Inconsistency Accumulation in Forward-Local Sequential Policies: A Lower Bound under Delayed Constraints

We characterize an architectural fault-line in sequential decision-making under delayed constraints, separating forward-local policies — policies that select actions using only a bounded trailing observation window — from policies equipped with a sequentially updatable extendability-preserving summary state. The separation has two halves. On the negative side, for every finite evaluation horizon h and every forward-local policy class, we construct a family of policy-indexed delayed-constraint environments in which non-extendable commitments accumulate without any policy-independent finite bound. Deterministic policies are forced into one non-extendable commitment per block; stochastic policies incur such commitments at a rate bounded below by N/|U| where |U| is the action-space cardinality, uniformly over the class. On the positive side, any environment family admitting a sequentially updatable extendability-preserving summary state admits a policy that achieves zero accumulated inconsistency. The architectural content of the paper is therefore not the impossibility alone but the identification of the precise representational primitive — an extendability-preserving summary — that closes the gap. Any system that seeks a uniform bound must incorporate a mechanism whose functional effect is to exclude non-extendable continuations prior to commitment. All discrete-case policy-level results are formalized and machine-checked in Lean 4, including the full measure-theoretic construction of the trajectory probability space, the bridge lemma identifying the conditional expectation of the per-block failure indicator with the policy's per-window commitment probability, and the main integration theorem yielding the N/|U| lower bound via the tower property. This paper extends the impossibility result on the non-observability of extendability from bounded projections (https://doi.org/10.5281/zenodo.19688367) into the stochastic accumulative regime. The broader projection-theoretic framework that both papers specialize is developed in https://doi.org/10.5281/zenodo.19633241.