Framework
Modal Realm Network
Kripke-frame semantics mapping possible worlds onto the hypercube
Kripke Frames on H9
The 512 vertices are interpreted as possible worlds. The accessibility relation R is defined by XOR transformations:
R(w₁, w₂) ⇔ ∃ c ∈ C : w₂ = w₁ ⊕ c
Necessarily (□)
A property holds necessarily at w if it holds at all accessible worlds — i.e., it is C-invariant.
Possibly (◊)
A property is possible at w if it holds at some accessible world — reachable through a specific transformation.
Axioms as Modal Properties
The five axioms of existence are modal-logical statements over this Kripke frame, constraining which patterns qualify as “existing” entities across the network of 512 possible worlds.