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So it seems like it might be based on quality and variety, which then creates a random item. There's probably a formula for optimal results, personally for the cauldron I was using a combination of unwanted decent quality items and then filling up the pot with chaff.
For the forge I was putting in 5 purple varied items and getting a random red item from the next tier, it's possible though that I perhaps didn't need as many as 5 items or that I could have filled up the pot with a few items of lesser quality to make up the numbers.
For cauldron I've been using
1 red
1 purple
3 blue
2 green
2 white
This gets me 2 Tears of a Star.
(edit)
A couple of times now I've had 3 Tears of a Star with these items, I'm not sure if it was random or a result of the kind of items I was putting in. I believe the times when I got 3, the blues and possibly the red I'd put in were gems, and the whites were stacks of ore/cloth ect. that I'd put in just to get rid of.
As before though, all 9 items/stacks were different.
ie. if I put in a stack of 6 mithril ore then that's counted as 1 item.
I'm not sure if it was just random, or if there really is a more optimal mix down to types of blues/red and/or the white objects being two small stacks.
In my case, 4x purple will most likely give me spirits instead of items
Edit: Wait, I think I know the problem, are you trying to craft 4 purples of the same item? That will definitely give you essence as stated in the guide. Stacks do not count, each purple has to be a different item.
Yes, it explains much now.
I still have an occasional spirit result, perhaps accessories can't be mixed with weapons and armors. Will verify in future encounters.
I hack that stat to 1000% and I got 5 gold items (each one is different) from 9 red items.
Normally it will give you 1 gold item.