Three new theorems relating Einstein’s notions of ‘‘strength’’ and ‘‘compatibility’’ to the field of the initial‐value problem are presented. These theorems result (i) in a first proof of Matthews’ conjectures concerning this relation for a wider class of systems of partial‐differential equations, (ii) in a new interpretation of Einstein’s compatibility condition, and (iii) in the exact relation between Einstein’s strength and Cartan’s degré d’arbitraire.

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