TASK: Run convergence/robustness checks for baseline scenario.

INPUT DATA:
- Same configuration as Prompt 5, but run two numerics:
  A) dt = 1.0 s
  B) dt = 0.5 s
- Use identical params and scenario.

METHODOLOGY:
For each z0:
1) Simulate with dt and dt/2 until termination.
2) Compare z(t) by resampling dt/2 solution at dt grid (take every 2nd sample).
3) Compute:
   z_diff_inf = max_k |z_dt[k] - z_dt2[2k]|
   tte_rel_err = |TTE_dt - TTE_dt2| / TTE_dt2
4) Event-location robustness:
   For each run, report the last two bracketing samples for the triggering event and the interpolated t*.

DELIVERABLES:
A) “STEP_HALVING_TABLE_v1” CSV:
   z0, z_diff_inf, tte_rel_err, pass_bool
B) “EVENT_BRACKET_REPORT_v1” JSON:
   for each z0: {reason, (t_k-1, g_k-1), (t_k, g_k), t_star}
C) Single line verdict:
   "ROBUSTNESS_PASS" or "ROBUSTNESS_FAIL"

VALIDATION (hard thresholds):
- z_diff_inf < 1e-4
- tte_rel_err < 0.01
All z0 must pass or verdict is FAIL.

OUTPUT FORMAT:
CSV, then JSON, then verdict line. No prose.