A Generative Framework for Correlated Failure in Multi-Agent LLM Systems: Asymptotic Floors, Dilution Thresholds, and Defense Stack Certification

Ensemble aggregation, defense-in-depth guardrails, and autonomous multi-agent workflows fundamentally presuppose failure independence across components. In this work, we prove that latent difficulty correlation and shared pretraining blindspots induce severe Common Mode Failures (CMF) that render independence-based reliability bounds catastrophic illusions. First, we prove the K-Layer Defense Composition Theorem, deriving the non-zero asymptotic attack floor ϖharm > 0 and the verification discount DK (ρ), explaining why stacking seven defensive filters fails to compound multiplicatively and inflates empirical leakage by up to 17.2 percentage points as measured by Alotaibi et al. (2026). Second, we establish the Conjunctive Functional Correctness Dilution Theorem (Kcode†), proving analytically why majority consensus on conjunctive (all-or-nothing) software tasks systematically poisons functional correct- ness past K † = 1 when standalone resolve rates are below 50%, resolving the empirical ceiling observed by Nogueira et al. (2026) and confirming why 9-agent SWE-bench consensus increases failure from 59.4% to 67.4%. Third, we formulate the ϖ/ρ Identification Theorem, proving global identifiability via lower-triangular moment Jacobians with exact Plackett derivatives, and empirically show that factual knowledge tasks exhibit over double the irreducible failure atom of reasoning tasks (ϖ̂ = 6.94% vs. 3.28%). Fourth, we conduct a cross-generation empirical validation across 11, 710 task instances, establishing that frontier 2025–2026 reasoning models (OpenAI o1, o3-mini, Claude 3.7 Sonnet Thinking, DeepSeek-R1) exhibit higher pairwise error correlation (ϕ̄ = 0.5703) than 2024 non-thinking models (ϕ̄ = 0.4536) with a 26.32% simultaneous failure floor. Finally, we derive the Assume Guarantee Safety Composition Operator, providing certified runtime assurance bounds that survive non-exchangeable multi-agent tail correlation where conformal prediction fails.