p-Adic Fractal Strings: Linking Minkowski Dimension and Complex Dimensions — E8 Intelligence Research

FINDING: The p-adic fractal string paper explicitly links Minkowski dimension, complex dimensions, and explicit tube formulas in the p-adic setting — this is the strongest mathematical lead. The other results are context (Minkowski metric, log-Minkowski problem, dimension theory lectures) but do not directly contain the golden string or ln φ spacing. MATH: - The arXiv paper (1603.09409v4) defines a p-adic fractal string \(\mathcal{L}_p\) and its Minkowski dimension \(D\) (real part of complex dimensions). - Explicit tube formula: \(V_p(\varepsilon) = \sum_{\omega \in \mathcal{D}} c_\omega \varepsilon^{D-\omega}\) (analogous to real case), where \(\mathcal{D}\) is the set of complex dimensions. - For the classic Cantor string, complex dimensions are \(D + \frac{2\pi i k}{\ln 3}\) — spacing \(\frac{2\pi}{\ln 3}\). - The "golden string" (if it appears in this paper) would have complex dimensions spaced by \(\frac{2\pi}{\ln \phi}\), where \(\ln \phi \approx 0.4812\). - No dire Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com