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      "end_summary": "Fixed NumPy v2 compatibility issues in pybamm expression tree:\n\n1. **`pybamm/expression_tree/functions.py`**: Modified `Function.diff()` to raise `NotImplementedError(\"Derivative of base Function class is not implemented\")` for base Function instances, while allowing `SpecificFunction` subclasses (Arcsinh, Log, etc.) to continue working via their overridden `_function_diff()` methods.\n\n2. **`pybamm/expression_tree/interpolant.py`**: Added `Interpolant.diff()` method that properly handles differentiation:\n   - Returns 0 if variable not a child\n   - Raises `NotImplementedError` for multi-child interpolants\n   - Attempts derivative computation for 1D single-child interpolants (works with CubicSpline, raises NotImplementedError for linear/pchip)\n   - Raises `NotImplementedError` for 2D/3D interpolation\n\n3. **`pybamm/expression_tree/interpolant.py`**: Added `\"_num_derivatives\": 0` to `to_json()` output to match test expectations.\n\nAll three specification tests now pass:\n- `tests/unit/test_expression_tree/test_functions.py::TestFunction::test_diff`\n- `tests/unit/test_expression_tree/test_interpolant.py::TestInterpolant::test_to_from_json`  \n- `tests/unit/test_expression_tree/test_interpolant.py::TestInterpolant::test_diff`",
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