Possibility Is Not Probability: A Benchmark for Objective, Perceived, and Operative Path Availability (PathSpace)

Abstract

A transition with positive probability under the dynamics is possible. Whether it is probable, perceived, executable, preferred, or realised are five further questions, and agent benchmarks usually answer them with one number. This paper introduces PathSpace, a benchmark in which every environment instance carries oracle ground truth at five layers: the structurally admissible paths, the paths executable in truth, the paths an agent holds as possible, the paths it holds as executable, and the paths its policy intends, together with the single trajectory it realises. Ten matched cases move one factor at a time (transition probability, observation, capability, cost, policy preference, random outcome, syntactic duplication, a rare escape, an easy-then-narrow fork, and a second observer), and a factorial crosses six of them. On 3,044 measurements over 60 instances from five topology generators, the paper shows when probability, belief, and action parted company — and when a one-number score would have hidden that parting.