Pearl, a Layer-1 blockchain with high-profile AI industry endorsements, markets its Proof-of-Useful-Work (PoUW) protocol as simultaneously securing the network and performing AI inference. We present the first systematic empirical measurement of a deployed PoUW system, finding that Pearl's 24 EH/s network -- representing approximately 320,000 GPU-equivalents consuming an estimated 112 MW -- produces zero useful AI computation. Budget GPU rental prices rose 38% and utilization surged from 57% to 94% following the mining software's public release, displacing legitimate research workloads. Our measurements span five dimensions: (1) network composition analysis of 8,012 workers shows all have inference-capable hardware, yet the dominant mining software contains no inference code; (2) the verification protocol accepts random matrices by design, confirmed by 44 pool-accepted shares from our open-source miner across NVIDIA, AMD, CPU, and Apple Silicon hardware; (3) statistical distribution checks are trivially defeated by adversarial Gaussian sampling; (4) mining economics are marginal at current PRL prices ($0.76), with ROI ranging from -1% to +67% depending on GPU tier -- near breakeven for most hardware; and (5) the mining computation is commodity integer arithmetic portable to any hardware platform, offering no vendor lock-in. These findings quantify the verifiability-usefulness tension identified theoretically by Leinweber et al., providing concrete measurements of its magnitude and economic consequences in a deployed system.