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    "# PADM2M Charlie Index Walkthrough\n",
    "\n",
    "This notebook documents the step-by-step exploration of the Charlie Index (C) and its derivative (C′) using the **PADM2M** model.\n",
    "\n",
    "We show the progression from raw data (Panel A), to smoothed representations (Panel B), to centered and aligned views (Panel C).\n",
    "\n",
    "The goal is transparency: nothing hidden, just progressively easier-to-read representations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b2920a3",
   "metadata": {},
   "source": [
    "## 1. Load data\n",
    "We start with the processed `padm2m_charlie_index.json` file produced by the pipeline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "69ed4883",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os, json\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.ndimage import gaussian_filter1d\n",
    "\n",
    "# Paths\n",
    "input_file = os.path.join(\"..\", \"processed\", \"padm2m_charlie_index.json\")\n",
    "fig_dir = os.path.join(\"..\", \"figures\")\n",
    "os.makedirs(fig_dir, exist_ok=True)\n",
    "\n",
    "with open(input_file, \"r\") as f:\n",
    "    records = json.load(f)\n",
    "\n",
    "time = np.array([r[\"time_ka\"] for r in records])\n",
    "C = np.array([r[\"C\"] for r in records])\n",
    "Cprime = np.array([r[\"C_prime\"] for r in records])\n",
    "\n",
    "def normalize(arr):\n",
    "    return (arr - np.min(arr)) / (np.max(arr) - np.min(arr))\n",
    "\n",
    "C_norm = normalize(C)\n",
    "Cprime_norm = (Cprime - np.mean(Cprime)) / np.max(np.abs(Cprime))\n",
    "\n",
    "time[:5], C[:5], Cprime[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcbd22de",
   "metadata": {},
   "source": [
    "## 2. Panel A: Raw data\n",
    "This is the unaltered view of C and C′. It shows all the natural noise and variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eb4d908a",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,5))\n",
    "ax.plot(time, C_norm, color=\"blue\", alpha=0.7, label=\"C (raw)\")\n",
    "ax.set_ylabel(\"C (normalized)\")\n",
    "ax.set_ylim(0,0.9)\n",
    "ax.set_xlim(left=0)\n",
    "\n",
    "ax2 = ax.twinx()\n",
    "ax2.plot(time, Cprime_norm, color=\"red\", alpha=0.4, label=\"C′ (raw)\")\n",
    "ax2.set_ylabel(\"C′ (normalized)\")\n",
    "ax2.set_ylim(-0.18,0.18)\n",
    "\n",
    "ax.set_xlabel(\"Time (ka BP)\")\n",
    "ax.set_title(\"Panel A — Raw Data\")\n",
    "fig.tight_layout()\n",
    "plt.show()\n",
    "fig.savefig(os.path.join(fig_dir, \"padm2m_panel_a_raw.png\"), dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "613a58b0",
   "metadata": {},
   "source": [
    "## 3. Panel B: Smoothed data\n",
    "We apply Gaussian filters to reduce noise while retaining structure.\n",
    "- C: σ = 5\n",
    "- C′: σ = 1.5 (less smoothing to keep detail)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9f785216",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_C = 5\n",
    "sigma_Cp = 1.5\n",
    "\n",
    "C_smooth = gaussian_filter1d(C_norm, sigma=sigma_C)\n",
    "Cp_smooth = gaussian_filter1d(Cprime_norm, sigma=sigma_Cp)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,5))\n",
    "ax.plot(time, C_smooth, color=\"blue\", label=f\"C (σ={sigma_C})\")\n",
    "ax.set_ylabel(\"C (normalized)\")\n",
    "ax.set_ylim(0,0.9)\n",
    "ax.set_xlim(left=0)\n",
    "\n",
    "ax2 = ax.twinx()\n",
    "ax2.plot(time, Cp_smooth, color=\"red\", label=f\"C′ (σ={sigma_Cp})\")\n",
    "ax2.set_ylabel(\"C′ (normalized)\")\n",
    "ax2.set_ylim(-0.18,0.18)\n",
    "\n",
    "ax.set_xlabel(\"Time (ka BP)\")\n",
    "ax.set_title(\"Panel B — Smoothed Data\")\n",
    "fig.tight_layout()\n",
    "plt.show()\n",
    "fig.savefig(os.path.join(fig_dir, \"padm2m_panel_b_smoothed.png\"), dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06c8bf70",
   "metadata": {},
   "source": [
    "## 4. Panel C: Centered & aligned view\n",
    "We normalize and center the signals so that C and C′ can be visually compared. This does not hide anything — it just aligns them to reveal correlation/divergence patterns more clearly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e7e2086",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_Cp_high = 4.0\n",
    "Cp_smooth_high = gaussian_filter1d(Cprime_norm, sigma=sigma_Cp_high)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,5))\n",
    "ax.plot(time, C_smooth, color=\"blue\", label=f\"C (σ={sigma_C})\")\n",
    "ax.set_ylabel(\"C (normalized)\")\n",
    "ax.set_ylim(0,0.9)\n",
    "ax.set_xlim(left=0)\n",
    "\n",
    "ax2 = ax.twinx()\n",
    "ax2.plot(time, Cp_smooth_high, color=\"red\", label=f\"C′ (σ={sigma_Cp_high})\")\n",
    "ax2.set_ylabel(\"C′ (normalized)\")\n",
    "ax2.set_ylim(-0.18,0.18)\n",
    "\n",
    "ax.set_xlabel(\"Time (ka BP)\")\n",
    "ax.set_title(\"Panel C — Smoothed & Centered\")\n",
    "fig.tight_layout()\n",
    "plt.show()\n",
    "fig.savefig(os.path.join(fig_dir, \"padm2m_panel_c_centered.png\"), dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90a5dd81",
   "metadata": {},
   "source": [
    "## 5. Notes\n",
    "- Panel A shows everything raw (full noise).\n",
    "- Panel B smooths but keeps independent scaling.\n",
    "- Panel C centers for visual comparison — the keystone representation.\n",
    "\n",
    "This sequence should form the foundation figure set for introducing the Reliford Principle."
   ]
  }
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