Persistent identifiers (PIDs) are crucial to enabling and achieving the goals of the FAIR principles, which describe how research data and other entities within the research lifecycle should be made Findable, Accessible, Interoperable, and Reusable (FAIR). The FAIR-IMPACT project works with PID service providers to better understand and address user needs, align with the EOSC PID policy, and promote the widespread adoption of PIDs. These objectives are addressed within a dedicated Work Package (WP) focused on PIDs, contributing to the relevant activity areas of the EOSC Strategic Research and Innovation Agenda (SRIA). Achieving these goals requires enhanced coordination between PID service providers and EOSC (EOSC), ensuring PIDs are available for a wide variety of research outputs, including publications, datasets, software, instruments, services, people, and organisations. Following the development of a joint value proposition by PID providers, a proposed coordination mechanism across EOSC, and streamlining the requirements for onboarding PID service providers into EOSC, this report outlines the shared long-term vision for PID service providers regarding the use of persistent identifiers (PIDs) in the EOSC.