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This paper has been withdrawn by the author, due to an error in Proposition 2.2.

Large Language Models~(LLMs) struggle with providing current information due to the outdated pre-training data. Existing methods for updating LLMs, such as knowledge editing and continual fine-tuning, have significant drawbacks in…

This paper has been withdrawn by the authors, due a oversimplified decoherence model. It will be substituted by a new work.

This paper has been withdrawn by the author due to a crucial error in equation.

This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.

The paper has been withdrawn

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This paper has been withdrawn by the author due to a crucial problem in Lemma 3. This equation must be changed.

The paper was withdrawn by the author. It contained various errors.

This paper has been withdrawn by the author due to a crucial sign error in equation 2.

This paper has been withdrawn by the author(s), due to a crucial error in eq. 6.

This paper has been withdrawn by the authors. Because of a misunderstanding, the paper was submitted prematurely to the arXiv. A replacement will follow.

This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.

This paper has been withdrawn due to an incorrect proof.

Major mistake. The paper has been withdrawn.

This paper has been withdrawn by the author due to the incorrect argument for the security.

This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).

The paper is withdrawn due to some errors.

This paper has been withdrawn due to an error, and no further revisions will be made.

This paper has been withdrawn by the author(s), due an error in the proof.