This paper introduces the Convergent Authenticity Model, a novel framework for understanding and enhancing Human-AI collaboration in organizational settings. Drawing from existentialist philosophies of Jean-Paul Sartre and Martin Heidegger, we explore the concept of authenticity as it applies to both humans and artificial intelligence (AI). The paper delves into how the authenticity in human team members, characterized by emotions and ethical judgment, synergizes with the operational authenticity of AI, defined by reliability and algorithmic precision. This constructive collaboration is crucial in addressing challenges posed by the Uncanny Valley and anthropocentric biases, which significantly impact perceptions and interactions in Human-AI teams. The model emphasizes the importance of balancing human emotional depth with AI's analytical capabilities, fostering a collaborative environment where both entities contribute uniquely to team dynamics. By integrating existential perspectives with practical organizational behavior, the Convergent Authenticity Model offers a framework for optimizing team effectiveness and navigating the ethical implications of AI integration in the workforce.