We formalize the compositional structure of a four-layer agent governance architecture comprising an atomic decision boundary, a stateful enforcement protocol, a behavioral invariant monitor, and a fair access allocator. We introduce a multi-scale composition model that distinguishes synchronous coupling at the request level from asynchronous coupling at the trace and population level. Key results: - Interface Compatibility: the composed system preserves the guarantees of all layers at their respective operating scales. - Feedback Convergence: the closed-loop system induced by thresholded feedback from the monitoring layer to the enforcement layer converges to a bounded deviation region under regularity conditions. - Irreducibility under Finite Observability: under finite observability (finite state spaces, bounded inter-layer summaries, local decision-making) and summary-based inter-layer interfaces, no composition of fewer than four layers can simultaneously guarantee strong atomicity, bounded non-identifiability of behavioral contracts, exact fairness at the actor level, and Sybil robustness. The irreducibility result establishes that the four-layer architecture is structurally necessary within this observability model, not an artifact of design choices. The four layers correspond to four orthogonal projections of the governance space — temporal (atomicity), state (enforcement history), behavioral (drift monitoring), and population (fair allocation) — and the irreducibility result shows that no single mechanism can cover two projections simultaneously under finite observability. Validated with a controlled ablation study (8 × 4 × 5 = 160 trials), a feedback convergence experiment (10 seeds, 1000 steps each), and an interface compatibility check (20 trials), using the real ACP risk engine and IML deviation estimator. This paper is Paper 4 of the 6-paper Agent Governance Series: P0 — Atomic Decision Boundaries (structural foundation). P1 — Stateful enforcement via ACP. P2 — Behavioral drift detection via the Invariant Measurement Layer (IML). P3 — Fair multi-agent allocation under shared governance infrastructure. P5 — Runtime execution validity under partial observability (RAM): provides the operational closure for L2 at runtime. Paper 4 proves the four-layer architecture (L0–L3) is irreducible. Paper 5 provides the operational closure for L2 at runtime. Full series (Agent Governance Series, Papers 0–5): P0 — Atomic Decision Boundaries: https://doi.org/10.5281/zenodo.19642166 P1 — Agent Control Protocol (ACP): https://arxiv.org/abs/2603.18829 | https://doi.org/10.5281/zenodo.19642405 P2 — From Admission to Invariants (IML): https://doi.org/10.5281/zenodo.19643761 P3 — Fair Atomic Governance: https://doi.org/10.5281/zenodo.19643928 P4 — Irreducible Multi-Scale Governance (this paper): https://doi.org/10.5281/zenodo.19643950 P5 — Reconstructive Authority Model (RAM): https://doi.org/10.5281/zenodo.19669430
Marcelo Fernandez (Sat,) studied this question.