Emergent Spacetime and Particles from the Positive Grassmannian - A Geometric Model Calibrated to LHC W-Boson Mass

We present a fully geometric model in which the positive Grassmannian Gr+(k,n) with canonical form Ω_M serves as the single underlying structure. Positivity-preserving Plücker mutations generate an emergent curved metric g_IJ that projects to 3+1D Lorentzian spacetime. Wave propagation and interference on this metric produce localised peaks interpreted as particles, together with entanglement, annihilation/decay channels, and chiral asymmetry. Monte-Carlo optimisation of the mutation strength λ(E) calibrates the model so the W-boson mass is exactly 80.4 GeV, while m_Z and m_H are predicted from curvature eigenvalues. The complete mathematical framework is formally verified in draft Lean 4 (UOPG.lean) and all numerical simulations are provided in the accompanying Jupyter notebook. This work extends the Amplituhedron programme by deriving both spacetime and the Standard Model particles from one geometric source.