I've never seen an agent loop "reorder, rewrite, or inject fresh timestamps" each turn other than mostly towards the end of the messages. Messing with a large part of the context every turn would be a fairly crazy thing to do.
It's a really lazy one too - there are so many open source harnesses, including e.g. Codex and Kimi-CLI, and of course the leaked Claude Code source, so it's trivial to verify if someone even just bothered to ask an agent to check actual source code examples.