OK, AV, how does this sound:
Why don't you
explain the difference between your position and Omphalos. That means you can't use unexplained words or terms like "embedded age" and "embedded history" and you really need to tell us exactly what you mean when you say "the earth is 4.5 billion years old" in terms of existence and appearance, or some other, fully explained, concept if you find it appropriate.
Because so far, what we have from you is the summary,
- The earth is 4.5 billion years old
- The earth has existed for 6,100 years
- I do not subscribe to the Omphalos hypothesis
So I see two different ways of fully explaining the first statement - either you could mean "the earth has existed for 4.5 billion years" but that contradicts point 2 or you oculd mean "the earth just appears to have existed for 4.5 billion years" but that contradicts point 3.
So you must mean something else by point one. What do you mean - explain yourself as fully as is possible.
Again that does not mean just saying "the earth has 4.5 billion years of embedded age" or something, because that is
not fully explained.