Relational Happiness Discrepancy Model (RHDM): A Conceptual Mathematical Framework for Social Presence, Expectations, Hope and Trust

This conceptual preprint proposes the Relational Happiness Discrepancy Model (RHDM), a mathematical framework for analysing event-level affective appraisal in interpersonal relationships. The model distinguishes realised relational affect from expectation discrepancy and introduces social presence as an estimable modulation rather than a fixed physical-presence multiplier. It further replaces an earlier sign-inconsistent hope–trust extension with a bounded negative-discrepancy buffer. The core appraisal equation is A = (R − E)₊ − [1 − λB(P,T)](E − R)₊, with R = nx and (z)₊ = max(z,0). A broader discrepancy-adjusted index is H* = R + κA. The framework is situated alongside expectancy-disconfirmation theory, reward-prediction-error models of momentary subjective well-being, affective forecasting, social-interaction research, hope theory and interpersonal trust. This Version 1 manuscript is conceptual. It is not peer-reviewed and reports no original participant data. Its mathematical propositions and behavioural hypotheses are intended for future empirical testing using repeated event-level or experience-sampling data.