What question did this study set out to answer?

This research aims to develop a geometric framework that explains particle masses using positive geometry.

April 13, 2026Open Access

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

Key Points

This research aims to develop a geometric framework that explains particle masses using positive geometry.
Introduced the Unified Ontology of Positive Geometry (UOPG) framework.
Utilized the Positive Grassmannian Gr+(2,4,C) for modeling particles.
Employed positivity-preserving Plücker mutations and quaternionic SU(2) embedding.
Applied Bayesian optimisation for numerical analysis and results verification.
Achieved exact W-boson mass of 80.4 GeV and vacuum expectation value of approximately 243 GeV.
The model reproduces realistic values for Z and Higgs bosons geometrically.
Demonstrated 1% accuracy relative to the observed electroweak scale.

Abstract

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 OmegaM = sumI log|det (CI) | 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 gIJ whose 4D Lorentz projection yields the exact experimental W-boson mass mW = 80. 4 GeV and a vacuum expectation value V approximately 243 GeV (within 1% of the observed electroweak scale). The model reproduces realistic mZ and mH 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.

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper