Axiom 1
Relational Existence
All things exist relative to other things
Formal Definition
∀ x ∈ X : Exists(x) ⇔ ∃ y ≠ x : (x,y) ∈ R ∨ (y,x) ∈ R
Interpretation
Nothing exists in isolation. An entity without relations to other entities does not exist — this is a structural, not epistemic, claim. In H9, every vertex has degree 9, so A1 is automatically satisfied: every realm relates to exactly 9 others through single-bit adjacency.
Philosophical Grounding
A1 connects to structural realism (reality = structure of relations, not intrinsic nature of relata) and the relational interpretation of quantum mechanics (physical quantities defined only relative to other systems).