Tolerance Needs a Multiplicity — hypothesis
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hypothesis.md
# Tolerance Needs a Multiplicity — hypothesis **Source:** Incoprea Theory Volume VIII, Theory 068 / Information & Computation. **Claim (verbatim):** "Fault tolerance requires redundancy of a specific multiplicity set by the failure model rather than by the number of replicas, so adding replicas beyond the requirement adds cost without reliability when failures are correlated." **Predictions (verbatim):** - P1 — Reliability should saturate at the required multiplicity. - P2 — Extra replicas should add correlated failures. - P3 — Independence assumptions should fail in shared infrastructure. **Refutation (verbatim):** Reliability rising indefinitely with replicas would favour count models. **Pre-registered test.** A replicated majority-quorum system faces two failure sources: independent per-replica failures and a shared common-mode failure that hits every replica. Compute reliability as the replica count grows, under the independent-only model and the shared-infrastructure model, and measure the marginal benefit of each added replica. **Fixed before running:** majority quorum (n/2 + 1 alive); per-replica failure probability and common-mode failure probability held fixed.