With just 10 minutes left, you have to stop Clive before his fortress levels London.
The destruction ends
Check the generator for Puzzles 128, but note that you can't save after this point. In doing so however, you've caused the fortress to start tearing itself apart. The transport pod is no longer working, so you must escape using the Laytonmobile. As you escape, you'll be met with a road blockage, triggering Puzzles 129.
After solving the puzzle, you will be treated to the ending. Everyone survives, the fortress is stopped, and the fake London is obliterated by its explosion. Clive reveals that he secretly hoped Layton would talk him out of his madness. Celeste reveals that she is actually Claire, who actually was sent 10 years into the future, but she will inevitably return to the past, to the exact moment of the deadly blast. Mystery 05 and Mystery 09 will be solved for good.
Enjoy the bittersweet ending! Just one final puzzle remains: Puzzle 130. Solve it, and you've solved every puzzle in the main adventure!