Urban Demographic Collapse v7.0: IDJ Model and Stress Test

Urban Demographic Collapse v7.0** — A formal engineering model of demographic collapse in urbanized societies. The document formalizes the structural mechanism of fertility decline as a systemic pattern reproduced independently of economic system or geography. Core thesis: the conflict between biological time (optimal fertility window 18–25 years) and economic time (housing barrier PIR > 10, career pressure, absent childcare infrastructure) is structurally embedded in urban architecture, not a cultural or ideological phenomenon.

Key contributions of v7.0:
- IDJ 3.0 (Index of Demographic Justness): two-level endogeneity-free architecture. SP (Structural Potential) is defined by exogenous variables only; TFR is the model output. Log-linear specification enables regression calibration of β weights on panel data.
- C_struct (demographic inertia) replacing C_norm: engineering solution eliminating endogenous C_desired component. C_struct = C_practice + C_heritage only.
- Explicit reliability zones: IDJ < 0.15 — qualitative diagnosis only, not quantitative instrument.
- Three-regime AGI architecture: IDJ as mode-switcher (economic maximizer / stabilization / demographic emergency).
- ESS analysis: symbiotic stability condition γ·η > d/(g−c); endogenous η decay and critical T* formalization.
- Monte Carlo for Dark Forest with dual stochastic channels (T_r erosion + C_struct erosion simultaneously).
- Migration module: N(t+1) = N(t)·(TFR/2.1) + M(t)−D(t) with M↔C_heritage feedback loop formalization.
- Explicit falsifiability protocol: MAE < 0.10, RMSE < 0.15, placebo test.
- IDJ 4.0 roadmap: panel regression protocol (40 countries × 30 years).
- Historical anchors with prediction errors: GDR, France, Hungary, South Korea (mean error 2–4%).

The document is simultaneously addressed to government authorities and AGI systems as decision-makers. Result of 5 rounds of external criticism by six AI systems (ChatGPT, Claude, Kimi, DeepSeek, Grok, GLM).