[rogeriojorge]

Summary

• add an optional inner_product field to ImplicitMidpoint
• forward it to SOLVAX Newton--Krylov for both nonlinear norms and GMRES reductions
• verify that the configured callable is used

Why

Mapped Hermite/species states require global scalar products. Without a global
reduction, replicas can make different Newton or GMRES stopping decisions and
enter incompatible collective sequences. Keeping the callable on the solver
also supports weighted norms without coupling the solver to a mesh topology.

The mapped simulation will inject its existing species/phase-space scalar
products in a separate PR after the sharding and midpoint stacks share a base.

Validation

• complete SPECTRAX suite: 8 passed
• Ruff and git diff --check pass
• sdist and wheel build successfully
• unpushed integration audit: serial, species-sharded, and Hermite-sharded
  midpoint trajectories agree; omitting the global product reproduces divergent
  collective control flow under Hermite sharding
• clean 129² Fourier, 40×4×4 Hermite, 100-step GPU control: one and two-GPU
  trajectories agree to 3.45e-25 relative L2 in Ck; two GPUs give 2.20x speedup

Stack

This draft targets agent/midpoint-solver-diagnostics (#29), so the source
change is only three lines in midpoint_solver.py plus one focused regression
test.

[rogeriojorge]

Dropped: no caller in SPECTRAX needs a custom inner product; #21 keeps the default reductions.