I spent nearly an hour trying to figure this one out.  To open the recipe for Piro Sotea, I had to synthesize Pure Water with the “Secret of Health” trait.  The only material that I had with that trait was Zaflwa Oil, but Zaflwa Oil had only the “fuel” property, and I somehow had to get it all the way to something that is “water”.

At the point in the game, nothing obvious worked as I was going backward from Pure Water and seeing what I can do to get a “Fuel” item.  Then I realized why the game had the expert cauldron, which automatically fails a synthesis if you take too long to do it.  If you fail a synthesis, you get Failure Ash, and I was still able to move traits from the ingredients to the Failure Ash.  The Failure Ash had the properties of “elixir” and “magic item”.  This synthesis chain will need you to be pretty far in the game, as one of the items you need to synthesize for this is only available once you get the Forest of the Fairies.

The synthesis chain is as follows:

1.  Synthesize Zaflwa Oil with any recipe, use the expert cauldron to purposely fail, get Failure Ash, move the “Secret of Health” trait onto the ash.
2.  Synthesize Elixir Base with the Failure Ash in step 1, keep the “Secret of Health” trait.
3.  Synthesize Natural Yeast with the Elixir Base in step 2, keep the “Secret of Health” trait.
4.  Synthesize Neutralizer R with the Natural Yeast in step 3, keep the “Secret of Health” trait.
5.  Synthesize Mineral Extract with the Neutralizer R in step 4, keep the “Secret of Health” trait.
6.  Synthesize Pure Water with the Mineral Extract in step 5, keep the “Secret of Health” trait.