{
  "schemaVersion": 1,
  "lessonId": "optimization-07",
  "contentHash": "1aaac0936877ab47a75da09c427f592954229043d5aa10544c154d7bba1644c4",
  "executedAt": "2026-10-20T10:45:39.979446+00:00",
  "environment": {
    "backend": "cpu",
    "deviceCount": 1,
    "python": "3.14.3",
    "jax": "0.9.2",
    "numpy": "2.4.4",
    "matplotlib": "3.10.8"
  },
  "stdout": "Jv / loss gradient: [3. 1.] [46. 19.]\nJv / loss gradient: [3. 1.] [46. 19.]\nPASS: optimization-07\n",
  "notebookCells": [
    {
      "sourceHash": "293764bce943f28b3d4df911ffde8e845037620dd36fc5ab674eb86b9a9d1b5e",
      "outputs": []
    },
    {
      "sourceHash": "7660c98fede305787b04eb49e85e4cb67d0f589c68cc7177ac3474952fa623ba",
      "outputs": []
    },
    {
      "sourceHash": "f5d4bec8ea9ac91103f66ae19b0d262ee65d9698f4b5e4e9bc13dde285eca4bf",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Jv / loss gradient: [3. 1.] [46. 19.]\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "80ac1973361990aa33217bcf05693eeb727c18c098755f9c312a96ebc675e87c",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Jv / loss gradient: [3. 1.] [46. 19.]\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "568166a66067dcbbfc5d6a1b9c29b0ea2c5d63125fdc8d9ddf3ce629ec433918",
      "outputs": []
    },
    {
      "sourceHash": "25df6d662f9d3f0c4e984c6a201f79fa0cfd7a2633dc4b0773dfba6c2dd4ee6c",
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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",
            "text/plain": [
              "Executed Matplotlib figure"
            ]
          }
        }
      ]
    },
    {
      "sourceHash": "eea67cf73eff64c6d647b57e08033692690b1ae6942b2df139c70a28c76c6abc",
      "outputs": []
    },
    {
      "sourceHash": "563fb2df2ff610595ed52c3acc99e00852e29c79a2aca0bcf975bcff1e9df479",
      "outputs": []
    },
    {
      "sourceHash": "81bd0b484bc6035fb4ac6146e1d30b8c4956b22c2880a176e6a16c607b3d28b0",
      "outputs": []
    },
    {
      "sourceHash": "7453d52b193409c8924c1491458ad2906bfda678fe1e539cc46e8d92d057dc58",
      "outputs": []
    },
    {
      "sourceHash": "ef5703239b92c9d9528c9c1bc63c0887713948e145923bfcd2c37e79fc8f18cd",
      "outputs": []
    },
    {
      "sourceHash": "0ae4816ccac4b8e8142abf1c4cbd6c40093c6f1e30e575404d5fa490a42b1a75",
      "outputs": []
    },
    {
      "sourceHash": "cbac04ea08d5c678c6ac19fc9bd74a31fb7c7ecf89c751f1c69730cae4d879db",
      "outputs": []
    },
    {
      "sourceHash": "378b5f70dc3cb5e2c094929500a8edd3b4ed6c11cf3e3a915c73006d4c8e4ab5",
      "outputs": []
    }
  ],
  "scope": "Recorded instructor reference run; all script assertions and notebook code cells passed. No accelerator performance claim."
}