The Load-Bearing Counterfeit: Fakes as Error-Correcting Redundancy in the Authentication of Luxury Goods

Every luxury house treats the counterfeit as an enemy: a theft of value to be raided, watermarked, and litigated toward zero. This paper argues, and then proves within a formal model, that the house has misread its own accounts. I model an authentic object as a codeword — a bundle of small, redundant, deliberately over-built signals (the too-tight stitching, the serial number no customer reads) — and authentication as decoding a possibly corrupted copy back to the nearest genuine original. Three consequences follow. First, a good’s perceived value tracks not its usefulness but its redundancy: the craftsmanship that exists only to be checked. Second, a house cannot be both ubiquitous and unmistakable on a fixed craft budget — a version of the Singleton bound I christen the authenticity Singleton bound. Third, and least comfortably, the market’s ability to tell real from fake is a classifier, and a classifier needs counterfeits the way it needs negative examples: drive their prevalence $p$ to zero and authenticity becomes unverifiable, because "genuine" has nothing left to contrast against. Value is maximized at a strictly positive counterfeit rate $p^{\star }$. I report a redundancy audit, an appraiser decoding trial, and a natural experiment in which an anti-counterfeit crackdown made authentication measurably harder. The counterfeit, it turns out, is load-bearing.