It looks like Cutleaf Stephanandra (Stephanandra incisa).

sorry, I forgot to add something for scale, the leaves are just about 1mm or smaller than a corn of rice

Compare it to Herniaria glabra. I cannot see the leaf details from the photo, but that is what it looks like to me.

Whatever it is, it's adorable! Also compare to Hemianthus callitrichoides. There are a bunch of these ground covers named here, but not necessarily pictured well:

https://www.stepables.com/scripts/STEPABLES_Lawn_Substitution.html

hi there

thanks for your posts

I looked into Herniaria,

and tried to enlagen a bit from the pic

I am quite sure, that this is something different, the tiny stalks are kind of smoother.

here is a cropped bit from the first pic, perhaps that helps for the details

but funnily enough, when looking through the pics again, I think there is some Herniaria glabra growing in a different spot ;-)

so, this is a different plant, and I would say: this is Herniaria

in the comparison it seems that Herniaria is somewhat "more nobbly" or branching,

I try tp post the first pic at another site and will report back,

thank, Lin

@Tiffany, I think the Hemianthus is too thirsty for that spot, but did not find detailed pics of the foliage to say for sure, thanks again

Are the stems wiry/woody like Thyme, or soft and herbaceous? (I know it's not thyme - I'm trying to get a feel for the texture.)

Can you get a close up of those tiny flowers/buds?

Hi Floral

I crushed one tiny stem and would say, soft,

a fellow plant person just threw Paronychia into the discussion,

I tried to look it up, there seems to be a species ,

P. kapela ssp. serpyllifolia, so there is the thyme in the name.

sorry, dont have another pic or better close up.

But I think that could fit, at least the genus,

funny, such a tiny non-descriptive plant, but I think you will always recognize it after dealing with it once.

I want all of these plants, so sweet! I think your fellow plant person's throw was accurate too.

https://plants.ces.ncsu.edu/plants/paronychia-kapela/

https://powo.science.kew.org/taxon/urn:lsid:ipni.org:names:435061-1

https://www.ukwildflowers.com/Web_pages/paronychia_kapela_ssp_serpyllifolia_silver_nailwort.htm

https://garden.org/plants/view/409706/Silver-Nailwort-Paronychia-kapela-subsp-serpyllifolia/

I belive Herniaia is what I have growing in a part of my yard……very easy to manage. Pulls out easily and transplants well to.

debra