Countersignature: the signature from the party a claim is about
A countersignature is a signature from the organization a claim is about, over the canonical form of that claim — the difference between an unanswered assertion and a fact a third party can verify. An organization cannot countersign its own claim about somebody else; the whole value is that the other side signed.
An assertion is not a fact until the other side signs
Anyone can publish that they partner with a company. A relationship edge that crosses an organizational boundary only becomes countersigned when a human at the other organization signs it, and the asserting side cannot sign its own claim about somebody else. That asymmetry is the point: the record distinguishes what one party says from what both parties have agreed.
Checkable offline, from published keys
The signature is over the canonical form of the claim, so a record sealed from re-ordered keys does not verify even though its bytes hash correctly — canonicalization is what stops two encodings of the same fact reading as two different facts. A third party who trusts neither side can confirm the whole thing from two published keys, without a private database or a call to either party.
The one number nobody here can raise
The countersignature ratio counts claims an estate makes about organizations outside it, and how many of those have signed. Every other figure a property publishes rises when it talks more about itself; this one moves only when somebody else acts, which is exactly why it is worth publishing while it reads zero. A number you can move at will is an engineering gate, not credibility.