A geometric derivation of the fine structure constant from a quasi-crystalline vacuum model

This paper presents an exploratory theoretical framework in which the quantum vacuum is a two-mode elastic medium whose tension-wave interference pattern has quasi-crystalline geometry. Rather than postulating the golden ratio, the tension ratio τ² emerges as the first stable attractor of a primordial evaporation dynamics — derived from three constraints of distinct physical origin in three dimensions. From this mechanism, without adjustable free parameters, the framework derives: α (0. 001%), lepton masses (0. 036%), all six quark masses (<2. 2%), Ω_Λ, G (0. 016%), ηB (0. 01%). The Hubble tension is reproduced at +8. 2% vs observed +8. 3% without tuning. The lock-in timescale κτ ≈ 2. 00 is a pure geometric constant of the tiling (new, S87). Developed iteratively over 87 sessions using a human-AI collaboration methodology described in the paper. Every numerical result is independently verifiable; Python verification scripts are available at scalnet. fr/nexum. This is an exploratory hypothesis, not a completed theory. Open problems are explicitly documented. Full derivation companion: https: //doi. org/10. 5281/zenodo. 19711985