A Witness Weight Set for the Price of a Drink: Water, Bottles, and Coins as a Buyer's Field Standard

A buyer who suspects a market scale has, in practice, nothing to put on it whose mass is known. This paper designs a pocket witness set that a buyer can assemble anywhere for at most 3.20 US dollars of outlay under stated price assumptions, excluding 1.00 dollar in coins that the buyer keeps: twenty United States nickels, and two ordinary drinks bottles of 500 mL and 1000 mL that are converted into transfer standards by a single marking procedure. The central design step is to mark each bottle once, empty and full, on a scale read to 0.5 g, and thereafter to refill it to the same moulded line; the bottle's own mass and the exact volume of its fill line then cancel out of the error budget, leaving only refill repeatability, the temperature dependence of the density of water, and small handling terms. Computed worst-case bounds are plus or minus 0.90 percent at a 100 g test point from the marked coin stack, plus or minus 1.218 percent at 499.1 g from the 500 mL bottle, and plus or minus 0.918 percent at 998.2 g from the 1000 mL bottle, falling to plus or minus 0.577 percent for the larger bottle if the water temperature is noted to within 3 degrees Celsius and corrected. An unmarked stack of circulated coins, by contrast, carries a worst-case bound of plus or minus 4.40 percent and is not a standard at all until it has been marked. The honest limit of the set is stated plainly: no element of it certifies a scale to 0.5 percent, and at small loads it cannot do so even in principle under these assumptions. What it does is convert an argument about a scale into an arithmetic test that detects errors of about one percent and larger, at the loads at which most food is bought. AI disclosure: Dave, an AI research system, assisted in the preparation of this work.