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Solar activity, along with its GCR, has been decreasing, not increasing. The subsequent model predicts that we should be getting cooling, not heating. So clearly the model is wrong. It doesn't take much nuance to understand that.
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For comparison, here are graphs of solar activity, along with several other natural factors, compared to temperatures as measured. As you can see, the only graph which the measured temperature tracks is the anthropogenic component:
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There is a very long TCS and ECS associated with the sun. Decades long and centuries long. Your thinking is too simplistic.