I got really bored one day, so I made a list of my solve paths for each puzzle, and called it:
I Wanna Lockpick ~ PATH OF LOGIC (Part 1)
I pretty much just slapped whatever my thought was when trying to formalize the puzzle into a big list, then tried to organize it a little bit.
It's still a big mess at parts, especially for some of the harder puzzles to formalize.
I might do this for part 2 as well, but that's quite a bit into the future.
(And I assume that the puzzles then will be harder, so... I'm dreading it.)
Edit: A brand new doc has been made for the newly released part 2!
It contains logical analysis for all newly added puzzles in part 2, and as a result, their solution. Enjoy.
I Wanna Lockpick ~ PATH OF LOGIC (Part 2) (also linked in the first doc)