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Vierbeins provide a bridge between the curved space of general relativity andthe flat tangent space of special relativity. Both spaces should be causal andspin. We posit intertwining the two symmetries of spacetime bundlesasymmetrically; disentangling the non-trivial Id between the base, curved spaceas a locally ringed space and its Zariski (co-)tangent space. This involves theintroduction of a "two-sided vector space" as a section of the smooth,stratified diffeomorphism bundle of spacetime. A change of paradigm from thefiber bundle approach ensues where the bundle space takes an active role andthe group actions are implemented through asymmetric "scalar multiplication" byelements of a skewed K-algebra on a free K-bimodule. Accordingly, the leftaction is augmented from that on the right algebraically by a left-sidedalgebra automorphism via a left alpha-derivation as a non-central Ore extensionof a Weyl algebra. Curiously, summoning the left $\alpha$-derivation in thecontext of spacetime symmetries may constitute the key to an asymmetricquantization of the theory. Furthermore, it is conjectured that causal and spinstructure may be endowed upon the spacetime itself, independently of thetangent space structure.

On the Geometry of Spacetime I: baby steps in quantum ring theory