The 'flat at infinity' condition introduces an absolute element in the sense of Kretschner and Anderson—a non-dynamical background structure that resists Mach's reduction of geometry to matter relations.

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Kretschner and Anderson(as used in physics and philosophy of physics): Physicists and philosophers who studied how space and time are structured in Einstein's theories of relativity.
Mach's reduction of geometry to matter relations(as used in philosophy of physics): Ernst Mach's idea that the shape and structure of space itself should be explained only by how physical objects are arranged and relate to each other, with no independent space existing 'underneath' those relationships.
absolute element(as used in metaphysics): A feature or property that exists independently and doesn't depend on anything else for its existence or meaning.
flat at infinity(as used in physics and geometry): A mathematical condition describing how space behaves at its extreme edges or boundaries—specifically, that space remains flat (like a sheet of paper) rather than curved, even when you go infinitely far away.

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