Update-Relevant Support: Hume's Missing Descent

The hidden-support account of confounding gives a negative result: the same baseline public law, even augmented by the true average treatment effect, may be compatible with either zero or arbitrarily large update-relevant structural gap. This paper develops the corresponding positive theory, with one correction: arbitrary finite environment classes determine a nonempty poset of adequate supports that need not have a least element. A finite three-state example shows why the existence hypothesis is substantive. In the public-fiber-saturated case, however, the poset has a least element: the quotient generated by public observation and the fiberwise level sets of the estimand contrast. Failed public descent then has an operational measure: the largest disagreement in the target estimand between admissible environments that share a fixed public law, with a global worst-case version obtained by ranging over public laws. This is the diameter of the corresponding partial-identification set, and in saturated finite cases it has closed-form fiber-range formulae. The ordinary log-cardinality support gap remains a useful qualitative obstruction, but it controls transport risk only after calibration by effect separation and reweighting richness. The epistemological payoff is that causal warrant is not regularity plus truth; it is regularity plus the right support for update. Hume's missing necessity becomes missing descent.