Title: A Structural Analysis of the Standard Halting Problem Proof

Title: A Structural Analysis of the Standard Halting Problem Proof
Author: PL Olcott
Abstract:
This paper presents a formal critique of the standard proof of the undecidability of the Halting Problem. While we do not dispute the conclusion that the Halting Problem is undecidable, we argue that the conventional proof fails to establish this conclusion due to a fundamental misapplication of Turing machine semantics. Specifically, we show that the contradiction used in the proof arises from conflating the behavior of encoded simulations with direct execution, and from making assumptions about a decider's domain that do not hold under a rigorous model of computation.
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