> My question is what should the /var/run/php/php7.0-fpm.sock have as
> permission?

It should have rw (read/write) access for whatever user/group nginx is running under (by default nobody).

Depending on which service (nginx or php-fpm) is running under correct user either change the nginx configuration/user to match the sock file ownership ( http://nginx.org/en/docs/ngx_core_module.html#user ) or check your php-fpm.conf for:

listen = in your case should be /var/run/php/php7.0-fpm.sock
and adjust accordingly:

listen.mode = 0660
listen.owner = ...

rr

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