerges from high closed curvature modes, and dark energy from the transverse curvature gradient of the manifold. The combined result is a singularity-free, finite, falsifiable cosmological model that replaces the standard Big Bang paradigm. All infinities and singularities are removed; all dark-sector behaviours arise from geometry; and early-universe structure occurs via curvature-mode phase rather than quantum fields or inflation. The ACORN Cosmology Pentapoly offers a unified geometric interpretation of all observed physics, grounded in five logically connected, standalone research papers, and proposes a testable alternative to ΛCDM cosmology.