{
  "completed_step": "C413",
  "next_proposed_step": "C414",
  "question": "Within the fixed C410 regular source menu, enumerate existing endpoint pairs exactly2K=1058 apart and test whether both ends remain sourced after one and two applications of the fixed−500 comparison. Preserve source roles and contexts; compare surviving pairs with the established529 rectangle while keeping its cumulative corners fixed. Search no new intervals, shifts, phases or axes.",
  "reason_selected_after_current_result": "The new500 graph has a complete finite source domain, but its precise support for paired529 endpoints has not been classified. This brings the new regular structure back to the Mirror/529 question without treating the2000-year chain as a new research direction. C414 is proposed only and requires a new instruction.",
  "executed": false,
  "authorization_remaining": 0,
  "fixed_scope": "Mirror/529; regular Gears Noah/Shem/Flood only; SP companion local. Fixed source inputs, no canonical/graph changes."
}