A Geometric Unification of Particle Physics, Gravity, and Cosmology from Three Planes

A purely geometric model is presented in which all fundamental particles, forces, masses, hierarchies, and cosmological phenomena emerge from three mutually perpendicular planes intersecting at an origin in 3+1 Minkowski spacetime. The planes divide space into eight octants defined by sign combinations. Positive or mixed-sign octants are observable; negative octants are permanently hidden. A central knot (intersection region) provides mass and symmetry breaking. Rotational twists differentiate generations, and a single force formula unifies all interactions. The model derives multiple constants (fine-structure constant exactly, cosmological constant exactly, gravitational constant exactly, Planck scale exactly, Planck time exactly, speed of light exactly), resolves major puzzles (hierarchy problem, dark sectors, point-like leptons, QCD mass origin, quantum measurement collapse, virtual particles, chiral asymmetry, flavour mixing unification, wave-particle duality, quantum tunnelling, alpha decay, thermodynamics, Compton scattering and Klein-Nishina formula, quantum entanglement, Feynman diagrams as emergent shadows, Galois groups as combinatorial invariants), and reproduces relativistic wave equations from quantized knot and plane operators — without extra dimensions, supersymmetry, or a fundamental Lagrangian. Version 3 resolves an issue with the running of the fine structure constant and includes new model predictions.