https://www.liarparadox.org/Linz_Proof.pdf
This Turing Machine description at the top of page 3
q0 WM ⊢* Ĥq0 WM WM ⊢* Ĥ ∞
q0 WM ⊢* Ĥq0 WM WM ⊢* Ĥ y1 qn y2
Is simplified and clarified to this: when Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
embedded_H is expressly not allowed to consider that Ĥ ⟨Ĥ⟩ reaches Ĥ.qn
and halts because this requires embedded_H to report on the computation
that contains itself thus breaking the rule that all computations must
be a pure functions of their inputs.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
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