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Retaining language-model prefix states trades recomputation against storage time. Optimizing each cached block independently can overcount savings: a resident block is usable only when the required preceding prefix is also available. We introduce Prefix-Certificate Retention (PCR), an exact finite-trace formulation for...
Model failover restores availability, but changes which financial institutions share decision errors. We formulate outage-contingent routing through a local market-impact response matrix and study expected squared price displacement. A symmetric construction shows that a shared backup can leave an order-one concentrati...
Tool-result caching reduces repeated execution in agent training, but also couples rollout randomness. We study a two-action model in which independent and shared execution preserve every rollout's conditional reward distribution. Despite this marginal agreement, sharing one stochastic result per group can reverse the...
Successful agent execution need not identify which future product improvement its user would value. We present a decision-specific audit that maps a declared observation channel and product-value contrast to compatible intervals and witness populations. Its foundations are established identification and decision theory...
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