Theoretical framework derives fundamental physics and particle spectra from complex spacetime geometry, suggesting profound insights into the universe.
The sign change of coordinates at the Schwarzschild horizon is usually treated as a coordinate artefact. This paper treats it as a physical process and follows the consequences. The resulting spacetime is (3+1)C: three complex spatial coordinates zk = xk +iwk (expanded real parts, com pact imaginary parts on S^3) and one complex time τ = t+iσ (macroscopic real part, compact Euclidean Hawking circle). From the Kähler structure of this spacetime and a single geometric parameter — the Berger deformation ε = 1.01027, fixed by the electron mass — all of fundamental physics follows without additional postulates. Part II derives, before any particle content is specified: the Heisenberg uncertainty relation (from the Kähler form ω = dx ∧ dw), special relativity (as holomorphic symmetry of τ = t + iσ), the dispersion relation E2 =p^2c^2 + m_0^2 c^4 (as the Pythagorean theorem of the ¯∂-norm), inertia and E = mc^2 (as Cauchy–Riemann mismatch resistance), confinement energy (as the temporal dual of the same Cauchy–Riemann mismatch), the equivalence principle mi = mg (as a det/tr identity), Einstein’s field equations (from Lovelock uniqueness), the fine-structure constant (from the Sasaki contact structure), and Bose–Einstein condensation and superconductivity (from compact-state coherence under the holomorphic Lorentz boost).Part III derives the complete particle spectrum: the gauge group SU(3) × SU(2) × U(1), the charge, colour, and chirality structure of the Standard Model, three fermion generations (topological; fourth excluded), matter/antimatter distinction, all fermion and boson masses, the electroweak mixing parameters, the CKM matrix (all 9 elements within 4,5%, including the CP-violating phase), the proton mass, and a complete dark-matter sector (mass spectrum, abundance, vanishing direct-detection cross section — all from the horizon flip, no new fields). In total, ∼43 quantitative observables are reproduced with a maximum deviation of 6% for geometric quantities and 1.3% for masses; downstream quantities (lifetimes, couplings, nuclear binding) agree to ≤3% after propagating framework-internal corrections — a self-consistency test that numerology cannot pass. Three independent determinations of ε (from me, mH, and MP) agree to 130 ppm. The framework makes falsifiable predictions: a mass-ratio-independent remnant spin a∗(q) ≈ 0.69 for binary black-hole mergers (testable with LIGO O4/O5), r = 0 exactly (testable with CMB-S4), and a neutrino luminosity gap in core-collapse supernovae (retro-consistent with SN1987A to 3%). The Kähler structure is not an addition to the Standard Model — it is its geometric origin. The Standard Model is the R3,1-projection of a (3+1)C geometry.
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Guido Widman (2026) studied this question.
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