The two seconds that set the terms of everything after
Every greeting makes an offer about closeness, formality and time, and the reply either accepts it or quietly renegotiates.
Watch two people meet and you can usually see the offer being made. One of them commits first: a shorter greeting or a longer one, a warmer tone or a cooler one, a name used or withheld. The other has a fraction of a second to respond, and the response is rarely a copy. It is an adjustment. Slightly warmer, slightly more careful, slightly briefer. What emerges is a negotiated position that neither person chose alone and neither could describe afterwards. It holds for the rest of the conversation, and often for the rest of the relationship, unless something deliberate is done to move it.
The terms being set are more specific than warmth. There is a time clause, for one. A greeting delivered on the move without slowing says that this is an acknowledgement rather than an opening, and both parties understand it. A greeting delivered with a stop and a turn of the body says that time is available. Getting this wrong is a common small injury: one person stops, ready to talk, while the other has already passed. There is also a status clause, carried by who speaks first, who waits, and whether a title appears. And there is a closeness clause, which is the one most people notice, because it is the one that stings.
The practical value in seeing a greeting as a contract is that contracts can be amended. If the terms that got set are not the ones you wanted, you can propose new ones later without drama. A second, warmer greeting the next time you meet. A deliberate use of somebody's name. A pause where last time you kept walking. People accept amendments readily, because most of them were not attached to the original terms either. They were just responding, quickly, to whatever arrived first.