Hi Chris.
The forge is procedurally generated and uses a seed based of your inputs(doesn't matter about the order) to determine the output. I have run all the available possible combinations of items through my forge algorithm and it looks like we have 15,000+ possible unique recipes. My hope is that players can figure out the basic logic that the forge uses. You might already know this, but I will give a quick rundown anyway.
The forge looks at the majority. If the majority is the same item, then it will try to give you a better version if the item. If the majority is the same type of item(module/weapon/tech) but different individual items, then it will give you an upgrade of one of the items. If all three items are from different categories, then it will give you a random item that is in an upgraded tier. Thats basically it.
I haven't generated the full recipe list for 1.20(i did it for the prerelease). If you join the discord, you might find an old recipe list somewhere if you ask for it, but chances are this list is already outdated.
People in the discord have suggested a recipe book, or some way of showing you what you can forge with your current items. I like the idea, and may implement it sometime in the future. It is not a top priority though, since the next couple of updates are still working at redesigning the core of the game. Maybe once I am satisfied with the core gameplay loop then we will start to see quality of life features like these being added. But you never know. Sometimes when I have some time at the end of an update and want to add some features, I just add them. So it could be at any time, but more likely later than sooner.
Thanks for the feedback. It would be great to see you in the discord to give more suggestive input and direct feedback straight to me. You will also get progress updates on what I'm working on and occasionally I ask members to vote on certain things.
Cheers!
(edit) Sorry for the wordy reply.