The literature on the construct state has traditionally assumed that the head of the construct state, and therefore the construct state as a whole, inherits its (in)definiteness value from the genitive DP; a phenomenon known as "(in)definiteness spread" - see Borer (1984, 1996), Ritter (1988, 1991), Siloni (1991, 1997), and Dobrovie-Sorin (2000), among others. This paper presents a semantic analysis of the construct state in Hebrew which departs from this view in that it claims that all construct states denote a unique individual independent of the nature of the genitive DP. The construct form of the noun (the head of the construct state) is given a lexical denotation of a functional noun (at type <e,e>). In the construct state, (the individual denoted by) the genitive DP serves as the argument to this function. The denotation of the construct state as a whole is a unique individual by virtue of being the output of a function, i.e. it does not depend on the nature of the argument of the function. New data is provided to support the functional nature of the construct form of the noun and to show that this function is determined in the lexicon. The implications of this analysis for the analysis of other properties of the construct state are also discussed.