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We have no evidence in favor of the linear no threshold model. That is not the same as saying that we have evidence against it.
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There is some evidence for hormesis - but yes no model is proven right now. LNT is the most conservative model and part of why it sticks around.

A good primer: https://pmc.ncbi.nlm.nih.gov/articles/PMC2477686/

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LNT does also damage, as people refusing necessary CT scans or countries switching of nuclear power because of fear.
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Sure but we don’t prove negatives for a reason - it’s impossible. We assume the null hypothesis.
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LNT is the null hypothesis. No one disagrees a linear model fits the data very well in high doses. If you want to argue that model doesn't work in low doses, you need a model with more parameters and sufficient data to fit it. The issue is that, at these low doses we want to differentiate, we're also looking at effect sizes that are hard to separate from noise, and sampling biases that are hard to erase. There's still lively and ongoing debate.
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Well problem is that humans are so noisy through lifestyle, enviroment and genes that any proof for either is really hard.
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Another problem is that there haven't been natural experiments in low dose exposures the way there unfortunately have been for high dose exposures.
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Weekly CTs are going to give you cancer
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Your link does not support, and in fact refutes, your claim
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