Social media, digital persona and identity construction

Read the following prompt: 'Social media encourages the cultivation of a polished digital persona, often creating a disconnect between how we present ourselves to the world and who we are in private.' Write a structured essay paragraph (150-200 words) that explores this tension. Define your own framework for identity, using the variables $I_p$ for your 'Public Persona' and $I_v$ for your 'Validated Internal Self'. Argue whether the gap, represented by $G = |I_p - I_v|$, is an inevitable consequence of modern maturity or a threat to mental health, specifically when the intensity of the gap exceeds a personal threshold $au$, such that $G > \tau$.