Abstract
<title>Abstract</title> <p>Evaluating socioeconomic vulnerability represents a critical challenge for social policies in emerging economies, particularly during the macroeconomic transition from regressive universal subsidies to targeted direct cash transfers. The primary obstacle to optimal state allocation is the informational asymmetry within the informal sector, where traditional Proxy Means Testing (PMT) systematically misinterprets depreciating physical assets as generative wealth and fails to account for the structural burden of informal debt. This paper proposes a novel microeconomic framework aimed at accurately detecting multidimensional household vulnerability without penalizing the working poor. We introduce the ''Algorithmic Vulnerability Gap'' (AVG), a deterministic mechanism that replaces static proxy scoring with a dynamic deficit calculation. The AVG isolates the precise monetary deprivation of a household by deducting its true generative capacity---aggregating declared income, geometrically depreciating assets ($\delta$), and subtracting algorithmically bounded informal debt ($\hat{D}_{inf}$)---from a strictly defined survival baseline. The framework is validated through a dual-methodological approach. First, a macro-scale Monte Carlo simulation ($N=10,000,000$ households) demonstrates the model's theoretical capacity to eliminate inclusion errors (0\% leakage) while dynamically outputting exact sovereign budget ceilings. Second, empirical robustness is verified utilizing the World Bank's LSMS-ISA Harmonised Panel ($N=148,421$ households) of Nigeria . The empirical application successfully translates categorical asset indices into continuous monetary proxies, deterministically calculating exact household deficits and outputting a precise sovereign liability (1.44 billion LCU). The combined results indicate that the AVG architecture provides a mathematically equitable and fiscally impenetrable solution for managing Unified Social Registries (USR).</p>