The Split Tally as a Cooperative Record: What Two Halves of a Stick Prove, and the Discrepancy Rule That Makes Them Useful

A split tally records a quantity as notches cut across a stick that is then split lengthwise, so that each party keeps a half bearing the same notches. This paper models that device as a produce cooperative's deposit record and gives it a working procedure. On a stick with 280 mm of usable length, a single row of unit notches at 4 mm spacing holds 70 notches; the zoned denomination scheme proposed here, units at 5 mm spacing in a 100 mm zone, tens at 9 mm in a 90 mm zone, and hundreds at 18 mm in a 90 mm zone, represents any quantity up to 599 kg, or 599.5 kg with a half-unit notch, at a resolution of 0.5 kg. One-sided alteration is the tally's strength: a notch added to one half only is always exposed when the halves are fitted together, giving a detection probability of 1.0 under the stated rule that halves are always compared, whereas a single written figure in one book carries a stated undetected-alteration probability of 0.01 per record, worth an expected 20.0 kg per year over 400 records at an assumed 5 kg per alteration. Joint fitting also reduces reading error: the probability of miscounting at least one zone falls from 1.49 percent for a half read alone to 0.15 percent when both halves are counted together, or from 5.97 expected miscounts in 400 settlements to 0.6. The cost of settling small disagreements without a dispute is a tolerance, and its price is stated plainly: settling on the lower figure whenever the halves differ by at most 1 kg can hide at most 400 kg per year over 400 settlements, which is 1.67 percent of a throughput of 24000 kg, in the worst case where every difference favours the same party. All results are simulated, not measured.