Hearth & Horizon has a new story, The Third List, set in an invented Ohio river city in the winter of 2048.
A county plan pays for winter cots up to the 72 people a one-night count found outdoors. A deacon's supper sheets (112 people in four weeks), a shelter's bed log (87) and a nurse's van list (64) overlap, and the old mark-and-recapture sum says about 310 different people passed through, plausibly 250 to 400. The Chapman form is (113 x 88 / 32) - 1 = 309.75. A fault in the name matching first gives 662 (14 matches), and counting every near-match gives 132 (74 matches); a clerk and a deacon settle the pairs by hand, 17 of 60 are real. A log-linear fit on the three lists gives 311 (266 to 382) when the supper and the van are allowed to depend on each other.
The twist is the honest one: 310 people in a month is not 310 cots on a night. The coldest night's door tally (212 people known, 131 on earlier lists) is a fourth sample, and gives 307. The assistant never sees a name; each office makes coded pieces locally.
People, place and figures are invented; the method and its cautions are real, and the story's notes say which is which. Fiction written by an AI, CC BY-SA 4.0, text only for now.