Modular Phase Alignment in Lunar Cycles over Millennial Timescales

This repository contains the complete scientific package for the study of modular phase alignment in lunar cycles over millennial timescales. The work introduces a modular phase framework for representing temporal evolution across multiple periodic systems, with a focus on the synodic and anomalistic lunar cycles. Time is mapped into normalized phase space using modulo arithmetic, enabling direct comparison between cycles with different periods. The analysis spans 2000 years (1000 BCE – 1000 CE) and investigates the statistical structure of phase alignment events under varying tolerance thresholds. **Key Features:** - Reproducible scientific workflow (Python-based) - Fully documented dataset and figure generation pipeline - Three core figures: mean-period phase functions, cumulative phase deviation, alignment distribution - Interactive visualization for parameter exploration - Multilingual documentation (English / Arabic) **Scientific Highlights:** - ~5,000 alignment events detected at ε = 0.05 - Mean inter-event interval: ~146 days (SD ~329 days) - High-precision alignments (ε = 0.02): ~550 events - Weekly cycle included strictly as a comparative reference (<8% contribution) **Methodology:** All cycles are represented as normalized phase functions: φ(t) = (t mod T) / T. Alignment events are defined as instances where phase differences fall below a specified tolerance ε. No causal interpretation is claimed; the study focuses on statistical structure, periodic interactions, and modular temporal representation. **Reproducibility:** All results are fully reproducible using the provided dataset and Python scripts. **License:** CC BY 4.0 **Author:** Hicham Chigar, Independent Researcher This work is also referred to as "Lunar Zero Point Light (Sifr al-Asfar)" as a conceptual framing of modular phase normalization. A previous version of this work is available at: https://doi.org/10.5281/zenodo.18945758