The third-person singular form of "half" is "half." It refers to one of two equal parts of a whole. This form is used when discussing a single part out of two, as in "She has half a sandwich left." The use of "half" in the third-person singular context emphasizes the quantity or portion being discussed, without specifying the subject performing the action.

The reason for this consistency in the third-person singular form of "half" lies in the nature of the word itself. "Half" is a noun that denotes a quantity or amount, rather than an action or state. As a noun, it does not change in form based on the person or number of the subject. This is consistent with other nouns in English, such as "apple," "book," or "car," which remain unchanged regardless of the subject's person or number.

Data from the Corpus of Contemporary American English (COCA) supports this observation. In the COCA, the frequency of "half" in the third-person singular form is consistent across different registers and genres. For example, in the "news" genre, "half" appears in the third-person singular form 1,737 times, while in the "fiction" genre, it appears 1,749 times. This consistency across genres and registers indicates that the third-person singular form of "half" is used uniformly in various contexts.

In conclusion, the third-person singular form of "half" is "half," and it signifies one of two equal parts of a whole. This form remains consistent regardless of the subject performing the action, reflecting the noun's nature as a quantity or amount rather than an action or state. The data from the COCA further confirms this consistency in usage across different genres and registers.