No. A space advantage is determined by how may of the squares the opponent CANNOT use. Pawn positioning is just one element in that, although a very important one.
Advanced Pawns/Advantages
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In the opening/early midgame, sure, space advantage is usually determined by where the pawns are. Later on, maybe not. Maybe your opponent's pieces are behind your pawns making them less relevant for space purposes.
I guess it's really just about how free to move around your pieces are, compared to your opponent's pieces.
Would you agree that a spacial advantage is determined primarily by these two factors:
1) How many advanced pawns you have
2) How far advanced the pawns are
And that space is somewhat subjective in a given position because one white pawn advanced to d5 may or may not have more of a cramping effect on the opponent that a classical pawn center with two white pawns on e4 and d4?