{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scale-Dependent Growth of Large-Scale Structure\\n",
    "## Protected Single-Pole Kernel Across Redshift\\n",
    "\\n",
    "This notebook provides a minimal working example of the kernel used in the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "source": [
    "import numpy as np\\n",
    "import matplotlib.pyplot as plt\\n",
    "\\n",
    "def mu_kernel(k, a, beta0, m_star):\\n",
    "    return 1.0 + beta0 * (k**2 / (k**2 + (a * m_star)**2))\\n",
    "\\n",
    "k = np.logspace(-3, 0, 100)\\n",
    "for z in [1.0, 0.5, 0.0]:\\n",
    "    a = 1.0 / (1.0 + z)\\n",
    "    plt.semilogx(k, mu_kernel(k, a, 0.03, 0.05), label=f'z={z}')\\n",
    "plt.legend()\\n",
    "plt.title('Protected single-pole kernel across redshift')\\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}