The Independence of the Unit of Account: Axiomatic Foundations and the Zero-Parameter Benchmark

The unit of account is treated in most monetary theory as inseparable from the medium of exchange. This paper states the conditions under which it can be separated, and derives a construction that meets them without discretionary parameters. Three mathematical axioms are stated - that the unit is a ratio rather than a level, that its denominator is a physical quantity rather than a price, and that it be defined without a trend term - together with seven institutional axioms that a published index must satisfy. Discretion is defined and audited specification by specification; the central proposition shows which specifications carry a revisable parameter and which do not. The construction P = G_t/G_t0, anchored to the above-ground gold stock, is then derived as the zero-parameter case, and its growth stability is stated as a testable condition that four candidate anchors (gold, silver, tin, copper) are checked against. The paper closes with what the construction cannot do: it does not remove commodity price risk, measurement error in the stock series, or the governance problem of who publishes the number. JEL classification: E40; E42; E52; F33; B12 Note. This working paper reproduces Chapter 3 of the monograph The Independence of the Unit of Account: A Theory of Monetary Function Decoupling with Empirical Evidence and Institutional Design (2026). It is a working paper and has not been peer reviewed. Replication package. The empirical chapters of the monograph are documented in an accompanying replication package (135 files) archived at Zenodo: https://doi.org/10.5281/zenodo.23255744 Companion material. One of three working papers drawn from the same monograph: WP1 (axiomatic foundations), WP2 (purchasing-power deviation), WP3 (policy exposure and null results).