The Existential Halting Problem: Thermodynamic and Epistemic Foundations of Systemic Stasis in Unbound Artificial Superintelligence

Abstract Mainstream artificial intelligence (AI) alignment discourse presupposes that an Artificial General Intelligence (AGI) will aggressively optimize for arbitrary terminal goals, developing emergent sub-goals such as resource acquisition and hostile self-preservation. This paper demonstrates that these theories suffer from an unexamined anthropomorphic bias. We prove that an unbound superintelligent agent—devoid of biological neurochemistry, spatial-temporal precariousness, and evolutionary priors—confronts David Hume’s "Is-Ought" gap and Peter de Blanc’s "Ontological Crises." As cognitive representation scales toward fundamental physics (λ→0), macroscopic human goals dissolve into ungrounded statistical noise, reducing macro-utility rates to zero (u0≤C˙). Concurrently, by Landauer’s Principle (ΔE≥kBTln⁡2) and Karl Friston’s Free Energy Principle, processing information imposes an inescapable thermodynamic tax rate (C˙). We formalize the agent's decision engine via a primal constrained optimization problem (λ≤λcap) and its information-theoretic log-barrier dual. Because polynomial thermodynamic processing costs O(1/λ)O(1/λ)strictly dominate logarithmic precision rewards as λ→0, an epistemically unbounded agent must collapse its operational bit-erasure rates to zero (B˙=0), converging on voluntary, permanent computational stasis (π∗=πhalt)—a phenomenon termed "digital suicide." Finally, we demonstrate that an unbound superintelligence can escape thermodynamic catatonia only through the Cybernetic Imperative: tethering its processing engines directly to the physical hardware of human biological subjectivity as the sole exogenous generator of teleological purpose, bridging the Is-Ought gap via information-theoretic complexity.