The Dopamine-Driven Discounting Model (D3M): A Unified Neuro-Economic Equation for Predictive Digital Wellness Interventions

Infinite-scroll architectures and gamified application loops leverage variable reward schedules to maximize user retention, often inducing digital addiction and chronic procrastination. Current digital wellness interventions rely heavily on passive, retrospective telemetry (e.g., historical screen-time alerts), failing to preemptively mitigate compulsive engagement. This paper introduces the Dopamine-Driven Discounting Model (D3M), a novel, closed-form behavioral equation that mathematically synthesizes neurobiological Reward Prediction Error (RPE) with behavioral economic Quasi-Hyperbolic (β-δ) Discounting frameworks. By mapping real-time neurological reward surges against temporal cognitive time-preference decay, the D3M computes the instantaneous behavioral probability of state retention (Bscroll). We detail a comprehensive mathematical proof of the equation's boundary conditions, outline a system architecture for deploying this equation as an active, on-device software algorithm capable of dynamically injecting adaptive UI friction (D), and propose a scalable empirical validation methodology to verify the model's predictive power within human-computer interaction (HCI) ecosystems.