What I can remember:
Harry lives with the Dursleys, he and Dudley go to the park. Harry plays with a girl while her mother watches.
The girl's mother eventually talks to Petunia on the park bench about taking guardianship of Harry. (I think the mother threatens Petunia.) Petunia agrees.
Once Harry moves in, he and the girl sleep in the same bed and play naked. (Not sexually, they are very young and don't care for clothes)
As they get a bit older, they are very smart and curious. They get homeschooled. They're taught all the normal subjects but in depth.
At some point they find out Harry is a wizard and they learn about magic too.
Somehow they figure a way for electronics to work around magic. He uses diamond to encase the wires and circuits and it negates the effect of magic. He also finds out a way to make diamonds himself and sells some to the goblins at Gringotts.
The mother finds that runes in the magical world are essentially the same as circuits for electricity in the muggle world.
I think they move into a manor and eventually have their muggle and magical friends over. I think they go bowling and have a Halloween party.
That's where my remembrance ends.
I hope someone can tell me the name or author of this fic. I'm almost positive I read it on FanFiction.net or AO3. Thanks in advance for any answers, wrong or right.