The Domain Name System (DNS) is essential to Internet naming and service discovery, yet it is also implicated in malicious domain use, phishing, malware infrastructure, botnet coordination, and other forms of abuse. Detection and mitigation systems must reduce malicious activity without unnecessarily blocking legitimate queries or imposing unacceptable resolution delays. This paper develops PROJECT DIANA (Digital Infrastructure and Adversarial Network Abuse), a mathematical framework for analysing the relationship between attacker autonomy, DNS defensive effectiveness, and DNS-level preservation of legitimate activity. The framework represents the environment as a stochastic dynamical system, models attacker autonomy as a parameter of a state-dependent policy, defines security and openness measures, and formulates a constrained optimisation problem and securityopenness Pareto set. It further specifies a feedback model for adaptive defence and a stochastic-game formulation for strategic interaction. A conditional monotonicity proposition is established for nested feasible sets. The manuscript identifies assumptions required to analyse equilibrium existence and local stability, while avoiding unsupported claims that greater autonomy must always reduce openness or that an equilibrium exists in every continuous-state game. DIANA is presented as a theoretical framework requiring further formal analysis and controlled empirical validation, not as an experimentally validated defence system Keywords: DNS security; DNS abuse; attacker autonomy; adaptive defence; security–openness trade-off; constrained optimisation; Pareto frontier; stochastic games; Markov perfect equilibrium; dynamical stability.