A smooth Reshetnyak-harmonic sphere with unbounded distortion

We construct a compact smooth Riemannian sphere and a smooth homeomorphism from the round sphere which locally minimizes Reshetnyak operator-norm-squared energy against every same-trace Sobolev competitor, but has essentially unbounded infinitesimal distortion. This gives a negative answer for the Reshetnyak member of the general-energy formulation of Meier-Vikman-Wenger Question 1.9 in the inspected arXiv:2503.08553v1, also posed as Question 1 on printed page 1625 of Oberwolfach Report 30/2025. Scalar calibration on a flat belt and a globally exact two-form calibration on conformal caps prove the unrestricted local comparisons, including competitors leaving the image patch. The map is not a global homotopy minimizer and is not Korevaar-Schoen harmonic. A separate angular-stress proof establishes the nonsharp distortion bound 4+sqrt(17) for locally Korevaar-Schoen-minimizing spheres into complete metric spaces. Its stress-zero step implies pointwise SL(2)-minimality by matrix convexity, so the established sharper Lytchak-Wenger bound also applies. The elementary constant is retained for a self-contained proof; no improved bound is claimed. Classical metric Sobolev, energy/area, Hopf/Sacks-Uhlenbeck, Lipschitz extension and calibration ingredients are credited. The bounded priority audit used 71 queries and 32 source entries, with explicit primary-text followups and metadata-only citation leads. No earlier exact match was authenticated in that inspected material, but first bibliographic priority is unresolved. The revised 2026 Meier-Vikman-Wenger journal mathematical text was inaccessible; source scope is pinned to the inspected 2025 formulation. No unchanged final wording, continued open status through 2026, first-priority or optimal-constant claim is asserted. A later source-access addendum records selected original Sacks-Uhlenbeck passages inspected through the web PDF reader, without claiming a local PDF hash. This six-page unrefereed research note is accompanied by its authored PDF/LaTeX source, unchanged historical candidate, independent analytic/computational/source/priority reviews and reproducible verification archive. The 257 exact author controls and source-free 673-check mixed replay are distinguished from the historical 675 checks with two PDF-input identity checks. Numerical diagnostics are not rigorous interval enclosures or formal proof certification. AI tools were used extensively in development, computation, verification, adversarial review and writing. Independent AI-assisted review is not independent human or journal peer review; neither has occurred. No copied third-party source documents are distributed.