The AI Quality Paradox: How Code Complexity Drives Rework in AI-Assisted Development

Adopting AI coding tools without proportional QA investment does not accelerate delivery — it amplifies technical debt. We model software development as a coupled ODE system where AI-generated code erodes the team's cognitive validation capacity (σ) at rate γ·v/σ, while QA restores it at rate η(1−σ). The resulting saddle-node bifurcation defines a critical QA threshold η_c = 4γv below which no stable equilibrium exists and the system collapses into unrecoverable technical debt.

Calibration across 1,594,764 file-touch events from 27 datasets and 7 language ecosystems (Python, JavaScript, Java, Go, C++, Ruby, TypeScript) yields: AI-assisted code erodes validation capacity ~12× faster than human code (γ_AI = 0.028 vs γ_human = 0.002); net velocity drops to 0.85× without QA but rises to 1.32× with a single dedicated tester (ROI: 18:1); the regime classifier sign(β(log_files)) identifies collapse trajectories from git log data alone, with no ODE calibration required.

All predictions are falsifiable. All 26 analysis scripts are documented with full source code in the Supplementary Materials. The paper includes an extraction script (extract_all.sh) that reproduces the entire 1.2M-event OSS dataset from public GitHub repositories.

Three documents: full paper (38 pp), executive summary (16 pp), supplementary code repository (110 pp).