Value as a Conventional Base Dimension: Anchoring, Neutrality, and the Breakdown Regime of the Monetary Unit

This paper asks whether economic value can be carried as a base dimension in the sense of the International System, and answers with a qualified yes. Anchoring a monetary unit to a dated economic reference is metrology, not reduction, exactly as the 2019 redefinition of the SI fixed units by freezing constants. The license for the dimension is a symmetry economics already names: invariance of real behavior under rescaling of the monetary unit is the homogeneity postulate, the absence of money illusion, so the value column V is exactly as sound as monetary neutrality and fails where it fails. The paper fixes a working system with columns V, R, and T, audits the standard equations of economics against it, and reports a pre-registered empirical programme, refutations at the same prominence as confirmations. The candidate dimensionless governor of the short-horizon breakdown, the regime number N, failed its tests and is withdrawn. What survives measurement: staggered repricing is observed directly at the individual price quote and under a forced synchronization, real at the quote and negligible in the cross-section; statutory thresholds track the unit's decay one for one under a frozen protocol while coin retirements overshoot it; market microstructure invariance, the strongest dimensional analysis in economics, proves to run on an unlicensed value dimension whose celebrated derivation loses uniqueness without the V column; cross-date comparison is shown to presuppose a dated conversion structure, a val up to scale, so deflation is the dimension operated without the name; and an audit of the Penn World Table bounds the one dimensional error this paper attributes to received practice while quantifying two that practice had not stated. A further finding may outlast the rest: dimensional admissibility does not determine an estimator, the gap being invisible from inside the framework because a wrong estimator type-checks. A dimension with a stated validity domain asks to be tested, not believed.