So yes, if you fund key 42 with no conditions, whoever signs first owns it. In the puzzle, the first signer already exists; a bot that shoves their transaction aside is just pickpocketing at mempool speed.
I do not agree, simply because it wasn't their key, so the ownership does not exist in the first place.
Are you aware that all puzzles with exposed public keys were signed before they got solved, since they had outgoing TXs? The sweeping TXs therefore classify as theft, according to your criteria.
Again:
not your key, not your coins. It is your key only when you actually create it yourself. Otherwise, it is not your key, it belongs to everyone and therefore anyone has the equal right to use it as they see fit.
“Not your key, not your coins” cuts both ways.
Until someone derives the private key, the puzzle coins are ownerless data on-chain, yes.
The moment A solves the puzzle and signs a spend, A is the key-holder ownership springs into existence at that instant, because control is proven by the valid signature.
A front-runner doesn’t discover a second key; he simply copies A’s work, rebroadcasts it with a higher fee, and pockets the reward. That’s no different from watching me unlock a safe, grabbing the cash before I can close the door, and claiming “the safe was public property.” The effort that created the new control was mine, not yours.
Outgoing test transactions by the puzzle creator don’t change that: they pre-dated any solver, and the creator explicitly offered the balance to whoever computes the key first. Once that computation is done, the solver holds the key. Copy-paste latency attacks don’t create equal rights they free-ride on another person’s cryptographic proof of ownership, that's all.