Probably a Sagina sp. Most people know the genus for 'Irish moss', Sagina subulata, though there are a number of species both native and introduced.

Thanks, Lycopus. We considered and eliminated Sagina subulata because it has five, not four, petals. But now we read that there are some Sagina species that have four petals, e.g. Sagina procumbens, although this is not always consistent.

Take a look at Polypremum procumbens. (Unless that's a diff name for the same thing?)

Polypremum procumbens is one I am not familiar with but that looks like a good possibility as well. A close look at the flowers should help rule one or the other out.

Agree with Polypremum procumbens.

Thanks, Purpleinopp, Polypremum procumbens is a perfect match in every detail. (It is not the same as Sagina procumbens).

Glad to share a suggestion, my fav plant in the lawn at the moment.

Thanks for the suggestion; P. procumbens may be what I have as well (I never decided what it is; my notes suggest that I've never counted petals).