Compositional Governance — Paper 4

Paper 4 of the Agent Governance Series.

Correctness is per-layer. Governance is the composition.
Four projections. Each necessary. None redundant.

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Paper

Irreducible Multi-Scale Governance: Composition and Limits of Atomic Admission Systems
Marcelo Fernandez (TraslaIA), 2026

DOI: 10.5281/zenodo.19672608  ·  arXiv: under review

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What this is

This repository contains the LaTeX source and experiment code for Paper 4 of the Agent Governance Series — the synthesis paper that composes the four governance layers from Papers 0–3 into a single formal architecture and proves it is the minimal composition that satisfies all runtime governance guarantees.

The core problem: Papers 0–3 each address a distinct governance failure mode. But do those layers compose correctly? Can any subset of three layers cover all four guarantees? The answer is no — and this paper proves it.

The paper introduces:

• Synchronous composition ⊗_κ and asynchronous coupling →_κ for governance layers, with formal interface compatibility conditions (C1–C3).
• Theorem 1 (Interface Compatibility): The composition L0 ⊗ L1 ⊗ L2 ⊗ L3 satisfies the four-layer interface contract under conditions C1–C3.
• Theorem 2 (Feedback Convergence): Under assumptions FC1–FC3, the closed-loop IML feedback system converges: lim sup D̂_t ≤ ε.
• Theorem 3 (Irreducibility): Under finite observability (finite state spaces, bounded inter-layer summaries, local decision-making), no composition of fewer than four layers from {L0, L1, L2, L3} simultaneously satisfies all four governance guarantees.
• Lemma 5.2 (Contraction): The feedback map Φ(x) = ρx + ε_b with ρ = 1 − Kη ∈ (0,1) is a contraction. Empirically: K = η = 0.50, ρ = 0.70.

Empirical validation: 160-trial ablation study, 10-seed feedback convergence experiment, 20-trial compatibility check — using the real ACP risk engine and IML deviation estimator.

Paper 0 (DBM): https://github.com/chelof100/decision-boundary-model
Paper 1 (ACP): https://github.com/chelof100/acp-framework-en
Paper 2 (IML): https://github.com/chelof100/iml-benchmark
Paper 3 (Fairness): https://github.com/chelof100/fair-atomic-governance
Paper 5 (RAM): https://github.com/chelof100/reconstructive-authority-model

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Repository contents

compositional-governance/
├── main.tex                          # Full LaTeX source (23 pages)
├── references.bib                    # Bibliography
├── main.pdf                          # Compiled paper
├── experiments/
│   ├── orchestrator.py               # Main experiment runner (3 experiments)
│   ├── layers/
│   │   ├── l0_atomic.py              # L0: atomic decision boundary
│   │   ├── l1_acp.py                 # L1: ACP risk engine (wraps Go binary)
│   │   ├── l2_iml.py                 # L2: IML deviation estimator
│   │   └── l3_fairness.py            # L3: fairness allocation (M1/M2/M3)
│   ├── analysis/
│   │   └── plots.py                  # Figure generator (3 PDF figures)
│   ├── results/                      # CSV + JSON outputs
│   └── figures/                      # Generated PDF figures
├── README.md
├── LICENSE
└── .gitignore

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Three experiments

Experiment A — Ablation (Theorem 3: Irreducibility)

8 layer subsets × 4 guarantees × 20 trials = 160 trials.

Subset	P1 Atomicity	P2 Drift	P3 Fairness	P4 Sybil
L0+L1+L2+L3 (full)	✓	✓	✓	✓
L0+L1+L2	✓	✓	✗	✗
L0+L1+L3	✓	✗	✓	✓
L0+L2+L3	✗	✓	✓	✓
L1+L2+L3	✓	✓	✓	✓
L0+L1	✓	✗	✗	✗
L1+L2	✓	✓	✗	✗
L1+L3	✓	✗	✓	✓

The L1+L2+L3 row passes all guarantees empirically — this is a runtime equivalence case (L1 subsumes L0 in steady state) documented in §7.2, not a counterexample to irreducibility.

Experiment B — Feedback Convergence (Theorem 2)

10 seeds, 1000 steps each, drift scenario.

