  Topological physics has revolutionised materials science, introducing
topological insulators and superconductors with applications from smart
materials to quantum computing. Bulk-boundary correspondence (BBC) is a core
concept therein, where the non-trivial topology of a material's bulk predicts
localized topological states at its boundaries. However, edge states also exist
in systems where BBC is seemingly violated, leaving any topological origin
unknown. For finite-frequency mechanical metamaterials, BBC has hitherto been
described in terms of displacements, necessitating fixed boundaries to identify
topologically protected edge modes. Herein, we introduce a new family of
finite-frequency mechanical metamaterials whose topological properties emerge
in strain coordinates for free boundaries. We show two examples, the first
being the canonical mass-dimer, where BBC in strain coordinates reveals the
previously unknown topological origin of its edge modes. Second, we introduce a
new mechanical analog of the Majorana-supporting Kitaev chain. We theoretically
and experimentally show that this Kitaev chain supports edge states for both
free and fixed boundaries, wherein BBC is established in strains and
displacements, respectively. Our findings suggest a previously undiscovered
class of topological edge modes may exist, including within other settings such
as electrical circuits and optics, and for more complex, tailored boundaries
with coordinates other than strain.
