The catalog, and what it refuses to order

One evidence kind dominates another only if it scores at least as high on every one of the five axes and strictly higher on at least one. The diagram below draws the cover relation - the transitive reduction of that order, so an edge means “nothing sits between these two,” not “these two are related somehow.” Levels run bottom to top by longest chain below; two nodes at the same level with no path between them are genuinely incomparable, not merely undrawn.

Over every one of the C(33,4) = 40,920 possible four-record removals from this catalog, the comparable fraction ranges from 36.9% to 60.8%. Which four records you drop decides where in a 23.9-point band this statistic lands. Whatever 49.6% describes, it is not a property of the five axes - it describes this exemplar set at least as much, and treating it as a property of the frame is an over-read.

Blackwell has no completion for credal evidence. Once information is a set of measures rather than a measure, "is E more informative than F" has no settled definition. Two adjacent honesty notes belong with it: componentwise dominance on hand-assigned rungs is a PROXY for Blackwell's order rather than that order, since no garbling kernel is constructed; and the intersection-of-decision-orders claim holds over the full weight simplex, not over the four decisions shipped here.

None known. Stated on the page rather than papered over.

Dominance is also not the only decision-free ordering available - it is simply the coarsest one. Mutual information, any single f-divergence, and Le Cam deficiency each order experiments without naming a decision too, and each disagrees with dominance about some pair. Blackwell’s order is the reference point here because it refuses to decide the most pairs, not because it is the unique way to avoid naming a loss function.

Every kind above carries a construct domain - empirical, formal, synthetic, or any - and every decision below declares which domains it admits. The gate applies before any weighting, because a domain mismatch is not a discount to be priced in: a machine-checked proof about your code carries exactly zero bits about a demand curve, however high its reliability. synthetic is admitted nowhere, for the reason Simulation / Monte Carlo’s own record already states - A deduction with extra steps. Upgrades your understanding of your model, never your model. Monte Carlo error is driven to zero by buying compute, which is why reporting it as uncertainty is a category error.

The corrected renderer partitions on this gate rather than discounting through it. The first draft instead multiplied a gated kind’s score by 0.16 and left it in the ranked column - unsound on its own terms, and a divergence from the estate severity mechanism it was modelled on, which rejects on a domain mismatch rather than discounting through one. That draft’s pricing projection ranked a machine-checked proof third and a Monte Carlo simulation eighth: a domain mismatch, weighted down but not removed, still outscoring evidence that actually reaches the decision. Live, not asserted: under all 4 scored decisions below, Simulation is refused with the identical reason - “synthetic evidence, not admitted here”

Pick a decision. The left-hand column re-ranks by that decision’s own weights; the right-hand column is not a lower tier of the same ranking, it is a different mechanism entirely - a domain mismatch, a failed axis gate, or a meet below the floor, and the reason named is exactly which one. A refused kind has no score to show, because scoring it would imply a ranking this decision never joined.