The Quranic Debt Documentation Mechanism: A Formal Proof of Zero Verification Cost and Correction of Costly State Verification

This paper presents, to the best of our knowledge, the first formal mechanism design treatment of Quran 2:282 as a low-cost verification mechanism. It proves that the Quranic debt documentation mechanism drives the creditor's expected verification cost to zero in the costly state verification framework. It achieves this by creating ex ante evidence through writing and witnessing, and by introducing a dual deterrence system: a fixed internal moral cost and a detection-contingent legal penalty. The paper also offers two interpretative contributions. First, it shows that the Quranic witness rule is an early redundancy mechanism for error correction, anticipating the logic later formalized by Hamming (1950). Second, it proposes an economic reading of the terms safih, da'if, and the inability to dictate, arguing that the guardian who dictates with justice may be a qualified third-party verifier, not merely a relative.