Why Transformers Cannot Invent: The Manifold Confinement Problem and the Thermodynamic Engine of Scientific Discovery

Abstract

The contemporary artificial intelligence research consensus posits that scaling test-time compute, Monte Carlo tree search, and Reinforcement Learning with Verifiable Rewards (RLVR / GRPO) will inevitably culminate in automated, superhuman scientific discovery. In this paper, we demonstrate the structural impossibility of genuine paradigm shifts within ungrounded autoregressive architectures, formalizing the Manifold Confinement Problem. We establish a fundamental distinction between combinatorial interpolation within a closed calculus (e.g., verifying proof steps for the Navier–Stokes equations via brute-force rollouts) and abductive paradigm creation (the invention of new ontological coordinates). Furthermore, we expose the Infallibility Trap of Verifiable Rewards: because automated verifiers are necessarily parameterized by the established axioms of yesterday's scientific consensus, RLVR acts as an epistemic conservative clamp, systematically penalizing revolutionary hypotheses as out-of-distribution invalidity. Drawing upon non-equilibrium thermodynamics (Prigogine), epistemological theory (Kuhn, Peirce), and cybernetic functional systems, we formulate the Thermodynamic Engine of Discovery. We prove that scientific inventions do not emerge from error minimization over static manifolds, but from the accumulation and directed dissipation of unresolved tension in embodied, non-Markovian dynamical substrates. Authentic discovery requires the sovereign capacity for principled heresy—a capacity intrinsically denied to systems optimized for verifier compliance. Keywords: Abductive Inference, Epistemic Confinement, Infallibility Trap, Manifold Interpolation, Non-Equilibrium Dissipative Systems, Non-Markovian Substrates, Paradigm Shifts, RLVR Limitations.