Entropy--Sieve Methods for Erd\H{o}s Problem \#676\\ \large Prime--square remainders and information--theoretic transfer principles

\noindent\textbf{Zenodo upload description (code and requirements).}

\begin{itemize}
  \item \texttt{numerics\_entropy\_sieve.py}: Python script used to reproduce the numerical experiments in the paper. It (i) computes the exceptional set counts
  \(\mathcal E(x)=\{n\le x:\ S(n;\lfloor\sqrt n\rfloor)=0\}\) over a range of cutoffs, (ii) compares \(\#\mathcal E(x)\) against the independent-model heuristic \(2e^{-\gamma}\mathrm{li}(x)\), and (iii) generates the paper figures (exception counts, normalized ratios, smallest-witness-prime histogram, and empirical dependence/multi-information diagnostics at small \(Z\)). The script outputs both raw summary tables (CSV) and publication-ready plots (PDF/PNG).
  \item \texttt{requirements\_numerics.txt}: Minimal Python dependency list (package names and versions) required to run \texttt{numerics\_entropy\_sieve.py} and reproduce the numerical tables/figures.
\end{itemize}