[DiadkoShmek]

LeapfrogMidpoint.step() ignores made_jump, so a resumed solve can combine pre-discontinuity history with the new vector field. Solving y'=1 from 0 to 1 with dt0=0.25, then resuming with y'=2, retained solver_state and made_jump=True, gives 1.75 at time 1.25 instead of the exact 1.5. Later steps can alternate between correct and incorrect states; endpoint-only checks can miss the error.

Select (t0, y0) as the history after a jump, using the existing Euler startup. Elementwise selection supports traced jump flags and the scalar promotion already supported by direct init/step calls. The solver-state representation and ordinary continuation remain intact.

Two compact regressions in the existing solver test module cover forward/backward restart values and analytic rate gradients, plus no-jump time/state promotion controls.

Validation on current main e950aa2 with CPU JAX 0.12.0.1:

• Exact final regression file on the base: two restart failures and two passing promotion controls.
• Final regressions and adjacent Leapfrog/basic-integration, HalfSolver and step-controller checks: 31 passed. One existing parametrization warning remains.
• A separate local analytic matrix checks all four saved post-jump states, gradients, float32/float64, mixed dynamic jump flags, complex state, and HalfSolver/clip-controller controls: 14 failing comparisons on the base / 24 passing controls; all 38 comparisons pass with the fix.
• Project-pinned Ruff 0.13.0 lint/format and Pyright 1.1.405 pass on both changed files; git diff --check passes.

The full repository suite, accelerators, general SDE coverage and performance were not evaluated. Implementation and testing were AI-assisted.