This paper develops a unified axiomatic framework for analysing suffering-like quantities in implementation spaces equipped with behavioural, performance, and resource constraints. We introduce a structural decomposition =+ = + =+, where the gauge component captures behaviour-preserving redundancies and the waste component measures excess dissipation above a minimal complexity envelope. Under this framework we prove a Dominance Theorem showing that every implementation can be replaced by a behaviourally equivalent one with strictly lower suffering and strictly lower resource use. This demonstrates that excess dissipation is not an intrinsic property of a task, but an avoidable design artefact. To study dynamics, we model self-modifying implementations as Markovian processes with a local drift condition, establishing a quantitative ε-instability theorem: the stationary fraction of high-suffering implementations is bounded above by an explicit ratio (L (ε) /κ (ε) ) ε (L () / () ) \, (L (ε) /κ (ε) ) ε. This reveals that any system with a uniformly negative drift on high-suffering states necessarily suppresses them in long-run behaviour. Finally, for idealised capability-indexed families of implementations, we show a capability-conditional elimination theorem: if improvement dynamics simultaneously strengthen negative drift and diminish tolerances, then the stationary mass of high-suffering implementations converges to zero. This formalises the intuition that increased capability, coupled with consistent self-correction pressure, systematically removes avoidable dissipation. The framework is lightweight, representation-independent, and compatible with both physical interpretations (dissipation, resource inefficiency) and algorithmic interpretations (excess computational cost). It provides a mathematically rigorous basis for evaluating implementation quality, compression of wasteful degrees of freedom, and the asymptotic behaviour of self-improving systems.
Takahashi K (2025) studied this question.