Substrate Geometry
Taking classical geometric primitives, the oloid, the Gömböc, mono-monostatic bodies, and iterating on them to improve real engineering substrates.
Computational rolling-contact mechanics that classifies shapes by physical invariants rather than by appearance: seven physics oracles, a 25.6× mean-temperature advantage on the TPMS heat-exchanger geometry, and a 58× improvement in contact distribution.
The programme produced the first openly verified Gömböc construction and a 13-member verified mono-monostatic catalog, both released with their computation rather than as a claim.
Paper I was endorsed on arXiv by Georg Nawratil (TU Vienna), after Hellmuth Stachel, who originated the oloid problem, read the work and referred it onward to him. The methodology paper is under review at the SMAI Journal of Computational Mathematics; the TPMS heat-exchanger paper is under review at Elsevier Results in Engineering.