Finite Distinguishability Budgets and Maintenance Bounds for Physical Observers

A finite physical observer cannot register, preserve, update, and operationally use an unlimited number of distinctions. This paper defines an observer-relative distinguishability budget NO = |Im(πO)| and bit capacity CO = log2 NO for finite record-bearing systems. Using established Bekenstein, holographic, channel, and Landauer-style update constraints as physical bridge inputs, we formulate accessible distinguishability as a bottleneck over internal memory, boundary access, communication channel, causal reach, and irreversible update throughput. We then define boundary-relative capacity deficit by comparing task-relevant rate-distortion demand R (τ) min(ε; Ψ) with accessible capacity. When demand persistently exceeds accessible budget, a finite observer must coarse-grain, compress, externalize, prune, relax the task, or fail. The paper does not derive gravitational entropy bounds, quantum gravity, the Standard Model, the Einstein equations, or the numerical coefficient in the Bekenstein-Hawking entropy formula. Its purpose is narrower: to make finite distinguishability a precise, auditable, and testable bridge between finite-system theory, information bounds, and physical observation.