Fabric Theory: A Universal Wave Framework for Fundamental Physics

A framework is presented in which all fundamental physics arises from the Dirac equation on a 5D spacetime with internal space CP² (the complex projective plane). The Schwarzschild metric factor f = 1 − 2w, under the coordinate map w = ½sin²ξ, becomes f = cos²ξ — the metric coefficient of the Fubini-Study metric on CP². The Fubini-Study geometry of CP², combined with the squared Dirac operator and a self-consistent eigenvalue condition, produces the confining potential V (w) = (3/8) 1/w + 1/ (1−2w) with no free parameters. A stationarity condition (modulus stabilization) fixes the last degree of freedom. From this single potential, 28 quantities are derived matching known measurements at 0. 1–16% accuracy with zero free dimensionless parameters and one dimensionful input: the fine structure constant (0. 16%), the Weinberg angle (0. 09%), all six generation mass ratios (0. 2–2. 5%), the CKM and PMNS mixing parameters (0. 1–16%), the neutrino mass-squared ratio (1%), the QCD string tension (2. 6%), the electroweak boson masses (0. 6–4. 2%), the cosmological constant (factor 1. 5), and the baryon asymmetry (~1). Structural derivations include the origin of all four forces, spin-1/2, charge quantization, three generations, chirality, CP violation, and anomaly cancellation. Six novel predictions are presented with specific falsification criteria: the Higgs self-coupling λ = 1/8 (testable at HL-LHC), phase supplementarity δCKM + δPMNS = π (testable at DUNE/Hyper-K), a neutrino mass m_ν = 0. 045 eV (testable by DESI/Euclid), dark matter undetectable by direct detection, a scalar resonance at 6, 835 TeV, and mode-dependent coupling in muonic atoms.