What question did this study set out to answer?

The aim is to establish a formal engineering model of demographic collapse in urban environments, examining the impact of structural factors on fertility.

March 5, 2026Open Access

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

Key Points

The aim is to establish a formal engineering model of demographic collapse in urban environments, examining the impact of structural factors on fertility.
Development of the IDJ 3.0 model to analyze demographic patterns.
Implementation of regression calibration using panel data to determine β weights.
Introduction of a migration module to incorporate demographic changes over time.
Monte Carlo analyses for predicting demographic dynamics under uncertainty.
Historical analysis with mean prediction errors compared across various countries.
Identified inherent conflicts between biological and economic timelines affecting fertility.
Demonstrated that urban architecture plays a critical role in demographic outcomes.
Unveiled the robust relation of demographic inertia through revised structural definitions.
Achieved compatibility with multiple countries' historical demographic data, reflecting predictive accuracy.

Abstract

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. - Cₛtruct (demographic inertia) replacing Cₙorm: engineering solution eliminating endogenous Cdesired component. Cₛtruct = Cₚractice + Cₕeritage only. - Explicit reliability zones: IDJ d/ (g−c) ; endogenous η decay and critical T* formalization. - Monte Carlo for Dark Forest with dual stochastic channels (Tᵣ erosion + Cₛtruct erosion simultaneously). - Migration module: N (t+1) = N (t) · (TFR/2. 1) + M (t) −D (t) with M↔Cₕeritage 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).

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