PreprintarXiv · 2026arXiv:2604.12238
Computational Validation of the Oloid as a Local Optimum in the Developable Roller Family
A 1,430-variant parametric search across the developable roller family identifies the oloid as a local optimum under a seven-oracle physics stack. Two-tier invariant vector resolves four linear metrics clustering at 8×10⁻⁷ and three nonlinear fatigue metrics that diverge sharply — evidence the winning geometry does something irreducible to linear contact mechanics.
PreprintarXiv · 2026arXiv:2604.17120
Sloan's Analytical Gömböc Does Not Produce Mono-Monostatic Bodies: Computational Verification, Extended Construction, and a Thirteen-Member Verified Catalog
Computational verification that Sloan's analytical construction does not yield mono-monostatic bodies under the stated parameterization, followed by an extended construction producing a thirteen-member verified catalog. Each catalog member is independently reproduced from open code.
PreprintarXiv · 2026arXiv:2604.17095
Computational Construction and Engineering Evaluation of Verified Mono-Monostatic Bodies
Engineering evaluation of the thirteen-member mono-monostatic catalog under the same physics oracle stack used in the developable roller study. Contact distribution, Hertz stress, thermal, wear, and fatigue compared across the catalog to identify which members are physically viable as rolling-contact primitives.