Let
X
X
be a nilpotent rational homotopy type such that (1)
S
(
X
)
S(X)
, the image of the Hurewicz map has finite total rank, and (2) the basepoint map of
M
M
, a minimal algebra for
X
X
, is an element of the Zariski closure of
Aut
(
M
)
{\text {Aut}}(M)
in
End
(
M
)
{\text {End}}(M)
(i.e.
X
X
has "positive weight"). Then (A) any retract of
X
X
satisfies the two properties above, (B) any two irreducible product decompositions of
X
X
are equivalent, and (C) any two irreducible coproduct decompositions of
X
X
are equivalent.