A comprehensive theoretical physics framework proposing that the universe optimizes through K3 surface geometry with Euler characteristic χ = 24. This framework derives fundamental constants from pure mathematics and makes precise, falsifiable predictions.
The Extremal Equivalence: Maximum efficiency equals minimum resistance equals stationary action
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The fundamental principle stating that nature optimizes for maximum efficiency through minimum resistance. This meta-law governs all physics from quantum to cosmological scales.
Rigorous mathematical proof showing why K3 surfaces with Euler characteristic 24 uniquely minimize the resistance functional under explicit assumptions A1-A6.
The electromagnetic coupling emerges from K3 geometry through the truncated octahedron efficiency factor Σ ≈ 2.367 and electromagnetic degrees of freedom N_EM = 20.
K3 breathing mode creates monochromatic gravitational wave detectable by LISA mission. Detection validates framework; null result falsifies it completely.
The number of fermion generations follows from K3 topology via the Atiyah-Singer index theorem, explaining why nature has exactly three generations.
Detailed exploration of K3 surfaces as 4-dimensional Ricci-flat manifolds, their moduli spaces, and connection to string theory compactifications.
Deep dives into specific aspects of the framework
This framework represents active theoretical research. All predictions are subject to experimental verification. The LISA gravitational wave test at 3.2000 ± 0.0003 mHz will provide decisive experimental validation or falsification.