According to PC 38.01(1), what does "custody" refer to?

The term "custody" as defined by PC 38.01(1) specifically relates to situations where an individual is under arrest or restraint executed by a public servant who is operating under lawful authority. This definition emphasizes that custody is tied to legal processes and the authority of law enforcement officers. The context of lawful authority is critical, as it establishes that the person in custody is not simply staying in a place voluntarily but is there because they are being detained for a legal reason.

In examining the other options, they do not capture the legal implications associated with the term "custody" as used in the Penal Code. The notion of voluntarily staying in one place lacks the enforcement angle of custody; control of a child by a parent is about guardianship and does not pertain to the legal implications of custody under arrest; and supervising a student at lunch reflects a more informal type of oversight, which again does not align with the legal framework defined in the context of custody.