Ω Relational Geometry introduces a minimal structural instrument for analysing nested relational systems across domains. Nested relations are represented as binary relational trees whose transformation space corresponds to associahedron geometry. Within this configuration space, a structural invariant μ is defined as the expected terminal depth of the tree. μP (T) = E䄲~dT (ℓ) In the uniform case this reduces to the mean terminal depth μ (T). The invariant provides a scalar measure over the configuration space of nested relational structures and acts as a minimal indicator of structural direction under local transformations. The instrument is derived from three earlier conceptual works: • Law of Existence (2026) • Admissible Distinction Condition (2026) • Constraint Continuity Hypothesis (2026) These works establish minimal conditions for distinguishable persistence. Ω Relational Geometry introduces a structural representation capable of operationalising these conditions across domains. Artificial intelligence systems were used as analytical instruments during the research process. Conceptual direction and authorship remain the work of the author. This work is intentionally released for cross-domain testing and attempted falsification.
Reuben Munro (2026) studied this question.