This collection assembles six companion papers that develop a single premise to its consequences: promote time to a complex variable tC = t + iτ and compactify its imaginary part onto a circle S¹, so that spacetime acquires one extra, compact dimension—the τ fibre—governed by the holomorphic metric: dZ² = c² dtC² − dx² − dy² − dz² and a single five-dimensional null-geodesic law. From this one structure, the six Parts recover, in turn, established physics: The Six-Part Derivation Path The Manifold Itself: Recovers Special Relativity and the mass-energy equivalence E = mc². The Phase of the Fibre: Recovers Electromagnetism, the local U (1) gauge principle, and the quantum Born rule. The Structure of Gauge Groups: Recovers the colour SU (3) and weak SU (2) gauge groups as two further distinct windings of the same fibre, so that the Standard Model gauge group SU (3) × SU (2) × U (1) is read off unified as three winding ratios of a single circle. The Mass Spectrum: Recovers the charged-lepton Koide relation Q = 2/3 along with a sharp Dirac–Majorana watershed at azimuth δ = π/12. The Gravitational Sector: Recovers General Relativity, tracing the Einstein coupling’s 8π factor directly to 2 × Ω₂ (twice the area of the unit 2-sphere). Underlying Unification Principles A common connection schema (connection = winding ⊗ anti-winding = adjoint ⊕ singlet) and a single node-stiffness action—the Dirichlet energy forced by the holomorphy of the metric—underlie the gauge, gravitational, Higgs, and matter sectors alike. The Truth Boundary and Falsifiable Prediction Throughout, the framework reproduces rather than modifies established physics: it fixes dimensionless ratios, group structures, and physical mechanisms, but explicitly delineates the dimensionful absolute scales (α, G, ΛQCD, and the electroweak vev v) as inherently non-derivable. Its one sharp, falsifiable signature—an anti-correlated cosmic drift of α and G, should the fundamental constants evolve with time—lies just beyond present experimental limits, within the reach of next-generation optical-clock searches.
Harvey Sang (Mon,) studied this question.