DKIM is the signature, not the allow-list. SPF says which servers may send. DKIM says this message was signed with a key that belongs to the domain, and the body was not rewritten on the way. You need both, then DMARC to tie them to the From address.
The public key lives at selector._domainkey.yourdomain.com. The selector is not universal. Google uses google. Microsoft uses selector1 and selector2, often as CNAMEs. This checker follows CNAMEs, which is why Microsoft records still show up.
What valid means here
A record is valid when p= holds a parseable key. Empty p= is a revocation, not a missing record. 1024-bit RSA still parses and still gets a warning. Signing is not tested. For that you need a real message and an Authentication-Results header.
Auto-detect is a shortlist, not a zone walk
DNS has no “list every DKIM selector” query. The tool checks a fixed list of names ESPs actually use. If your provider picked krs or a date stamp, it may be on the list. If they picked something weird, type it.
The rest of the authentication stack is in the SPF, DKIM, and DMARC guide, and you can confirm SPF on the same domain with the SPF checker.