Are Biblical Hebrew Construct Noun Phrases Bicephalic?

In the Latin tradition of grammatical analysis of Biblical Hebrew Construct Noun Phrases (CNPs), the construct noun is termed regens ‘ruler’ and the absolute noun rectum ‘ruled’. Yet in the Hebrew grammatical tradition, it is viewed the other way round: the construct noun is nismak ‘bound’ and the absolute is somek ‘unbound’. Sperber noted this contrast in perspectives: “According to the Hebrew way of thinking it is exactly vice versa [to the non-Hebrew way]: the second noun remains unchanged and even gets the article if determined, and causes the first noun to undergo certain changes”. At the external clausal level, the Latin view makes sense, because the construct noun fills a participant role in the clausal structure. At the internal phrase level, the Hebrew view makes sense, because the absolute form is a fully-fledged noun phrase and, moreover, the construct noun cannot appear independently, which is unexpected. Contemporary linguistic analyses of the CNP strongly favor the Latin tradition, arguing that the absolute form is a syntactic complement to the construct head. But could there be an alternative analysis, according to which CNPs are bicephalic, ‘double-headed’—the absolute noun heading the CNP internally and the construct noun the CNP externally? Arguments for such an account will be examined.