The Ratchet on Mandatory Links How many places in a loop still require a human to approve: a computable model, an ordering prediction, and the exponent that decides whether the count has a floor

Abstract How many places in a loop still require a human to approve is a quantity that appears as an input in the criterion for timeliness [13] and as a binary verdict in the criterion for decoupling [14]. This paper gives it a dynamics. Each mandatory link is written as a pair: the delay d incurred by keeping a human in that link, and the cost c incurred by removing the human from it. Writing v for the price the market places on saving one unit of human delay, the link is removed once v·d > c, so the surviving fraction of mandatory links under pressure v equals P(d/c ≤ 1/v). Result one: the order of removal is fixed by the ratio d/c, largest first, independently of how important the link is and of how hard it would be to automate. Result two: whether the count has a floor is decided by the tail of the removal-cost distribution, not by the initial number of links. With lognormal removal costs the fraction decays faster than any power law and is already 2.35×10⁻⁵ at a pressure of one hundred, which means zero for any realistic loop; with a power-law right tail of index α the fraction decays as v to the power −α, and at a pressure of one hundred with α = 0.5 it is still 0.108, so a residue survives at any finite pressure. Result three: the more strongly delay and cost are correlated, the more fragile the loop, because the ratios concentrate on a shared threshold and the whole segment goes at once when it is crossed; at a correlation of 0.9 a pressure of five already empties the loop, whereas at zero correlation 7.7 per cent still survives. A policy consequence follows directly: adding mandatory links buys a constant factor, while changing the tail of one link's removal cost buys an exponent. Any remedy of the form "add another layer of approval" is computable in this model and decays to nothing as pressure rises. Three falsifiable predictions are registered. The cheapest is an ordering prediction: in industries that have already automated, the order in which approval steps were automated should follow the ranking of the ratio. Its power boundary is given with it, and below a Spearman correlation of 0.5 the prediction has no discriminating power. Appendix B expands that prediction into a candidate industry list, item-by-item coding rules, and a worksheet that can be filled in directly.