Apple's "The Illusion of Thinking" and the Rebuttal

This research paper from Apple is been quite controversial for several reasons, first of which, Apple lagging behind the AI race: https://machinelearning.apple.com/research/illusion-of-thinking.
Are reasoning models like o1/o3, DeepSeek-R1, and Claude 3.7 Sonnet really “thinking”? Or are they just throwing more compute towards pattern matching?
Apple designed an experiment using Tower of Hanoi to test these models. Well turns out, it was a memory problem, the models were failing because they were going out of context.
Asking the model to be more concise in fact enabled o3 to solve the Tower of Hanoi, as shown in the paper of The Illusion of the Illusion of Thinking — this paper also sign as the first time an LLM, Claude Opus, is listed as an author on arXiv.

https://x.com/rohanpaul_ai/status/1933296859730301353
LLMs are not the only one faking it either: The Illusion Of Human Thinking.