U: the order of uncertainty

The two top rungs are where real pricing teams fail, and the two failures are not the same failure. Each rung states its own limit plainly.

Both limits are structural, so neither is bought off with a larger sample. The width at rung 5 is a property of the identification problem; the bound at rung 6 is a property of a channel outside the model. That is what leaves an out-of-model track record as the only routinely available promoter at the top of this ladder, and it is why the last rung ships with a cap instead of a probability.

A LossCap bounds the consequence, not the distribution. It is what remains sayable when the tail is genuinely unknown: not that the error is smaller than some region, but that the error costs less than some amount.

The mechanical difference is what each one quantifies over. A distributional bound quantifies over outcomes, and every draw from the law lands inside the stated region - a claim available only from inside a model class. A LossCap quantifies over exposure instead. It names the worst realized loss you have agreed to carry and the action that stops the loss there, and asserts nothing about the shape of the residual.

The rung-6 pricing line already carries one:

"Competitor repricing is unmodeled and could contribute 4 volume points, +/- $36k on this SKU; our exposure is capped by a 30-day revert clause."

The 30-day revert clause does not predict the elasticity, and does not bound the competitor repricing the model never represented. It bounds what a wrong elasticity can cost: thirty days of mispriced margin on one SKU, then the price goes back. Unmodeled and capped are compatible states, which is the point of the rung.

The cap is worth exactly what its enforcement is worth, and that is the failure condition. If the revert depends on a decision nobody owns, or on a system that cannot reprice inside a month, then the cap was never a cap. That is why it sits at rung 6 rather than substituting for the rungs beneath it. A cap tells you what a failure costs. It never tells you whether one is coming.

The obvious move at U3 (Calibrated predictive (error on error)) is to put a model over the model: if the coverage claim might be wrong, estimate the error on the error. It does not work, and the near-miss version of why is repeated often enough to be worth stating exactly. Rung 3 is not promoted by:

A hierarchical model. Dist(Dist(A)) collapses to Dist(A) under the Giry monad multiplication - integrate out the mixing measure - so stacking hyperpriors produces fatter tails and never an escape from the regress. Two qualifiers the first draft dropped. (1) This is monad multiplication, not the tower property; the tower property is the conditional-expectation identity that makes the collapse decision-irrelevant, which is a different fact. (2) The collapse is decision-irrelevant only because Bayes risk is AFFINE in the predictive measure, so a decision maker sees the marginal and nothing else. That is exactly the assumption rung 4 abandons: a credal set has no mixing measure to integrate, so there is no marginal to collapse to, and the regress genuinely stops being a regress. The escape from error-on-error is not more levels, it is refusing to mix.