Semantic Clarification and Symmetric Correction of Exponent Labels — On 0 as an Exponent Converter Rather Than an Exponent Value

Exponentiation is one of the most fundamental structures in mathematics, underlying concepts of dimension, measure, and dimensional analysis. This paper identifies a calibration gap in the current exponent labeling system: the label 0 simultaneously serves six semantic roles—exponent index origin, multiplicative identity, additive identity, positive/negative boundary point, geometric existence baseline, and measure zero point—among which the multiplicative baseline (x^0=1) and additive baseline (0) are in direct conflict. Starting from three basic mathematical facts (multiplicative baseline, additive baseline, exponent index labeling), this paper rigorously derives the contradiction and proposes a symmetric correction scheme: 0 serves purely as an exponent converter (not an exponent value), while +1 and -1 are the positive and negative unit exponents (both equal to x^0=1, in opposite directions). The paper proves that this correction is fully compatible with the current mathematical system (all computed values remain unchanged) and resolves six boundary problems near the origin. Dimension theory, as a geometric application of exponent relations, derives its labeling issue from this underlying contradiction.