Decision Theory with Bruises: Optimal Commitments under Irreversible and Bounded Observation

We develop a formal decision framework for bruise-bearing agents: finite observers whose actions carry irreversible side-effects that accumulate over time, whose observations are bounded by finite information capacity, and whose ability to undo past consequences is limited by a depletable recovery budget. The agent’s state is a triple — physical state, accumulated bruise, and remaining recovery — with dynamics in which commitments necessarily shrink future action sets via monotone feasibility constraints. We define a cumulative recovery frontier capturing the maximum bruise reduction achievable from budget by any multi-step allocation, and prove a point-of-no-return result: in the plane, the curve defines an absorbing boundary beyond which no policy can restore access to high-value actions, regardless of the controller’s intelligence. A commitment timing threshold establishes that the optimal time to commit depends jointly on observer capacity (which determines a logarithmically scaling observation window), bruise aversion , and recovery budget . A fully worked toy model with explicit parameter values and closed-form thresholds illustrates the mechanics across three qualitatively distinct regimes. The framework synthesises prior results on imperfect erasure, commitment–loss duality, reachability under recovery constraints, bounded memory horizons, and capacity-limited observation into a unified decision-theoretic language, bridging the physics of irreversibility with sequential decision-making. Connections to reversible reasoning in LLMs, real options theory, optimal stopping, and constrained MDPs are made explicit. Full references to the underlying technical results are provided in the paper. All structural results are independently verifiable; all predictions are falsifiable.