The Containment Depth Bound: A Formal Proof for Epistemic Quarantine Systems

A complete formal proof of the Containment Depth Bound governing 
sequential Epistemic Quarantine checkpoints in LLM hallucination 
containment systems. The theorem states: for single-checkpoint 
detection rate rho and target escape probability epsilon, the 
minimum checkpoints guaranteeing P(escape) <= epsilon is 
k* = ceil(log(epsilon)/log(1-rho)). Includes proof from first 
principles, numerical verification at three epsilon values, 
escape probability table, discussion of the independence 
assumption, and connection to fault-tolerant computing and 
boosting theory. Empirically grounded with rho=0.12 from 
HotpotQA adversarial benchmark: k*=24 for 95% containment, 
verified as (0.88)^24 = 0.0465. Companion to the full CIS paper.