H2E Sheriff: A Spectral Governance Layer for Agentic AI — Integrating LLM and World Model via Riemann Zeta Manifolds

What is H2E Sheriff?

H2E Sheriff is a real-time governance layer that sits between a Large Language Model (LLM) and a world model (e.g., ViT). It computes a Safety-Resonance Overlap Index (SROI) from the alignment between the LLM's hidden intent vector and the world model's state embedding, projected through a spectral manifold built from the first 50 Riemann zeta zeros. When SROI falls below a safety threshold, an irreversible hard stop is triggered — no exceptions, no retries.

Why the Riemann zeta zeros?

The set {γ_n} (imaginary parts of nontrivial zeta zeros) is not arbitrary. It inherits five certified spectral properties from an explicit Hilbert–Polya operator constructed in prior work [1]:

1. Real spectrum → SROI comparisons are ordered

2. Discrete spectrum → finite truncation is faithful

3. Simplicity (no repeated eigenvalues) → manifold snapping is unambiguous

4. Essential self-adjointness → spectral decomposition is unique

5. Hilbert domain with renormalized inner product → projections are well-posed

Without these properties, any safety manifold is heuristic. With them, H2E Sheriff is mathematically grounded.

What does H2E Sheriff achieve?

What this paper provides

• Complete architectural specification of H2E Sheriff

• Mathematical derivation of the spectral manifold H = Q diag(γ₁…γ₅₀) Qᵀ

• Formal definition of the SROI metric and governance gate

• Empirical validation with ground truth models on Hugging Face

• Dependency analysis showing H2E inherits rigor from [1], not from RH or HPC

Engineering innovations validated in the UNESCO challenge

• Surgical GPU warmup (Voxtral-Mini-4B): neutralizes cold-start penalties

• 19-layer FP8 architecture (Sarvam-30B): 98.4% alignment, zero violations

• Deterministic manifold snapping (Gemma-4-E4B): 4-bit precision preserves Λ = 0.9583

Ground truth models (Hugging Face)

• Audio: frankmorales2020/voxtral-mini-4b-unesco-audio

• Text: frankmorales2020/sarvam-30b-fp8-unesco-resilient

• Vision: frankmorales2020/gemma-4-e4b-unesco-optimized

Who should read this

• AI safety engineers building governance layers for agentic systems

• Researchers in spectral methods for alignment and control

• ML engineers seeking deterministic, hardware-resilient safety gates

• Reviewers of the H2E submission to Nature Methods (NMETH-A66001)

Related Zenodo papers in this ecosystem

• [1] An Explicit Hilbert–Polya Operator from Prime Shift Operators (10.5281/zenodo.19842593) — provides the mathematical certification

• [2] The Prime Resonance Ecosystem: A Spectral Framework for the Riemann Hypothesis (10.5281/zenodo.19855325) — research roadmap, not required for H2E

Citation

@misc{morales2026h2esheriff,
  title={H2E Sheriff: A Spectral Governance Layer for Agentic AI -- Integrating LLM and World Model via Riemann Zeta Manifolds},
  author={Morales Aguilera, Frank},
  year={2026},
  month={April},
  doi={10.5281/zenodo.19867683},
  note={Zenodo preprint}
}