The Existing World Principle: Two Orthogonal Proofs and a Meta-Proof

We propose the Existing World Principle: A reality incapable of sustaining observers—or any internal distinguishability from non-existence—is ontologically equivalent to non-existence. Only realities that support observers (subsystems registering distinctions) are non-trivial and must allow unboundedly many distinct events (potential infinity toward the future). Finite closed universes exhaust change after a finite number of events, halting registration of distinction and collapsing into equivalence with the void. Thus, finite bounds are not merely unlikely—they are logically incoherent for any ontologically meaningful reality. The principle derives deductively from three minimal primitives: events (state changes), negation (¬), and conjunction (∧), independent of specific dynamical theories. Two orthogonal proofs establish it: Observer-Registration Proof: Finite events → exhaustion of change → no sustained distinction → equivalence to non-existence. No-Possible-Enforcement Proof: In a closed universe, any finite bound enforcer exhausts within the event budget, leading to self-contradiction. A meta-proof shows robustness: non-vacuous finite bounds require counterfactual discrimination, incurring an encoding cost that exceeds the bound (contradiction) or renders them empty (indistinguishable from unbounded cases). This reduces synthetic assumptions in universe modeling, particularly in quantum gravity and cosmology, by grounding key results in pure logic. The principle precedes debates on thermal death or timeless physics by addressing the fundamental conditions for distinguishability from nothing.