Economic relativity: a cut rule for perimeter valuation in equity ownership networks

Abstract

We introduce the Cut-Based Valuation (CBV), a unified framework for consolidated value in equity/flow networks. The central idea is that economic value is never absolute: it is always defined relative to an observer Omega, which fixes perimeter, measurement basis, units/FX/PPP, discounting, informational regime, and control rules. Given Omega, the Cut Theorem shows that the consolidated value of a perimeter P depends only on boundary quantities across the cut P -> O, while internal reconnections are valuation-invariant. This provides (i) sufficient statistics for valuation with linear computational complexity, (ii) standardized reporting through the Perimeter-of-Validity and Cut Summary, and (iii) transformation laws that clarify how different observers relate. Applications span IFRS consolidation, national accounts, fund-of-funds, pyramids, and clearing networks, all seen as special cases of a general principle of economic relativity. Case studies (market capitalization by country, keiretsu, fund-of-funds) illustrate how CBV eliminates double counting while ensuring comparability and auditability. To address practical concerns, we establish robustness bounds that quantify how errors in initial data propagate to consolidated values, and we introduce a dynamic CBV-Fisher protocol for intertemporal comparisons, ensuring consistency with official chain-linking practices. These additions clarify the time scale of application, the role of averaging procedures, and the horizon of reliable measurement. Finally, we make explicit the scope and limitations of CBV: it is a normative measurement/consolidation rule in linear accounting environments, while in macroeconomic closures or with nonlinear payoffs it must be coupled with equilibrium or clearing models.