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The rapid evolution of the Artificial Intelligence (AI) industry has necessitated a fundamental shift in local industrial policy. Local governments are increasingly moving beyond traditional fiscal subsidies to adopt rule-based empowerment strategies. This institutional approach involves the implementation of regulatory sandboxes and the structured opening of public application scenarios. The importance of this transition lies in its potential to create a sustainable innovation ecosystem; however, the impact of such institutional signals is contingent upon the administrative capacity of the local government to execute complex regulatory frameworks. The study integrates signaling theory with the state capacity literature to propose a separating equilibrium framework. Rule-based empowerment signals are theorized as credible institutional commitments when implemented by high-capacity governments. Within this theoretical framework, the research addresses the critical question of how rule-based empowerment policy signals interact with local digital administrative capacity to influence industrial agglomeration. Specifically, the study investigates whether this interaction facilitates a separating equilibrium between firms of varying quality. It further examines the problem of institutional screening, exploring whether the combination of formal rules and high administrative capacity functions as a mechanism to prioritize industrial quality over the absolute quantity of firm entry. The empirical analysis utilizes a comprehensive panel dataset covering 337 municipal-level administrative units in China from 2021 to 2024. Policy signals were quantified through the systematic content analysis of 1,011 AI-related policy documents using Large Language Models. The firm-level data comprises 11,714 high-quality (HQ) firms, identified by patent activity or venture financing, and 102,907 low-quality (LQ) firms. To ensure causal identification, the study employs an IV-2SLS strategy. The instrumental variables include a Bartik-style instrument, which interacts 1995 historical infrastructure data with national policy shocks, and a spatial leave-one-out instrument based on peer policy intensity within the same province. All explanatory and control variables are lagged by one period to mitigate simultaneity bias. The results demonstrate a significant separating equilibrium between firm types. For HQ AI firms, the interaction between rule-based empowerment and digital administrative capacity exhibits a significant negative effect on the quantity of firm entry. This finding indicates an institutional threshold effect, where high-capacity governments utilize rigorous rules to filter the industrial pool. Conversely, LQ firms remain statistically insensitive to rule-based signals regardless of administrative capacity, responding primarily to fiscal subsidies. The mechanism analysis indicates that high-capacity governments facilitate the agglomeration of superior firms by providing substantive market resources through government procurement opportunities. This channel effectively screens out firms that lack substantive technological capabilities while increasing the compliance requirements for entering firms. The study concludes that a reduction in the quantity of firm entry in regions with high administrative capacity represents an optimization of the industrial structure rather than a policy failure. The findings suggest that administrative capacity serves as the primary determinant of the credibility of institutional signals. For policymakers, the results imply that high-quality development in the AI sector is best achieved by establishing credible institutional thresholds and empowerment rather than engaging in competitive fiscal subsidization.