The paper's main unconditional estimate is false in the 1x1 case, though its conditional reduction of the conjecture may still be worth examining.
Mathematische Annalen, Volume 341, pages 789–824, (2008)
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Transcendence degrees of fields generated by exponentials of products
The paper's main unconditional estimate is false in the 1x1 case, though its conditional reduction of the conjecture may still be worth examining.