I recently found the paper of Berarducci + Mantova [[1](https://arxiv.org/abs/1503.00315), [2](https://arxiv.org/abs/1703.01995)] saying that surreal numbers are equivalent to trans-series.  These are very different objects:

* trans-series are used in physics to correct, Laplace transforms [[3](https://arxiv.org/abs/1511.05977)]
* [Surreal Numbers](https://en.wikipedia.org/wiki/Surreal_number), originate in Logic and describe [combinatorial game theory](https://en.wikipedia.org/wiki/Combinatorial_game_theory), but may be used in Analysis [[4](https://arxiv.org/abs/1307.7392)].


Has anyone checked this equivalence?  Is it correct?