Add Lie-Trotter integrator for SGHMC

[bkozyrskiy]

Description

This PR adds an optional Lie-Trotter integrator for SGHMC.

The existing SGHMC behavior remains unchanged by default: build_kernel() still uses the original Euler SGHMC diffusion unless a custom integrator is passed. The new integrator provides a splitting-based SGHMC update with a deterministic leapfrog Hamiltonian step followed by an exact Ornstein-Uhlenbeck momentum update.

Related issues / discussions

N/A

Checklist

General

• [x ] The branch is rebased on the latest main
• Commit messages are clear and descriptive
• pre-commit run --all-files passes (black, isort, flake8, mypy)
• Tests cover the changes (mamba run -n blackjax python -m pytest tests/)

Code quality

• Public functions have docstrings following the NumPy style guide
• Naming follows existing conventions (logdensity, jax.tree.map, jax.random.key(), jnp.clip(min=, max=))
• All new code is JIT-compatible

New sampler / algorithm (skip if not applicable)

• There is an open issue discussing this algorithm (use the sampler proposal template)
• Follows the three-layer pattern: init / build_kernel / as_top_level_api
• Registered in blackjax/__init__.py
• An example notebook has been added or updated