At 8 Å for residues 1–70, 2K39 and 6V5D contact graphs can agree with model weight ratios ≤3 but not ≤2.

For chain A, author residues 1–70, sequence separation greater than 2, and C-alpha distance <8 Å, the 2K39 and 6V5D ensembles differ on eight majority-contact labels. Using one positive model-weight vector per entry, a planned ratio grid first gives matching graphs at R=3; exact integer witnesses retain the 2,270 initially shared labels and produce a 168-edge graph. At R=2, individual bounds and exact rational dual certificates exclude all 256 possible shared assignments on the eight differing pairs, even when other labels may change. Coordinate values are fixed, and the initial labels also remain fixed within the recorded ±0.0005 Å coordinate-axis bounds. The minimum feasible continuous ratio was not determined. These calculations apply only to the stated structures and rules; they do not establish physical state probabilities or biological causes.

ubiquitin · protein structure ensembles · contact graphs · model weights · linear programming · rational certificates