AGI is Mathematically Impossible 2: When Entropy Returns - Infinite Choice Barrier, Shannon Revisited

In a second paper on PhilArchive, Max M. Schlereth of USTP St. Poelten argues that artificial general intelligence is "mathematically impossible". Where the first paper used computability theory, this one offers an information-theoretic proof of what Schlereth calls the Infinite Choice Barrier: in decision spaces governed by heavy-tailed distributions with a tail exponent of at most 1, entropy does not converge, and "additional information increases uncertainty rather than reducing it", a phenomenon named IOpenER (Information Opens, Entropy Rises). Such spaces, the paper claims, cannot be decided by algorithmic systems "regardless of compute scale or architectural depth", and its Layer Hypothesis predicts more semantic divergence from deeper models under structural instability. An author's note of June 2025 says that the reasoning collapse Apple's The Illusion of Thinking later reported in advanced reasoning models closely mirrors the paper's predictions.

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