Reproducibility code for ``A dynamical systems viewpoint on Hofstadter's (Q)-sequence: ratios, long-memory signatures, and a localization-inspired spectral analysis

\description{This repository provides the complete reproducibility package for the accompanying manuscript on Hofstadter's nested recursion (Q(n)). It contains C and Python implementations that (i) compute the Hofstadter (Q)-sequence up to (N) and cache it in a binary file, (ii) generate dynamical diagnostics of the ratio process (r_n = Q(n)/n) including time-series sampling, return maps, box-counting estimates, surrogate comparisons, and DFA/Hurst analysis, (iii) scan the one-parameter deformed family (Q_\alpha) and produce validity and bifurcation-style summary plots, and (iv) construct a deterministic ``(Q)-potential'' for a 1D tight-binding Hamiltonian and reproduce the localization/spectral diagnostics used in the paper (eigenvalue curves, IPR scatter and finite-size scaling, robustness sweeps in (n_0) and (M_{\rm ref}), and transfer-matrix Lyapunov exponent scans versus energy and disorder strength (\lambda)). A Google Colab notebook is included for one-click execution. The notebook installs dependencies, compiles the C helpers, reproduces all figures into `figs/`, generates CSV outputs, writes SHA256 checksums, and packages the results for archiving. Default parameters match the ``Option-1'' settings used in the manuscript; a small ``quick test'' configuration is provided for fast verification. \textbf{Contents} \begin{itemize} \item \texttt{HofstadterQ\_Reproducibility\_Colab.ipynb}: end-to-end Colab workflow \item \texttt{code/}: C helpers + Python figure generator \item \texttt{requirements.txt}: Python dependencies \item Outputs: figures (.png), summary CSV files, and SHA256 checksums \end{itemize}