Rij(t)R_{ij}(t) is the relational score between agent ii and agent jj at time tt. This scalar value determines the current zone placement (e.g., White, Green, Yellow, etc.) in the Adaptive Relational Zoning (ARZ) framework.
Vk,ij(t)V_{k,ij}(t) is the value of the kk-th relational variable (e.g., honesty, consistency, reciprocity, betrayal indicators, emotional effort, etc.) between ii and jj at time tt. These variables may include both positive (e.g., acts of trust) and negative (e.g., breach of expectation) contributions.
wkw_k is the weight assigned to the kk-th variable, reflecting its relative importance in the domain of interaction. For instance, emotional consistency might be weighted higher in familial relationships, while reliability may dominate in business contexts.
CC is a contextual constant capturing structural, cultural, or systemic biases (e.g., inherited distrust due to historical trauma, or institutional goodwill).
Design Rationale:
Additive Modularity: Allows domain-specific tailoring of the model. A romantic relationship might include emotional resonance and physical presence, while a transactional one may emphasize reliability and speed.
Time Dependence Vk,ij(t)V_{k,ij}(t): Ensures adaptability by tracking changes in behavior or perception over time. This reflects the reality that relationships evolve, decay, or intensify as new actions are taken and past behaviors accrue or degrade in significance.
Weighted Factors: Encourages agent-specific modeling, enabling the system to capture heterogeneous valuation systems---not all agents prioritize the same values equally.
Inclusion of CC: Accounts for relational priors---e.g., previously established goodwill or structural distrust---thereby preventing the model from being memoryless or purely reactive.
Zone Classification Thresholds (Sample Ranges):
While the boundaries are context-specific and adjustable, we propose a flexible threshold scale for initial modeling:
Zone
Relational Score Rij(t)R_{ij}(t) Range
Interpretation
White
R>+15R > +15
Fully integrated trust & identity alignment
