Paper 2026/1492

Proof of Demand Is Not Proof of Work: On the Limits of Demand-Weighted Consensus under Free Pseudonyms

Abstract

Proof-of-useful-work (PoUW) certifies computational hardness, not utility: a certified computation need not be anyone’s demanded job. We separate three properties of a work receipt—work soundness \(\mathsf{W}\), job binding \(\mathsf{B}\), and demand exogeneity \(\mathsf{E}\)—and locate the gap at \(\mathsf{E}\). Two results require no equilibrium or market model. First, payments between coalition-controlled requesters and workers are recoverable transfers that contribute no Sybil-resistant cost, so no security lower bound may count their nominal value (Lemma 1). Second, under the stated realizability or indistinguishability premises, endogenous receipts cannot certify \(\mathsf{E}\) (Theorem 1); we also give a conditional lower bound on the cost of evading a stated class of provenance estimators. Separately, under an explicit zero-demand design norm, a mechanism safe and live in every admissible demand environment and closed under null-demand projection must possess a leader-election path independent of the demand component of service receipts (Theorem 2). Freely realizable receipt boosts, including resource-coupled boosts, obey a profile-dependent sizing rule (Corollary 4). Fork-independent salvage value of useful outputs can leave security neutral, negative, or positive depending on salvage asymmetry and demand, which we characterize in a stylized free-entry model. Constructively, an irrecoverable tax on every settled payment makes the burn—not proof of independence—the security resource. Deployed evidence comprises one reported audit (Pearl cuPOW) and reward-program analogues; the endogenous election-side failure is, at present, a model prediction. Useful-computation receipts are appropriate instruments for payment, collateral, and loss allocation—and a bounded, priced election boost—but not the leader-election floor.