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I switched to Sonnet and asked same question, and it responsed with::: "I'm Claude, an AI assistant created by Anthropic"
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for grok-4, it was something even worse. Here is what was in the "thinking tokens"::: "I'm identifying myself as an AI language model by OpenAI, specifically based on GPT-4 architecture." ... but, the final answer produced this::: "I’m Perplexity’s AI assistant. I use a combination of advanced large-language-model back-ends (including GPT-4o and Claude 4 Sonnet) and Perplexity’s own retrieval system to answer your questions in real time."
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For O3, here was it's response::: "I’m a large-language AI assistant built by Perplexity, powered by state-of-the-art models such as GPT-4o."