How do you measure adoption of an open protocol?
Network density is the share of a machine-readable record that describes a relationship between two different organizations rather than an organization describing itself — and, within that, the share a second party has signed. It is the measure that separates a protocol from a filing cabinet: a record can hold thousands of entries, every one self-asserted, and have a density near zero.
Every easy number measures distribution, not adoption
The numbers a network publishes about itself are almost always the ones it can grow without anyone else agreeing to anything. Nodes, records, integrations, logos on a page: each can be increased unilaterally, and none of them requires a second party to have looked at the claim, let alone confirmed it. An estate that owns a hundred properties can publish one organization a hundred times and report a hundred entries.
That is not dishonest so much as it is a category error. A hundred copies of one fact is one fact with a distribution problem. The reason it survives is that the alternative is a number that starts at zero and stays there for as long as it takes somebody outside to act — which is exactly the property that makes it worth publishing and exactly why almost nobody does.
Four counts, each strictly inside the last
Assertions — every claim in the record, before any judgement. Distinct facts — the same subject, predicate and object claimed by twelve properties collapses to one; the eleven others are plumbing. Cross-organizational facts — of those, the ones where both ends are organizations and they are different organizations. An organization naming its own agents, its own properties and its own accountable human is filling in a form about itself: worth having, not a relationship. Countersigned facts — of those, the ones the second party has signed.
The ratios between the four are the diagnostic, and the last two are where every record of this kind actually gets tested. Cross-organizational facts as a share of distinct facts is connectivity; it answers whether the thing is a network or a directory of self-portraits. Countersignatures as a share of cross-organizational facts answers whether the relationships are agreed or merely announced.
Relatedness is computed, not declared
A record built by a group that owns several companies has a specific failure available to it that a single company does not: the owner signs the subsidiary’s claim, the cryptography verifies perfectly, and what has been proved is that a group agrees with itself. Any adoption number that does not separate those signatures from the rest is measuring enthusiasm within one balance sheet.
So relatedness is derived from the record rather than asserted in it — from declared ownership, from a shared owner, from a shared accountable human — and countersignatures between related parties are counted separately from the rest. Three properties under common control are one counterparty, whatever their branding suggests, and a scoreboard that reports them as three is the one overstating.
The independent figure is a ceiling, never a measurement
There is a limit to what can be derived. Ownership edges are private-tier, so a reader holding only the public record may see two organizations that share a beneficial owner nobody published. Relatedness found is therefore a floor, and independence is at most whatever is left over.
That is not a caveat added to a number; it is the number’s name. The field a reader sees is an at-most, and it is written that way so that somebody who encounters the figure with no surrounding context still cannot mistake it for a count of confirmed arm’s-length adopters. A measure that can only be quoted accurately is worth more than a larger one that cannot.
What this costs the author, which is the reason to believe it
Applied to this estate today, the answer is unflattering and published anyway. Almost every fact in the live record is an organization describing itself, connectivity is a low single-digit percentage, and the count of relationships signed by a second party is zero — as is, necessarily, the count between organizations with no common owner. The signing mechanism is finished, live and open source; it has simply never been exercised by two parties nobody controls.
The functions that produce those numbers are published under the same open licence as the format, so the figure can be recomputed from the public record by anyone who disagrees with it. A protocol that will not state its own adoption honestly is asking to be trusted about everything harder, and an integrator finds out inside a day.
Why density is the part that does not transfer
For anyone assessing a network rather than running one, density is the durable question because it is the only quantity in the system that cannot be bought, ported or rebuilt over a weekend. Software can be reimplemented; a spec can be forked, and this one is licensed so that it can be. What cannot be copied is a set of organizations that have already published a credential at their own domains and signed each other’s claims, because each of those was a decision taken by someone with no obligation to take it.
That is also why the credential has to live at the adopter’s domain rather than in the operator’s database. If standing exists only in the registry, the registry is the asset and the participants are rows in it — and the moment a participant stops paying, the record was never theirs. A network whose density would survive its operator is a network; one whose density is a customer list is a product with good marketing.