{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Research Stack Manifold Visualizer\n",
    "\n",
    "Interactive visualization of PIST/SVQF/FAMM quaternion manifold structures.\n",
    "\n",
    "**Layers:**\n",
    "1. PIST shell generation (integer-based coordinates)\n",
    "2. Quaternion sieve (counter-rotation band-pass)\n",
    "3. FAMM frustration pruning (stress tensor filtering)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import sys\n",
    "from pathlib import Path\n",
    "\n",
    "sys.path.insert(0, str(Path(\"/home/allaun/Documents/Research Stack/5-Applications/scripts\")))\n",
    "from manifold_visualizer import ManifoldMapper, QuaternionField"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Generate Manifold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mapper = ManifoldMapper(resolution=32)\n",
    "result = mapper.map_manifold()\n",
    "print(f\"Survivors: {result['post_famm']} / {result['total_points']}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Visualize S³ Stereographic Projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(12, 5))\n",
    "\n",
    "# Raw shell points\n",
    "ax1 = fig.add_subplot(121, projection='3d')\n",
    "raw_pts = np.array(result['sample_points'][:50])\n",
    "# Stereographic projection\n",
    "x = raw_pts[:, 1] / (1 - raw_pts[:, 0] + 1e-10)\n",
    "y = raw_pts[:, 2] / (1 - raw_pts[:, 0] + 1e-10)\n",
    "z = raw_pts[:, 3] / (1 - raw_pts[:, 0] + 1e-10)\n",
    "ax1.scatter(x, y, z, c='blue', alpha=0.6, s=20)\n",
    "ax1.set_title('S³ Manifold (Stereographic)')\n",
    "\n",
    "# Quaternion phase space\n",
    "ax2 = fig.add_subplot(122, projection='3d')\n",
    "ax2.scatter(raw_pts[:, 0], raw_pts[:, 1], raw_pts[:, 2], c='red', alpha=0.6, s=20)\n",
    "ax2.set_title('Quaternion Components (w,x,y)')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Frustration Heatmap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulate frustration across k-t grid\n",
    "resolution = 32\n",
    "frustration_map = np.zeros((resolution, resolution//2))\n",
    "\n",
    "for k in range(resolution):\n",
    "    for t in range(resolution//2):\n",
    "        mass = (k+1)*(t+1)\n",
    "        theta = 2 * np.pi * k / resolution\n",
    "        phi = np.pi * t / resolution\n",
    "        # Approximate frustration from curvature\n",
    "        frustration_map[k, t] = np.abs(np.sin(theta*2) * np.cos(phi*3))\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.imshow(frustration_map.T, aspect='auto', cmap='hot', origin='lower')\n",
    "plt.colorbar(label='Φ (frustration)')\n",
    "plt.xlabel('k (shell index)')\n",
    "plt.ylabel('t (time step)')\n",
    "plt.title('FAMM Frustration Heatmap — Φ > 1 regions pruned')\n",
    "plt.axhline(y=resolution//4, color='cyan', linestyle='--', label='φ = 1 threshold')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
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