Additional material is highlighted with ***.***
and a correction with *****.*****

Dolphin:
"E.g. if you have two observations: (5,5,5,5) and (5,5,5,5) you might add a 6 to the first one so you get (5,5,5,5,6). But if you already had somewhere a (5,5,5,5,6) then you have just gone and muddled your supposedly newly-uniquely identified observation with one of your others."

Could you explain it with U=unknown
and the sequence as U1-1, U2-1, U3-1, U4-1
where the first number tells the sequence and
the number after the hyphen tells which version
of the sequence we mean?

For example, if you add another unknown to U2-1, it will aways be *****U2 *****
which we could call *****U2a***** for (Unknown2 with added unknown)? *** The number after the U2a- would tell its new place in the sequence.***
And you could describe the new sequence after adding unknowns

*** AS IN the following example***

First sequence
U1-1, U2-1, U3-1...

Add unknowns and show the new sequence:

U1a-2, U3a-2, U2a-2


If what I have just said seems incomplete to you, please tell me where.

Then I would understand better what you meant.