Those are two very different concepts, AV. If I build a house out of 10,000 year old wood and then I radiocarbon date the house by measuring the wood it would show up as 10,000 years old. (In case you actually care, this is why one normally does not date a sedimentary rock by radiometrically dating the individual grains.)
Now, the wood literally had been around for 10,000 real honest to goodness years. The house was assembled from the wood making the house much, much younger.
What your Embedded Age paradigm says is God created every assemblage of atoms as if it were all much much older by the passage of physical time than it actually had experienced. There was NOTHING in the assemblage that had endured the actual passage of physical time God "embedded into it".
Those are extremely different concepts.
In fact you yourself said the act of embedding age "requires omnipotence", which means you cannot come up with an analogy that will be comparable. Clearly by your own description the bike analogy cannot even be considered close to embedded age.
Now if all "embedded age" means is building something new out of old parts, then anyone can do that. And would hence not be in accord with your initial definition of Embedded Age on post #1 of this thread.
I've been thinking about AV's idea for a while, playing devil's advocate in my own head and how it could work. And I think a closer example of his idea would be using replicators from Star Trek.
This is how my imaginary game went:
Imagine that we replicate an apple. The apple appears to be ripe and weeks old from the initial bud in a tree to the actual fruit. However, it's only seconds old. So, while it's ripe(mature), it's also young and has no history to speak of, except for a few atoms being pushed together in a second or so. Of course, I'm assuming God could do it instantly so I thought that maybe there would be no history, as AV claims.
Now, I kept going further. What if we replicated a tree that's 40 years old. A tree would have to have the signs of growth because they're not mere signs, they're actually part of the infrastructure and foundation for more growth. So, a replicated tree, while it may be mature (40 years old) and young (only created seconds ago,) would also have to have rings, which are unmistakable signs of history embedded because a tree could not be without those stages of growth.
But again, we go back into what AV means when he uses the word history. When I asked him, he said:
You don't need to understand it --- it doesn't exist.
Take any definition out of the dictionary you want, but it won't apply at the moment of creation.
However when I quoted the dictionary definitions and showed him here:
331 how there is history for objects older than 6,000 years old, he ignored me. Twice.
As I'm sure he'll ignore it again or merely pick one sentence, say something like "I see how you changed from X to Y in this sentence." Anything to avoid or dodge the point.