mktlib — reference implementation of the Möbius–Klein transform

mktlib is an open reference implementation of the Möbius and Klein transforms: a unitary, FFT-backed (O(N log N)) analysis–synthesis framework for harmonic analysis on non-orientable manifolds. It provides the transform pairs mt/imt on the antiperiodic (Möbius) sector, kt/ikt and kt_twisted/ikt_twisted on the two sectors of the Klein bottle, and kt3/ikt3 with their twisted counterparts on the solid Klein bottle. Alongside the transforms it offers sector handling (the deck transformation, the projectors and the sector split), differential operators following the sector rules, a sector-correct Helmholtz decomposition with its inverse, a divergence-free projection, a unitary sector-preserving split-step Schrödinger solver, and the component-wise parity rule of the three-dimensional case. The two-dimensional routines perform a dimension check and raise an error on three-dimensional input instead of returning a silently wrong result. The library ships with a 76-test suite covering unitarity, the Parseval identity, exact inversion in both directions, adjointness, dimension counting, sector properties, operator identities, Helmholtz reconstruction, the convergence order of the solver, the explicit Gram matrix of the basis, the condition number on the sector (exactly 1, i.e. exactly unitary) and stability up to a 256x128 grid. A separate benchmark compares the spectral solver with standard grid methods on two Poisson problems: on a twisted circle the transform reaches machine precision on 64 grid points, second-order finite differences give an error of 1.4e-3, and a periodic Fourier solution that ignores the twisted topology stays at O(1) error and does not converge under grid refinement. The library is released under the MIT License; the accompanying papers are under CC BY 4.0.