The vielbein formalism embeds tensor calculus within a broader framework where ψ components are defined relative to local Lorentz frames, not arbitrary coordinate systems, dissolving the incompatibility Weyl identifies.

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Local Lorentz frames(as used in general relativity and physics): Small regions of space where you can use the physics of special relativity (Einstein's theory for non-gravitational situations) as a good approximation, rather than needing the full complexity of general relativity.
Tensor calculus(as used in physics and mathematics): A branch of mathematics for working with quantities that have multiple components and change in specific ways when you switch between different coordinate systems or reference frames.
Vielbein formalism(as used in differential geometry and general relativity): A mathematical technique in physics that describes space and gravity by using multiple local reference frames (like having different measuring sticks at each point) instead of trying to use one global coordinate system for everything.
Weyl(as a historical reference in physics): Hermann Weyl (1885-1955) was a German mathematician and physicist who identified a mathematical problem about how to connect measurements made in different reference frames in a consistent way.

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