In its current form, the Definition "Chi-square distribution" is ambigous as it contains (i) a definition of the chi-square distribution from the standard normal distribution and (ii) a definition of the chi-square distribution based on its probability density function (PDF). The PDF in (ii) needs to be derived from the definition in (i), e.g. following this proof in Wikipedia, and the derivation needs to be added as the Proof "Probability density function of the chi-square distribution". Then, the second version should be removed from the Definition "Chi-square distribution".
In its current form, the Definition "Chi-square distribution" is ambigous as it contains (i) a definition of the chi-square distribution from the standard normal distribution and (ii) a definition of the chi-square distribution based on its probability density function (PDF). The PDF in (ii) needs to be derived from the definition in (i), e.g. following this proof in Wikipedia, and the derivation needs to be added as the Proof "Probability density function of the chi-square distribution". Then, the second version should be removed from the Definition "Chi-square distribution".