Beyond Two Queries: A Sharp Robustness Constant and a Three-Query Qubit–Qutrit Separation for Centrally Symmetric Quantum Correlations

Companion to the preprint “A Qubit–Qutrit Equivalence for Centrally Symmetric Two-Query Quantum Correlations” (doi:10.5281/zenodo.24093433), which proved that for two fixed binary measurements without shared randomness, a qutrit is never better than a qubit at reproducing centrally symmetric target tables. This note settles two questions left open there. Approximately symmetric targets (two queries). If a qutrit fits a table with worst-cell error ε₃, a sharp qubit pair fits it with error at most ε₃ + δ/2, where δ measures the asymmetry of the table. The constant is proved to be best possible. Three queries. The equivalence fails. Every qubit triple of binary measurements satisfies a simple inequality I ≤ 9, which follows from an identity on 3×3 correlation matrices. A triple of projective qutrit measurements reproduces an eight-point centrally symmetric table exactly with I ≥ 9.0505, so every qubit needs worst-cell error larger than 9.7×10⁻⁴ on it. This is a computer-assisted proof based on exact rational certificates, checked by two independent programs. The qutrit advantage is small: about 10⁻³ in worst-cell error. Numerically, the best qutrit value found is I* = 9.0507284088558548…. A candidate minimal polynomial of degree 13 is reported, confirmed to 3000 digits. Its symbolic derivation and the global optimality of I* remain open, and are labelled as numerical findings. Files: the preprint (PDF), and a reproducibility archive (ZIP) with all exact certificates, the original scripts, an independent audit, the full research record including failed and superseded runs, and a SHA-256 manifest. Quick check after unpacking: python3 -I audit/verify_certificates.py . (pure Python, about 1 s). Not peer reviewed. A large language model assisted with derivations, computations, certificate scripts and drafting; the author takes full responsibility for the content.