{
  "completed_step": "C398",
  "next_proposed_step": "C399",
  "question": "For all ten admitted common P/J coordinate edges—six cumulative and four regular—solve the unique E return pivot and check the appropriate frozen source menu. Derive one signed formula for the return-loop geometry and state its complete source-supported domain.",
  "reason_selected_after_current_result": "The branch test gives a specific closure obstruction. A complete ten-edge check can determine whether any other existing common P/J edge supplies the missing E return, including the cumulative side.",
  "executed": false,
  "authorization_remaining": 5,
  "fixed_scope": "Mirror/529; regular Gears Noah/Shem/Flood only; SP companion local. Fixed source inputs, no canonical/graph changes."
}