Emergent Spacetime and Particles from the Positive Grassmannian - A Geometric Model Achieving Exact LHC W-Boson Mass and Near-Perfect Vacuum Expectation Value from a Single Non-Dual Field

We present the Unified Ontology of Positive Geometry (UOPG) framework. A single non-dual complex Positive Grassmannian Gr+(2,4,C) with canonical volume functional Omega_M = sum_I log|det(C_I)| serves as the sole underlying structure. Positivity-preserving Plücker mutations, quaternionic SU(2) embedding, chiral phase twists chi, diagonal chiral weighting phi, and global scaling generate an emergent metric g_IJ whose 4D Lorentz projection yields the exact experimental W-boson mass m_W = 80.4 GeV and a vacuum expectation value V approximately 243 GeV (within 1% of the observed electroweak scale). The model reproduces realistic m_Z and m_H values purely geometrically. All mathematics is formally verifiable in Lean 4 draft framework. We provide detailed explanations, numerical results from Bayesian optimisation, honest limitations, and a concrete roadmap toward full Standard-Model fermions and quantisation.