The Second Reconstruction of Capital: A Unified Regime-Conditional Architecture for Post-Cambridge Aggregation

The Cambridge Capital Controversy (CCC) established that heterogeneous capital goods cannot, in general, be aggregated into a distribution-independent scalar K suitable for neoclassical marginal productivity theory. A constructive post-Cambridge resolution exists by changing the object of aggregation. First, in a minimal Sraffian circulating-capital price system, we prove that any value-based scalar capital aggregate K= (r, w) q generically depends on the profit rate r even when the physical bundle q is fixed (a Price Wicksell effect), implying circularity in theories that determine r from K. Second, we perform an object switch: capital is defined as a profile distribution over techniques p^n-1. On the simplex, majorization/Lorenz geometry supplies a label-free structural partial order, and Shannon/R\'enyi entropy supplies Lorenz-consistent scalar summaries for reswitching and combinatorial heterogeneity (Regime A). However, stabilized multiplicative regimes central to long-run accumulation exhibit an entropic inversion: under fixed-mean normalization, Shannon differential entropy in the log-normal family is non-monotone in the Lorenz parameter and therefore fails Lorenz-consistency as an equality/robustness proxy. We therefore introduce a stabilized module (Regime B) based on Lorenz-consistent Gini proxies RI=1-G and R₈₈=G, and we make regime identification a falsifiable restriction via a Hausman comparison between a semiparametric ^semi=1- G and a mean-normalized log-normal MLE-implied ^MLE. We derive influence-function standard errors for, enabling confidence intervals and specification testing. To address the multidimensional ``flattening'' problem, we add a dependence coordinate (Lock-In) via mutual information / copula entropy and a bounded proxy R₈ₕ, with discrete-kernel smoothing for sparse ordinal contingency tables. For dynamics, we replace heuristic drift plots with inferential stochastic-dominance tools: we estimate log cell-size drift (y) nonparametrically with confidence bands, test drift saturation (criticality), and implement Restoring Force Dominance (RFD) tests with a dependence-robust wild cluster bootstrap. Beyond conditionality: ergodic-growth aggregation. In any ergodic multiplicative accumulation environment, the long-run growth criterion is the Lyapunov/log-growth rate r= g (Birkhoff--Oseledec). Under regime switching with stationary occupation mass (Stability) = and state-dependent growth factors proportional to (RI, R₈₈), geometric-mean aggregation follows, yielding the Cobb--Douglas meta-objective R₌₄ₓ₀ (;) =RI () ^ R₈₈ () ^1-. The unique interior equilibrium is therefore the maximum ergodic growth point G (^) =1-, and is interpreted as an estimable environmental/regime parameter rather than a free preference weight. The resulting scientific object is a post-Cambridge structural state vector\ (\, OME (p) \ (Regime\ A), \ RI, R₈₈, \, \ R₈ₕ, \ (), \ \, ), is price-invariant, regime-conditional, statistically testable, and robust to the entropic fallacy.