Everyone thinks that the AHR aliens put the wormhole equations in John's brain, but why? They never said they did.
What might have happened was this: They stored the equations inside John's father's ring. That's why they gave it back to him at the end of AHR. Unfortunately, D'Argo let the ring float out into space in Family Ties.
Here's my list of facts, which I like to call, "30's List of Facts". I'll go in order.
1. John's dad's ring is his (John's) good luck charm. It is one of the last symbols of Earth John had.
about A Human Reaction:
2. The fake Dad had custody of the ring for at least (approx.) 12 hours.
about Nerve:
3. The fake Dad said to John, "You'll have to find it yourself. The unconscious knowledge we've given you will guide you--nothing more."
about The Hidden Memory:
4. Crichton says, "I'm not blocking anything... about wormholes!"
5. Scorpius thinks Crais is blocking stuff about wormholes, too, even though we know he's not.
6. Gilina says to Aeryn, "Scorpius thinks that is has something to do with his precious wormholes, but it doesn't.".
Aeryn responds, "What does it have to do with?"
Gilina says, "Me. He's protecting me. But as soon as Scorpius finds out he knows nothing about wormholes... he'll... he'll kill him."
7. Crichton tells Stark, "Oh, he thought it was about his doomsday device--about wormholes. It wasn't. It was only about the time I kissed a girl."
about Family Ties:
8. It was written by Rockne S. O'Bannon and David Kemper.
9. D'Argo falls unconscious and lets John's dad's ring float away.
about Liars, Guns, and Money, Part 3: "Plan B":
10. The clone is being rather vague about whether it got the wormhole info or not. "I believe I've burrowed far enough. The information was well-hidden by the Ancients. I suspect even Crichton is unaware of the specifics."
So let me restate my case again: The AHR aliens saw John's dad's ring as one of the few remaining symbols of John's home planet. They took the ring and put wormhole equations in it. Then they showed John what they put in the ring for a few brief seconds, then established the neural block to not let John see that memory. Then they gave the ring back to John so it would act as his guide to figuring out how to get back home.
Then John got captured by Scorpius, and Scorpy broke through the AHR aliens' neural block--as a result, John finally got to see that memory. The AHR aliens had figured that John would have already discovered wormhole technology by the time he broke through the memory, so they figured he would immediately come to the conslusion that the wormhole equations were on his ring. Unfortunately, they didn't anticipate Scorpy's capture, and the Aurora Chair. And Scorpy would not have realized the significance of the ring, because they didn't show the specific memory of the AHR aliens giving John back the ring, and Scorpy wouldn't know that the ring belonged to John's father.
Then John gave the ring to D'Argo. D'Argo fell unconscious in space and let the ring float away.
Later on, Scorpius managed to contact his neural clone and ask him if he (the clone) had gotten to the wormhole information. The clone gave him the rather vague response: "I believe I've burrowed far enough. The information was well-hidden by the Ancients. I suspect even Crichton is unaware of the specifics."
And a few solar days after that, Crichton gets the chip out of his brain. Scorpius shows up and takes it, saying that he hopes the info on the chip is more understandable than Crichton.