What question did this study set out to answer?

The research aims to develop a geometric model that describes the emergence of spacetime and particles from the positive Grassmannian.

March 31, 2026Open Access

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

Puntos clave

The research aims to develop a geometric model that describes the emergence of spacetime and particles from the positive Grassmannian.
Implemented a geometric model based on positive Grassmannian Gr+(k,n) with a canonical form.
Used positivity-preserving Plücker mutations to derive an emergent curved metric for spacetime.
Applied Monte-Carlo optimization to calibrate mutation strength for accurate particle mass predictions.
Successfully calibrated the model to yield a W-boson mass of 80.4 GeV.
Predicted masses for the Z-boson and Higgs boson based on curvature eigenvalues.
Validated the mathematical framework and provided comprehensive numerical simulations.

Resumen

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.

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