Pentagon Physics is a theoretical physics programme with a single founding claim: all Standard Model parameters and fundamental constants are theorems of the self-referential equation σ = 1/(1+σ), which has one positive solution — φ = (1+√5)/2.
The equation is the only self-referential equation with no free parameters. Any other coefficient introduces a free parameter and breaks uniqueness. The equation specifies itself. Everything else follows by algebraic necessity.
The geometric object forced by the axiom is the 600-cell — a regular polytope in four dimensions with 120 vertices and the binary icosahedral group 2I as its symmetry group. Its adjacency matrix has nine distinct eigenvalues, all in ℚ(√5). A discriminant condition selects exactly two propagating modes (gravity and electromagnetism) and freezes seven as Standard Model parameters.
Each result below has zero free parameters. Every coefficient is forced by the spectral geometry of the 600-cell or the algebraic structure of ℚ(√5). None are fitted to observation.
All papers are open-access preprints on Zenodo, each carrying explicit kill conditions and zero free parameters. Click any DOI to read.
Independent Researcher, Edinburgh. Enquiries regarding Pentagon Physics, collaboration, or the technical papers are welcome.