{
  "schemaVersion": 1,
  "lessonId": "internals-02",
  "contentHash": "b4c3b8720c5f59e80a50216fbd223c61ea013199a86108a3d73205efb94fc75a",
  "executedAt": "2026-10-20T10:50:09.725259+00:00",
  "environment": {
    "backend": "cpu",
    "deviceCount": 1,
    "python": "3.14.3",
    "jax": "0.9.2",
    "numpy": "2.4.4",
    "matplotlib": "3.10.8"
  },
  "stdout": "Jacobian: [[-0.7         0.4       ]\n [ 0.92106099 -1.4       ]]\nJVP: [-0.96        1.52527319] VJP: [ 1.49212199 -2.6       ] adjoint pair: 2.570546385606924 2.570546385606924\nHessian-vector product: [ 1.74991568 -3.38303348]\nJacobian: [[-0.7         0.4       ]\n [ 0.92106099 -1.4       ]]\nJVP: [-0.96        1.52527319] VJP: [ 1.49212199 -2.6       ] adjoint pair: 2.570546385606924 2.570546385606924\nHessian-vector product: [ 1.74991568 -3.38303348]\nForward columns and reverse rows agree\nExact HVP: [ 1.74991568 -3.38303348] Gauss-Newton product: [ 2.07686964 -2.51938247]\nChanged-point adjoint verified\nDirection linearity holds; the Jacobian changes with the base point\nBilinear Hessian symmetry and finite-difference product verified\nPASS: internals-02\n",
  "notebookCells": [
    {
      "sourceHash": "26930fcce005548ffadf077d9a760bc955f778e4aa0b364f78b49ab352f65f36",
      "outputs": []
    },
    {
      "sourceHash": "53c8b9d33f90e049d200074d12354242b296d1d17c4e4ac843d911a5e2c0362e",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Jacobian: [[-0.7         0.4       ]\n",
            " [ 0.92106099 -1.4       ]]\n",
            "JVP: [-0.96        1.52527319] VJP: [ 1.49212199 -2.6       ] adjoint pair: 2.570546385606924 2.570546385606924\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "61bd143423b05dcdead7d5d30272c9aabc850916010504dd051022b5c443ce01",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Hessian-vector product: [ 1.74991568 -3.38303348]\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "0f61a54e9f5fb6e1ff910fa44d2fc5b32b3155cf78d09567fb6a0451202aff3c",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Jacobian: [[-0.7         0.4       ]\n",
            " [ 0.92106099 -1.4       ]]\n",
            "JVP: [-0.96        1.52527319] VJP: [ 1.49212199 -2.6       ] adjoint pair: 2.570546385606924 2.570546385606924\n",
            "Hessian-vector product: [ 1.74991568 -3.38303348]\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "a15b15540d2b831957c84138342fe2efe2d94d2670cf850ce339e1a92956e6a9",
      "outputs": []
    },
    {
      "sourceHash": "25df6d662f9d3f0c4e984c6a201f79fa0cfd7a2633dc4b0773dfba6c2dd4ee6c",
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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",
            "text/plain": [
              "Executed Matplotlib figure"
            ]
          }
        }
      ]
    },
    {
      "sourceHash": "c93a0b857496ac96bc88842b60d7d62b37dc652dc0216fda545f556fa4bacc6e",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Forward columns and reverse rows agree\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "9afe791ac7c07f1e5e86c70b1670ea77677ef9c438dccd1d67002415df92585d",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Exact HVP: [ 1.74991568 -3.38303348] Gauss-Newton product: [ 2.07686964 -2.51938247]\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "47dd0d4a6c4602230854f961ed660d59244978d8ba49af044593ef728ea66754",
      "outputs": []
    },
    {
      "sourceHash": "7b3265d5c4d4f3a347bdc3539f7183fe30e5c8c018dc36b3392d36981b2cbda2",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Changed-point adjoint verified\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "86ac12ac4c46fc64ce3d53a485dcc50ccab53a749c541472c519fe785728731f",
      "outputs": []
    },
    {
      "sourceHash": "f259868362260f7a94af770fb4192ec2a2f1b3a1f99f778856d503e168f0a14b",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Direction linearity holds; the Jacobian changes with the base point\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "46b3fff7ef0216531b349ddb1225cc72069495d97a34d4f2bb2c7af19b6e8a46",
      "outputs": []
    },
    {
      "sourceHash": "94fa7af34f35883bf094f730fa52f9fbc058cdff3f5c37be6d6ce4c8d2ac0556",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Bilinear Hessian symmetry and finite-difference product verified\n"
          ]
        }
      ]
    }
  ],
  "scope": "Recorded instructor reference run; all script assertions and notebook code cells passed. No accelerator performance claim."
}