The Cambridge Capital Controversy establishes that any scalar value aggregate of capital,K = π(r, w)q, is profit-rate dependent and therefore cannot ground marginal-productivityexplanations of the profit rate r without circularity. The paper resolves this identification failureby an object switch: capital is defined as a capital state, a price-free profile distribution pt ∈ ∆n−1over technique bins, rather than as a scalar. Majorization on the simplex yields a label-freepartial order of structural concentration, and it is shown that for n ≥ 3 no scalar index can be anorder-isomorphism for this partial order; any scalar necessarily collapses incomparabilities andtherefore cannot encode the full Lorenz-consistent structure. Endogenizing technique viabilityyields a melting-iceberg theorem: the equilibrium number of active bins n∗(r) is a nonincreasingstep function of the profit rate, with discontinuous support collapses that scalar K can smoothover.New evidence is provided using U.S. BEA Fixed Asset Tables 3.1ESI/3.2ESI and Moody’sBaa–Aaa credit spreads (annual, 1947–2023). Structural volatility is measured by the Lorenz-jump statistic Jt := maxk |Lpt (k) − Lpt−1 (k)|. The data exhibit a double dissociation: in 2000,J2000 = 0.004245 while the credit spread is 0.741667 percentage points; in 2020, J2020 = 0.001220while the spread is 1.125833 percentage points. In 1980 and 2008, both Jt and spreads are high.Over the merged annual sample, corr(Jt, Spreadt) = 0.2018, implying weak linear comovementrather than literal orthogonality. The joint signal (Jt, Spreadt) therefore identifies crisis typesthat are not detectable from spreads alone.
Kevin Fathi (Sun,) studied this question.