Quantitative Topology of the Quranic Corpus

This draft/preliminary paper presents a computational framework for quantifying the latent structural topology of the Quranic text, treating it as a discrete time-series signal. By applying Higuchi Fractal Dimension (HFD) analysis to verse-length sequences, we identify a global fractal dimension of approximately D approx. 1.96. In the context of signal processing, this value situates the text in a state of high structural density, distinct from the theoretical limits of stochastic noise (D approx. 2.0) and the lower-complexity signatures often associated with standard narrative prose (D approx. 1.3). Furthermore, unsupervised dimensionality reduction reveals a "Unified Semantic Core," characterized by a dense nucleus of foundational themes surrounded by a diffuse periphery, optimally represented by nine distinct semantic fields (k = 9). Chronological mapping of these clusters demonstrates a quantifiable phase shift in structural entropy between the Meccan and Medinan periods (p < 0.05). Finally, we introduce a Semantic Coupling Matrix to measure narrative coherence, identifying a "Distributed Network Architecture." This architecture exhibits a resistance to context drift, where thematic affinity shows near-zero decay over distance (Slope approx. 0). These metrics provide a quantitative baseline for the text’s structural complexity. This study suggests that topological data analysis can serve as a robust methodology for characterizing high-entropy religious texts, offering a foundation for future comparative studies in computational philology and generative text analysis.