At a glance, calcite or quartz. But then you said it's harder than quartz. I don't think so. You should re-check that. Being from Arkansas, a diamond state, and describing greasy, a diagnostic test for diamond, are you thinking it's diamond? It's related to the rare Herkimer Diamond. Good luck to you.
I don't know what it is?
My grandpa use to help me identify my finds this and another unknown (coprolite possibly ) we were working on identifying when he died in July. I thought I should continue what we started.
Grandpa thought it was possibly a diamond,
because it was greasy,
the multiple hardness test results,
no conchoidal fractures,
the four sided cleavage
the multiple positive diamond responses when a tester was used on a flat area of the specimen.
Grandpa and his mother had found yellow and brown diamonds in the same area. Great-grandma in early 1900’s found a 10 Ct yellow diamond (her dad had cut in NYC) in the same area
Thanks for your comments