Beyond Reswitching: A Rank-Theoretic Obstruction to Scalar Capital Aggregation — Theory, Empirical Evidence from 43 Countries, and Replication Code

This deposit contains the theory paper, empirical companion paper, and replication notebook for a rank-theoretic falsification of exact scalar capital aggregation. The theory paper proves that exact scalar aggregation under competitive pricing requires the Jacobian of the map from the hidden heterogeneous-capital state to the observable triple (output, profit rate, wage) to have rank at most one, and establishes the converse on regular neighborhoods via the constant-rank theorem. The result extends to Banach-valued capital states and to nonlinear capital accumulation dynamics via the observability codistribution. Explicit no-reswitching Sraffian families — including families with pairwise non-comparable techniques and heterogeneous labor — generate rank-two observable maps, proving reswitching is sufficient but not necessary for aggregation failure. Accounting corollaries show that Cobb–Douglas fit is an algebraic identity once factor shares are fixed, and that one-dimensional measurement corrections (chain-weighting, hedonic adjustment, rebasing) cannot repair a rank-two failure. The empirical paper computes the obstruction index from the World Input-Output Database (WIOD 2016 Release) covering 43 countries, 56 industries, and years 2000–2014. The second singular value is strictly positive in 645/645 country-year-rate tests (100% falsification). The obstruction survives 2% multiplicative noise in all 43 countries, persists under heterogeneous industry profit-rate proxies (43/43 countries), and strengthens under dynamic observability in the G7 panel (7/7 economies). Cross-industry Cobb–Douglas regressions yield R² > 0.90 in 74.9% of country-years, yet 98.8% of those high-fit cases have obstruction ratios σ₂/σ₁ > 0.10, confirming that fit is not identification. Implications for climate-economy models relying on scalar capital are discussed. The replication notebook (Python/NumPy, Google Colab) implements the full pipeline — parsing, Leontief resolvent construction, SVD extraction, stress tests, bootstrap, heterogeneous-rate robustness, dynamic observability, and fit-vs-obstruction diagnostics — with no proprietary dependencies. Requires freely available WIOD 2016 Release data files.