docs: fix 404 broken links

- Replace non-existent Python examples with actual files
- Fix all placeholder yourusername URLs to ThotDjehuty
- Remove references to non-existent optimal_control.md theory doc
- Update examples to reference: hmm_regime_detection.py, parallel_de_benchmark.py, polaroid_optimizr_integration.py, timeseries_integration.py

examples/notebooks/04_real_world_applications.ipynb

@@ -2,10 +2,18 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "id": "a2ac7765",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "✓ All modules loaded successfully!\n"
+     ]
+    }
+   ],
    "source": [
     "import numpy as np\n",
     "import pandas as pd\n",
@@ -38,10 +46,32 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "id": "bc76553e",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Generated 730 days of market data\n",
+      "\n",
+      "Price range: $20,745 - $82,080\n",
+      "\n",
+      "Regime distribution:\n",
+      "regime_name\n",
+      "Bull       424\n",
+      "Bear       214\n",
+      "Neutral     92\n",
+      "Name: count, dtype: int64\n",
+      "\n",
+      "Return statistics:\n",
+      "Mean: 0.0004 (9.14% annual)\n",
+      "Std: 0.0400 (63.46% annual)\n",
+      "Sharpe: 0.14\n"
+     ]
+    }
+   ],
    "source": [
     "def generate_realistic_market_data(n_days=730, start_price=50000):\n",
     "    \"\"\"\n",
@@ -194,14 +224,36 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 4,
    "id": "d16db370",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Fitting HMM to detect market regimes...\n",
+      "\n",
+      "✓ HMM fitted successfully!\n",
+      "\n",
+      "Learned Transition Matrix:\n",
+      "         State 0  State 1  State 2\n",
+      "State 0    0.339    0.247    0.414\n",
+      "State 1    0.252    0.441    0.306\n",
+      "State 2    0.459    0.215    0.326\n",
+      "\n",
+      "Emission Parameters:\n",
+      "         Mean Return  Volatility  Annual Return  Annual Vol\n",
+      "State 0      -0.0370      0.0297        -9.3169      0.4716\n",
+      "State 1       0.0019      0.0117         0.4693      0.1850\n",
+      "State 2       0.0369      0.0281         9.3038      0.4462\n"
+     ]
+    }
+   ],
    "source": [
     "# Fit HMM to detect regimes\n",
     "print(\"Fitting HMM to detect market regimes...\")\n",
-    "hmm = HMM(n_states=3, random_state=42)\n",
+    "hmm = HMM(n_states=3)\n",
     "hmm.fit(df_btc['return'].values, n_iterations=100, tolerance=1e-6)\n",
     "\n",
     "print(\"\\n✓ HMM fitted successfully!\")\n",
@@ -764,8 +816,22 @@
   }
  ],
  "metadata": {
+  "kernelspec": {
+   "display_name": "rhftlab",
+   "language": "python",
+   "name": "python3"
+  },
   "language_info": {
-   "name": "python"
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.13"
   }
  },
  "nbformat": 4,