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 multi-agent workflows fundamentally pre-suppose component failure independence. In this work, we prove that shared pretraining blindspots and latent difficulty correlation induce severe Common Mode Failures (CMF) that render multiplicative reliability bounds invalid. First, we prove the K-Layer Defense Composition Theorem, deriving the asymptotic attack floor ϖharm > 0 and verification discount DK (ρ), explaining why stacked defenses fail to compound exponentially and validating our predictions against the empirical measurements of Alotaibi et al. (2026). Second, we establish the Sub-Majority Capability Dilution Theorem (K†) and the fundamental CMF Duality: while latent difficulty correlation cushions sub-majority committees (α < 1−ϖ2 ) against deterministic collapse (F∞ < 100%), finite consensus systematically dilutes accuracy relative to standalone champions, explaining why pooled SWE-bench Verified consensus degrades resolution from 40.6% (Top-1) to 32.6% (Top-9, p = 7.2 × 10−7; 31.10% under randomized tie-break at K = 10). Third, we establish the ϖ/ρ Identification Theorem: pairwise correlation (K = 2) is fundamentally unidentifiable, whereas K ≥ 3 agent pools achieve local identifiability on the interior parameter space via joint co-failure moments. Across 11, 710 benchmark evaluations (11, 442 unique tasks across 38 models), within-suite splits confirm that error correlation tracks task structure at fixed model pool: multi-step competition mathematics induces heavy correlation ( ¯ϕ = 0.6667) versus general reasoning ( ¯ϕ = 0.5140) across the identical seven 2026 frontier reasoning models. Finally, we derive the Assume-Guarantee Safety Composition Operator, providing model-based safety formulas that capture joint tail correlation.