We present a fully geometric model in which the positive Grassmannian Gr+ (k, n) with canonical form ΩM serves as the single underlying structure. Positivity-preserving Plücker mutations generate an emergent curved metric gIJ 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 mZ and mH 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.
Chhaniyara Savan (2026) studied this question.