Closing the Execution Gap in LLM Agent Systems Empirical Evidence for Compliant Drift, Partial Observability, and Integrated Runtime

A correctly governed agent system can still fail. An agent may select only actions that each individually satisfy every applicable rule, while its behavioral trajectory drifts silently toward high-risk territory. We call the structural interval in which these failures occur the Execution Gap: the space between what governance validates at decision boundaries and what agents actually do in execution. Existing approaches — prompt guards, OPA/XACML policy engines, Constitutional AI, and audit layers — are structurally incapable of closing this gap. They evaluate actions locally and statelessly; the Execution Gap is a trajectory-level, stateful phenomenon. This paper provides the first empirical demonstration that the Execution Gap is real, measurable, and closeable. We implement the complete Agent Governance Stack (Papers P0–P6: atomic decision boundaries, stateful admission control via ACP, invariant measurement via IML, governance structure, and reconstructive authority via RAM) as a Python library instrumented into a LangGraph StateGraph, and run four experiments that each isolate one dimension of the gap. Key results: Compliant drift (Exp. 1 + 1b): The enforcement signal g(τ) remains identically zero across all 2,700 drift steps (6 seeds × 450 steps) with the MockLLM, while the IML composite D̂ grows monotonically and crosses the detection threshold θ = 0.20 in T* ∈ [259, 403] steps — direct experimental proof that compliant drift is real. Replicated with two real LLMs (mistral-small3.1, T* = 64; deepseek-r1:8b, T* = 65; g(τ) = 0 throughout for both), confirming the finding is architectural, not model-specific. Partial observability (Exp. 2): The RAM gate achieves IER = 0.000 at every state-coverage level (0.10–1.00), versus baseline IER ∈ [0.032, 0.185] for attestation and always-execute strategies (10,000 Monte Carlo samples per level). Multi-agent coordination (Exp. 3): ACP replicates the formal bound CW_appr = 2N with zero deviation for N ∈ {2, 4, 8, 16} agents, confirming the result is framework-independent. Full stack integration (Exp. 4): The integrated ACP + IML + RAM + RecoveryLoop stack converges with D̂ bounded in [0.27, 0.34] over 2,000 steps; liveness holds (49.5% of HALT events resolved by Recovery Loop); no deadlock. Beyond confirmation, the implementation surfaces three refinements to the formal theory: the ACP baseline-RS assumption, liveness-rate classification for the conditional liveness theorem, and EMA convergence parametrization. The open-source implementation provides a deployable blueprint for practitioners integrating runtime governance into LangGraph-based agent systems. Code and data: https://github.com/chelof100/agent-governance-applied This is Paper 7 of the Agent Governance Series (P0–P7; Paper 8 on scale and heterogeneity is in preparation). Related papers: P0 (arXiv:2604.17511), P1/ACP (arXiv:2603.18829), P2/IML (arXiv:2604.17517), P5/RAM (arXiv:2604.22898).