Leue Modulation Coefficients (LMC): A Smooth Continuum Embedding of Bounded Arithmetic Data

This repository contains a complete and self-contained presentation of the Leue Modulation Coefficients (LMC), a bounded arithmetic sequence derived from the local trace of an elliptic curve. The main purpose of the project is to construct a smooth, globally defined modulation field from discretely sampled LMC data and to study its effect on elliptic differential operators. The included research paper develops a continuum model in which the discrete LMC values are embedded into a smooth field using compactly supported mollifiers. The resulting field is uniformly bounded, infinitely differentiable, and suitable for use as a coefficient modulation in elliptic and parabolic partial differential equations. A conductivity model derived from the LMC field is introduced, together with energy estimates and analytic stability properties. The paper also contains a fully reproducible numerical example. This Zenodo package includes: the full research paper (PDF), a complete Python implementation generating the LMC field and conductivity model, a numerical plot comparing discrete LMC values with the smoothed continuum field, a cover letter and supporting documentation. The project provides a modular and reproducible framework for embedding bounded arithmetic data into analytic continuum models. It is intended as a basis for further research in multiscale analysis, smoothed arithmetic modulation, and PDE coefficient modelling.