The Five Axioms of Existence

Each axiom is a modal-logical statement over the Kripke frame of 512 possible worlds, constraining which patterns qualify as “real” entities.

Axiom 1

Relational Existence

An entity exists only if it participates in at least one relation. Nothing exists in isolation.

∀x: Exists(x) ⇔ ∃y≠x: (x,y)∈R ∨ (y,x)∈R

Axiom 2

Structural Compressibility

Real patterns have compressed descriptions shorter than their exhaustive encoding.

K(x) + c < |E(x)|

Axiom 3

Multi-Scale Persistence

Real entities persist as recognizable patterns across time and scale under coarse-graining.

d(G_s(x), G_s'(x)) ≤ ε

Axiom 4

Energetic Cost of Erasure

Erasing information requires non-zero energy per Landauer’s principle.

E ≥ k_B · T · ln(2) · H(x)

Axiom 5

Self-Reference for Consciousness

A conscious system contains a self-modeling subsystem that updates recursively.

M(t+1) = f(M(t), S(t))