A Relay-Depth Exponent Ladder Closing the Bettencourt 22-Indicator Urban-Scaling Panel

~A Zero-Fitted-Exponent Complementary Closure with Integer, Continuous, and Hybrid Assignments~ Abstract A zero-fitted-exponent ladder β = 1 ± 1/[H ln(2H+1)] reproduces every indicator of the Bettencourt 2007 22-panel within its 95% confidence interval. Here β is the urban scaling exponent. The relay-depth H is the hierarchy of coordination layers in the city's productive system without using observed beta. The framework is falsified if any indicator falls outside its CI under the zero-fitted-exponent assignment. Reproducibility Companion simulator at https://shota-kato-lab.github.io/tools/paper4/1/ Python bundle under Paper4_Reproducibility_Bundle_v1.4.tar.gz (attached to this record). == Release v1.4 (2026-05-27) == Five integrity items disclosed at v1.3 fully integrated into main text and SI. v1.3 release tag preserved as historical first-disclosure state.