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What’s Wrong with Contagious Purity? Debunking the Myth that Jesus Never Became Ritually Impure

The view that Jesus could not be affected by impurity and that Jesus was able to spread his purity to others is based on faulty assumptions and invalid inferences.
Tangled up in Techēlet: Tzitzit (Ritual Tassels) in the Time of Jesus

Although the wearing of tzitzit is enjoined in Scripture, we do not find records of its actual observance until the Second Temple period.