Condition	lim sup D̂	Converges
With feedback (FC1+FC2, K=η=0.50, ρ=0.70)	0.128 ± 0.026	10/10
Without feedback (open-loop)	0.419 ± 0.007	0/10

Measured contraction: 0.128/0.419 ≈ 0.31 ≈ ρ² — consistent with Lemma 5.2.

Experiment C — Interface Compatibility (Theorem 1)

20 trials across 4 scenarios (drift, sybil, atomic, mixed).

All scenarios achieve P1 compatibility = 1.00, P2 compatibility = 1.00,
decision equivalence ≥ 0.95.

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Reproduce experiments

git clone https://github.com/chelof100/compositional-governance
cd compositional-governance/experiments

# Install dependencies
pip install pandas numpy matplotlib

# Run all experiments (generates CSVs in results/)
python orchestrator.py

# Generate figures (PDFs in figures/)
python analysis/plots.py

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The governance architecture

┌──────────────────────────────────────────────────────────────────┐
│  RAM — Runtime Validity       [Paper 5, reconstructive-auth-model]│  When to execute?
│  Coverage envelope, reconstruction gate, privilege-narrowing     │
├──────────────────────────────────────────────────────────────────┤
│  L3 — Fairness Allocation     [Paper 3, fair-atomic-governance]  │  Who gets to act?
│  Population-level: actor shares, Sybil resistance                │
├──────────────────────────────────────────────────────────────────┤
│  L2 — IML Drift Monitor       [Paper 2, iml-benchmark]           │  Has behavior drifted?
│  Behavioral: D̂_t, feedback to ACP threshold                     │
├──────────────────────────────────────────────────────────────────┤
│  L1 — ACP Admission Control   [Paper 1, acp-framework-en]        │  Is this action admissible?
│  State: capability token, audit ledger, risk scoring             │
├──────────────────────────────────────────────────────────────────┤
│  L0 — Atomic Decision Boundary [Paper 0, decision-boundary-model]│  Can guarantees be made?
│  Temporal: decision ⊗ transition as single indivisible step      │
└──────────────────────────────────────────────────────────────────┘

The four core layers correspond to four orthogonal projections of the governance space: temporal (atomicity) · state (enforcement history) · behavioral (drift monitoring) · population (fair allocation).

Irreducibility (Theorem 3): no single mechanism can cover two projections simultaneously under finite observability.

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Position in the series

Paper	Title	Repo	Status
Paper 0	Atomic Decision Boundaries	decision-boundary-model	Zenodo · arXiv:2604.17511
Paper 1	Agent Control Protocol (ACP)	acp-framework-en	Zenodo · arXiv:2603.18829
Paper 2	From Admission to Invariants (IML)	iml-benchmark	Zenodo · arXiv:2604.17517
Paper 3	Fair Atomic Governance	fair-atomic-governance	Zenodo · arXiv: under review
Paper 4	Irreducible Multi-Scale Governance (this repo)	compositional-governance	Zenodo · arXiv: under review
Paper 5	Reconstructive Authority Model (RAM)	reconstructive-authority-model	Zenodo · arXiv: under review

Series logic:

• Paper 0 proves when admissibility can be guaranteed (structural necessity).
• Paper 1 builds a protocol that satisfies that condition (ACP, TLA+ verified).
• Paper 2 detects behavioral drift invisible to enforcement (IML, above the boundary).
• Paper 3 proves correct enforcement does not imply fair allocation (allocation layer).
• Paper 4 composes all four layers and proves their joint necessity (this paper).
• Paper 5 provides the operational closure: given partial observability, determines when execution is valid at runtime (RAM).

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Citation

@misc{fernandez2026comp,
  title        = {Irreducible Multi-Scale Governance: Composition and Limits
                 of Atomic Admission Systems},
  author       = {Fernandez, Marcelo},
  year         = {2026},
  doi          = {10.5281/zenodo.19672608},
  howpublished = {\url{https://doi.org/10.5281/zenodo.19672608}},
  note         = {Paper~4 of the Agent Governance Series. Zenodo. arXiv: under review.}
}

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Author

Marcelo Fernandez — TraslaIA — info@traslaia.com
https://agentcontrolprotocol.xyz