131072 tile? Is it possible?

NOTE: This video is a proof of concept, NOT a game recording.
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What is the highest possible tile in the 2048 game?
There have been mathematical proofs that any tiles higher than 131072 are impossible, but none have proved whether the 131072 tile is possible under optimal conditions.
This video is a proof of concept (POC) showing the final steps of constructing an 131072 tile.