MEANING-CRDT: Conflict-Free Replicated Semantics in Dyadic Social Systems

We present a formal model of shared meaning in dyadic relationships — couples, co-authors, partners — built on state-based Conflict-Free Replicated Data Types (CRDTs). Each agent maintains a local semantic state: a position, an importance weight, and a logical timestamp across a finite set of meaning dimensions. When concurrent updates conflict, a resolve policy maps competing states to a single joint outcome. We define and analyze three such policies: Dominance (DOM), Last-Writer-Wins (LWW), and Care-weighted averaging (CARE). Using total dissatisfaction, fairness, convergence, and identity preservation as evaluation criteria, we establish seven results: (1) CARE uniquely minimizes total system loss under a quadratic objective; (2) at equal importance weights, CARE reduces the overridden agent's loss fourfold relative to DOM; (3) LWW produces non-convergent oscillations under reactive timestamp-racing agents; (4) CARE with adaptive position dynamics yields exponential convergence of disagreement and a finite accumulated meaning debt; (5) DOM asymptotically erases the subordinate agent's contribution, while CARE preserves both; (6) CARE is equivalent to Bayesian precision-weighted belief fusion under Gaussian assumptions; (7) CARE is incentive-incompatible — agents always gain by inflating declared importance — connecting the model to mechanism design and motivating cost-of-influence extensions.