xu-2024-cantor-pairing-flattens-2d-enumeration
IN premise — summaries/2026/08/24/xu-2024-hallucination-innate-s2-training-and-validation-iteration.md
Created 2026-08-24T17:11:29+00:00
Xu et al. (2024) use the Cantor pairing function k = (i+j)(i+j+1)/2 + j to flatten the 2D enumeration of (model index i × training-state index j) into a single sequence {ĥ₀, ĥ₁, …}, enabling the diagonalization construction of a defeating ground-truth function.
Summary
The authors collapse a two-dimensional problem—matching each model to each training scenario—into one flat numbered list using a classic pairing trick. That flattening is the key step that lets them walk down the diagonal and build a ground-truth signal guaranteed to defeat every model in the list.