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The Minimal Resolution Conjecture is known and has been verified for Projective Spaces of dimension 2 and 3. Also there many counter examples for example for 11 points in a Projective Space of dimension 6, 12 points in a Projective Spaces of dimension 7. However, for Projective Spaces of dimension 4, it is believed to be true but the complete proof has not been written up so far. F Lauze (see the ref)tackled part of the resolution in his thesis, I have tackled the other part here in this book - my PhD work. I hope to have the complete proof soon.