How sharp is a finite-time guarantee for a splitting algorithm? An upper bound can be correct without revealing the best constant, whether equality is possible, or what kind of example comes closest. This candidate answers those questions for an averaged primal-dual comparison gap in Davis–Yin three-operator splitting. Across the full unrelaxed step-size range, the exact denominator after K iterations is K plus one minus alpha L. In the natural splitting metric the coefficient is one half of the corresponding coefficient for the sum of primal and scaled dual squared distances. The proof is an exact identity: the difference between the bound and the gap decomposes into convexity slacks, smooth interpolation deficits, variances and explicit squares. Every term has the sign needed for the upper bound. A two-dimensional family approaches equality and proves that neither coefficient can be improved. The geometry also explains non-attainment. One iteration can attain the bound, but after two or more iterations no finite-dimensional instance with positive denominator attains either supremum in the open step range. The revision also treats the critical endpoint alpha L equal to two. For K at least two, the exact denominator becomes K minus one. Strict convexity of f rules out endpoint attainment, but attainment in the unrestricted endpoint class is not claimed to be resolved. The sharpness construction uses arbitrary admissible comparison pairs. It does not establish the same constant when comparisons are restricted to saddle points, and it is not a last-iterate rate, an objective-error rate or a lower bound for other algorithms. Exact arithmetic replay checks representative identities in ordinary and optimized Python and rejects deliberately corrupted trajectories and constants. Those checks support the formulas but do not replace the universal proof. This is an unrefereed AI-assisted research candidate. The paper, evidence and code are linked on the Evidence Press release page. This briefing uses an AI-generated voice and is not additional scientific evidence.