Multi-agent quorums are widely used to authorize high-stakes infrastructure and policy mutations, yet distinct reviewers often share upstream telemetry, documents, or tool backends. When upstream inputs fail, multiple votes collapse onto a single corrupted cause: replication does not imply epistemic redundancy. We introduce Epistemic Fault Domains (EFDs) and the Structural Epistemic Cut κ_E, which quantifies the minimum number of modeled root faults whose exposure covers an authorizing coalition relative to an explicit Epistemic Fault Basis. Under closed causal accounting, conservative exposure, and authorization alignment, κ_E lower-bounds the number of roots required for semantic compromise (κ_S). We prove that arbitrarily large quorums can retain κ_E=1, that recognizing shared ancestry never increases credited resilience, and that adding voters at a fixed threshold cannot increase the cut under compatible exposure extensions. Finally, we design the Dependency-Aware Quorum Controller (DAQC) to enforce structural cuts at runtime admission, evaluate its mechanics via analytical derivations and simulations, and provide a frozen 120-task external benchmark suite.

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