Finite Distinguishability Budgets and Maintenance Bounds for Physical Observers

Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory This paper introduces FDS-T1, the finite-observer physical bridge paper in the Distinction Theory / Active Finite Distinction Systems (DT/FDS) research programme. The central claim is that a finite physical observer cannot register, preserve, update, and operationally use an unlimited number of distinctions. The paper defines an observer-relative distinguishability budget NO = |Im(πO)| and bit capacity CO = log2NO for finite record-bearing systems. Using established Bekenstein, holographic, channel, and Landauer-style update constraints as physical bridge inputs, the paper formulates accessible distinguishability as a bottleneck over internal memory, boundary access, communication channel, causal reach, externalized records, and irreversible update throughput. It then defines boundary-relative capacity deficit by comparing task-relevant rate-distortion demand with accessible capacity. When task demand persistently exceeds accessible budget, the paper argues that a finite observer must enter at least one budget-exit class: coarse-graining, compression, externalization, pruning, task relaxation, or failure. The paper also introduces budget crossing and bottleneck-switching kinks as testable signatures of finite-observer capacity limits. This paper does not claim to derive the Bekenstein bound, holography, Landauer’s principle, the Einstein equations, quantum gravity, the Standard Model, or the numerical coefficient 1/4 in the Bekenstein-Hawking entropy formula. It uses established entropy and thermodynamic constraints as physical bridge inputs. Its contribution is narrower: to make finite distinguishability a precise, auditable, and testable bridge between finite-system theory, information bounds, and physical observation. This version is intended as a stable public timestamp for the FDS-T1 finite-observer bridge claim family, including finite observer projection, distinguishability budgets, accessible capacity bottlenecks, boundary-relative capacity deficit, maintenance bounds, budget-exit classification, and budget-crossing signatures.