A Preliminary Formalism of Pre-Asymmetry in Generative Relational Theory: On the Formal Conditions Preceding Relational Asymmetry

Generative Relational Theory (GR) treats relational structures as historically situated, relationally constituted, and generatively evolving. This orientation repeatedly requires distinctions among difference, asymmetry, relational differentiation, and the conditions under which such distinctions become meaningful. This paper develops a preliminary formalism for pre-asymmetry: the conditional domain in which the antecedents of a determinate relational asymmetry are analyzed without assigning them a single ontological origin. Three regimes are kept open: antecedent symmetry, asymmetry that is primitive relative to the selected model domain, and a pre-differentiated regime in which the transformations required for a symmetry judgment are only partially defined. The third regime motivates partial operations, inverse-semigroup structures, and restriction-categorical representations of definedness. Once symmetry is sufficiently articulated, group actions, orbits, stabilizers, and residual subgroups provide a precise language for relational interchangeability and for one route to symmetry-reduction-generated differentiation. The paper keeps structural formalization distinct from dynamical explanation: perturbative reduction, bifurcation, stochastic selection, high-susceptibility amplification, and historical accumulation are formulated as candidate mechanism families. A bounded application to relational power further shows that typed asymmetry requires an additional trajectory-shaping condition before it becomes power-relevant. The framework preserves ontological suspension while making the formal conditions of symmetry and asymmetry available for conditional analysis.