[thaumaturgy]

You are choosing a narrow definition of "sex" that isn't supported in current medical literature. Yale for example defines "intersex" as "describing a person whose biological sex is ambiguous" (https://medicine.yale.edu/news-article/what-do-we-mean-by-se...). In 2001, a UN committee was formed to establish some guidelines on the definitions of sex and gender, and "in the study of human subjects, the term sex should be used as a classification according to the reproductive organs and functions that derive from the chromosomal complement" (https://journals.physiology.org/doi/full/10.1152/japplphysio...). Scientific literature is still a bit fuzzy on the issue, especially when describing atypical sex or gender-related matters in humans, and researchers sometimes prefer the term "gender" because of cultural sensitivities (ibid.).

> Intermediate gametes do not exist.

These are called ovotestis in some people with particular forms of intersex conditions. A subset of ovotestis includes gametes containing both "male" and "female" reproductive tissue.