Crelay-Topo Backward Analysis -- 2026-09-15
==========================================

The proposed carrier strategy now has a complete forward validation: 94 actions,
three recorder cycles, agent1 at location19. The final cycle remains open with
the ghost on plate3. No minimum-length claim is made. See subgoal-solutions.txt
for the retained sequence and subgoal3-complete-validation.txt for evidence.

Backward dependencies and their validated realization
-----------------------------------------------------

1. Cross gate9 to location19.
   Plates6, 7, and 8 must remain occupied while agent1 crosses. The solution
   assigns tray1 to plate6, connector1 to plate7, and box1 to plate8. Agent1
   remains available to walk to the goal; it is not a final plate occupant.

2. Deliver all three live objects beyond gate8.
   Agent1 carries tray1, with box1 on the tray and connector1 on box1, through
   gate8 from location15 to location21. Only then is the stack unloaded and
   the connector retrieved. The beam may disappear after this crossing.

3. Activate receiver1 for the gate8 crossing.
   Ghost connector1* at location9 links transmitter1/repeater1. The ghost
   stands on plate3 to open gate4. Live connector1 remains paired to
   repeater1/receiver1 while elevated on the carried box/tray stack. The
   complete replay validates the approach to location15 and crossing to
   location21 under the current beam and gate rules.

4. Open gate7 with switch2.
   Switch2 is reached at location14 through gate6 and screen1. Live tray1
   holds plate4; the ghost stands on plate5 holding the loaded ghost tray.
   Agent1 crosses empty-handed, turns switch2 on, and returns before removing
   tray1 from plate4. Ordinary gate5 closes, but recording gate5 remains open
   for the ghost's later return toward location2 and beam setup.

5. Recover the carrier after the switch trip.
   Agent1 retrieves tray1 and stands on plate5 alongside the ghost. A local
   release of tray1* settles box1 onto the equal-height live tray. Connector1
   stays on box1, with its pairings intact. Co-location alone is not transfer.

6. Prepare the elevated live stack.
   Pause the ghost with tray1* at location5. Agent1 uses the blower to place
   box1 on that tray, then makes a second blower trip to connect connector1
   on box1. Live agent1 does not use ghost box1* as a jumping support.
   Current connector pickup removes pairings, so the sequence explicitly
   reconnects during the second loading trip. Retaining pairings at pickup
   remains an unimplemented technology option, not an assumption of this path.

7. Preserve the early doors and provide the ghost beam resources.
   Start cycle 3 from Subgoal 2: connector1 is on plate1, box1 on plate2, and
   tray1 grounded at location7. Their ghost copies preserve plates1/2 while
   the live cargo is removed. After the handoff, the ghost returns its tray
   to plate1 and retrieves connector1*. The explicit ground-and-pickup swap
   avoids holding both objects at once. Box1* stays on plate2 throughout.

8. Establish the starting checkpoint.
   Cycle 1 puts connector1 on plate1. Cycle 2 uses the blower and ghost tray
   to recover box1 from location6 and put it on plate2, leaving tray1 grounded
   at location7. Both cycles close normally. These retained subgoals are unchanged.

Scope and alternatives
----------------------
These resource assignments describe the validated solution; they are not claims
that every solution must use the same assignments or number of actions. The
original objects, geometry, wiring, and locations were not changed for this replay.
No extra box, connector, tray, or location was needed.

The old four-cycle intermediate checkpoint and speculative alternatives are
preserved in Historical-Analysis-before-2026-09-15.txt. No additional Subgoal 4
is needed for the current retained complete solution.
