Q is the most widely used metric of cognitive ability, yet its construct validity has been debated since its inception. This paper applies the Adaptive Compression Advantage Theory (ACAT; Murata, 2026) to demonstrate that IQ tests do not measure intelligence as a unitary construct. Instead, they measure a weighted projection of a multi-dimensional compression-efficiency vector α(d) onto a subspace dominated by two dimensions: α_verbal (linguistic compression) and α_logical (formal-symbolic compression). Human cognitive capacity is more accurately represented as a vector α(d) = [α_verbal, α_logical, α_spatial, α_social, α_musical, α_kinesthetic, α_naturalistic, ...] in which each component represents compression efficiency in a specific domain. IQ collapses this high-dimensional vector into a scalar through a projection that discards the majority of cognitive variation. We demonstrate that the g factor—the positive manifold among cognitive subtests—emerges naturally from shared neural infrastructure constraints rather than from a unitary intelligence construct. We derive why IQ predicts academic and occupational outcomes (because these environments are also α_verbal/α_logical-weighted), why it fails to predict creative achievement and entrepreneurial success (because these require domains IQ does not measure), and why the concept of “smart” is a social construction reflecting the economic value assigned to specific α(d) components. The framework generates ten testable predictions and proposes the α(d) profile as a replacement for scalar IQ in cognitive assessment. Keywords: IQ, intelligence, g factor, rate-distortion theory, cognitive assessment, multiple intelligences, compression, ACAT, domain specificity, dimensional projection, educational assessment, meritocracy