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The Ehlers-Pirani-Schild (EPS) constructive axiomatisation of generalrelativity, published in 1972, purports to build up the kinematical structureof that theory from only axioms which have indubitable empirical content. Itis, therefore, of profound significance both to the epistemology and to themetaphysics of spacetime theories. This axiomatisation is, however,self-consciously terse, rendering it difficult to ascertain whether itsucceeds. In this article, we provide a pedagogical walkthrough to the EPSaxiomatisation, filling relevant conceptual and mathematical gaps and renderingexplicit controversial assumptions. There are two companion papers, in which wediscuss the significance of constructive approaches to spacetime structure moregenerally (Part II), and (with Emily Adlam) consider extensions of the EPSaxiomatisation towards quantum general relativity based upon quantum mechanicalinputs (Part III).

Constructive Axiomatics in Spacetime Physics Part I: Walkthrough to the Ehlers-Pirani-Schild Axiomatisation