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Abstract

Permissionless systems resist Sybil attacks by binding influence to scarce resources. Yet influence concentration persists across systems built on computation, capital, and other reusable resources despite substantial differences in protocol design. This raises a fundamental question: is influence concentration primarily a consequence of protocol rules, or of the structural properties of the underlying resource itself? In this paper, we address this question from a resource-centric perspective through the adversarial cost function C ( s, T ), defined as the minimum expenditure required to sustain influence equivalent to controlling s independent participants over a time horizon of length T . Using this framework, we develop an axiomatic resource taxonomy that connects resource structure to adversarial cost scaling. Our analysis shows that resource-mechanism pairs satisfying divisibility, additivity of influence, temporal reusability, and identity transferability admit influence amortization, yielding C ( s, T ) = o ( sT ). Conversely, throughput-bounded, non-transferable, window-local resources enforce C ( s, T ) = ( sT ), with marginal cost ( s, T ) = ( T ) increasing with the time horizon. Together, these results reveal a fundamental asymptotic separation between resource classes that admit influence amortization and those that enforce linear cost. These results shift the focus of decentralization from protocol design to resource design. If influence concentration is a structural consequence of the properties that make resources parallelizable, then redesigning consensus rules alone cannot eliminate it. The same properties also enable concentrated control to be projected across many nominally distinct participants through delegation, pooling, or identity replication, obscuring the relationship between visible identities and underlying control. The search for stronger decentralization must therefore begin with the choice of the underlying resource.