Sheaf-Guarded Updates: Streaming Structural Verification for Evolving Agent State

Self-evolving scientific agents need update-time verification: does the agent's internal state remain coherent after a local self-modification? We model agent state as a growing graph equipped with a cellular sheaf and use coboundary checks, H1H^1 H1 obstruction, Dirichlet energy, and Laplacian spectra to detect represented structural contradictions before commit. Under explicit policy and regularity assumptions, we prove conditional Lyapunov stability results for density and spectral-gap dynamics. A cellular decomposition localizes cohomological recomputation to O(1)O(1) O(1) amortized per-edit cost under bounded-cell and cached-assembly assumptions, enabling maintenance at V=5V{=}5 V=5M vertices with 35 μ35\;\mu 35μs median per-edit latency and zero assembled-cohomology drift on a single commodity machine. On ProofDAG, a controlled proof-dependency coherence test, per-edge coboundary testing achieves exact separation (F1=1.000\textrm{F1} = 1.000 F1=1.000) under exact representation and F1≥0.94\textrm{F1} \geq 0.94 F1≥0.94 under 14%14\% 14% relative noise. A 990-lemma study with live LLM proposals across 10 mathematical domains shows that coarse natural-language loading causes structural aliasing: valid and contradictory coboundary distributions overlap, identifying loader fidelity as the binding constraint for autonomous commit decisions. A Lean/mathlib benchmark confirms the exact-loader path on 507 declarations and 954 kernel-certified dependency edges across 6 namespace groups, with zero clean residuals (max 2.61×10−162.61 \times 10^{-16} 2.61×10−16) and all 62 controlled corruptions detected. We present an implemented demonstration of bounded-cell sheaf-cohomological verification under streaming graph mutations at multi-million-vertex scale.