The map

Where the literature lives

Four regions and a wall. Almost everything is on the left, improving the coverage certificate; the wall is the information gap, built from the no-go theorems; and one quadrant on the right is nearly empty. That emptiness is the point of this site.

Every dot is a paper from the bibliography (hover for the one-line reading, click to open). The left half works in the coverage currency: the top quadrant relaxes the assumptions the guarantee needs, the bottom refines what the certificate says — sharper laws, broader loss classes, group-conditional targets, smaller sets at fixed coverage. None of it moves the forecast: by the results mortared into the wall, no re-levelling of coverage can add conditional information. The right half works in the sharpness currency: the top quadrant measures what marginal calibration leaves on the table; the bottom quadrant belongs to the wrapped model, not to conformal prediction. The dashed markers are open problems.

Why the wall is one structure rather than eight separate results: a procedure whose guarantee holds for every continuous distribution is, by the classical characterization of distribution-free statistics, a function of the ranks. The information that conditional coverage and sharpness require lives in the concomitants: the x-values riding alongside the order statistics. The rank σ-algebra discards them by construction. The left half of the map works inside the rank σ-algebra; the right half asks about what it discarded; the bricks are quantitative versions of that one decomposition.

Placement within a region is alphabetical-ish and means nothing; the region does. Boundary cases are noted in their tooltips (localized and group-conditional methods spend information about x inside the wrapper, which is as close as the coverage currency gets to the wall). Dashed outlines are problems, not papers. Corrections welcome — especially nominations for the empty quadrant.