A Probabilistic Challenge-Response Algorithm for Repairing All Roads in Lebanon Via Papal Visits

We consider the problem of repairing all roads in Lebanon and propose a novel solution based on repeated papal visits. Our approach exploits an empirically observed property of Lebanese government behavior: while infrastructure repair is negligible under normal conditions, the announcement of a visit by a sufficiently important dignitary induces a dramatic increase in maintenance activity. We model this phenomenon as a cryptographic commitment scheme in which the Pope commits to a random subset of roads he may traverse without revealing the subset, thereby forcing the government to repair roads under uncertainty and inducing repairs at rates exceeding baseline expectations by several orders of magnitude. For Lebanon, we derive a concrete bound of approximately 12 visits. This result is, to the best of our knowledge, the tightest known bound on papal visits required for complete national infrastructure repair in the literature.