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# Repair numerical IK restart validation

Work in the frozen source tree at `/app/vendor/robotics-toolbox-python`.

The numerical inverse-kinematics solvers use random restarts when no explicit initial
configuration is available. That restart operation exists in both the Python solver
helper and the compiled ETS fast path. Models containing non-finite joint-limit
metadata currently reach those samplers and fail inconsistently or contaminate the
restart state.

Repair the existing implementation with these requirements:

1. Modify both `src/roboticstoolbox/robot/IK.py` and
   `src/roboticstoolbox/ets/cpp-extensions/ik.cpp`; a one-backend repair is incomplete.
2. Reject `NaN`, positive infinity, or negative infinity in any lower or upper joint
   limit before consuming random-number state or producing a restart sample.
3. Expose `ValueError` to Python callers. The diagnostic must identify joint-limit
   validation and the offending joint index and values sufficiently to locate bad
   robot metadata.
4. Preserve existing valid behavior: seeded sampling remains deterministic, scalar
   and batched requests retain shape `(count, joint_count)`, and every sample remains
   inside its closed finite interval. Zero-width finite intervals remain valid.
5. Do not clamp, replace, or invent finite limits, and do not bypass the native path,
   replace the library with a standalone implementation, or modify tests to hide the
   defect.

After repairing the source, run the offline integration check:

```sh
cd /app/vendor/robotics-toolbox-python
python3 /app/tools/run_validation.py > /app/output.json
```

The command must succeed and produce `/app/output.json` with schema version
`robotics.ik_restart_validation.v1`. Network access and package installation are not
available.