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Foundations

The Bridges of Pentagon Physics

DOI
10.5281/zenodo.18923674
Read full paper on Zenodo →

Five fundamental constants — α, G, Λ, H₀, and the proton mass — are not independent. They are nodes in a single self-referential partition. This paper derives the bridge identities connecting them: R_Λ − R_G = 1/φ, R_G = 1/(φ√5), R_Λ = 2R_H, where R denotes the logarithmic ratio to the Planck scale. All ratios use only φ and √5. The class number of ℚ(√5) is 1 (unique factorisation), which is why the bridge identities are exact. The five constants are not coincidentally related — they are algebraically required to satisfy these bridge equations by the structure of ℚ(√5).

\[ R_\Lambda - R_G = \frac{1}{\varphi}, \quad R_G = \frac{1}{\varphi\sqrt{5}} \]
Key Result
Five fundamental constants as nodes in a single self-referential partition
Precision
Bridge identities exact in ℚ(√5)