Claim: According to Einstein notation (a notational subset of Ricci calculus), when an index variable appears twice in a single term and is not otherwise defined, it implies summation of that term over all the values of the index; also, the upper indices are not exponents but are indices of coordinates.
Evidence: As part of mathematics it is a notational subset of Ricci calculus; however, it is often used in applications in physics that do not distinguish between tangent and cotangent spaces. According to this convention, when an index variable appears twice in a single term and is not otherwise defined (see free and bound variables), it implies summation of that term over all the values of the index. The upper indices are not exponents but are indices of coordinates, coefficients or basis vectors.