Edo Clock (不定時法) (江戶時刻)

THE EDO CLOCK (不定時法) — how Japan told time before 1873: twelve toki named by the earthly branches (子の刻, the rat's hour at midnight), announced by temple bells whose counts ran BACKWARD — nine, eight, seven, six, five, four, twice a day. THE COUNTDOWN IS A THEOREM, asserted at load: the cosmological count assigned each period n × 9 strikes (nine, the perfect yang number: 9, 18, 27, 36, 45, 54) but only the LAST DIGIT was rung — and 9n mod 10 for n = 1…6 is exactly 9, 8, 7, 6, 5, 4. The mysterious descending bells are modular arithmetic. AND THE SYSTEM STILL SPEAKS, each a law: OYATSU (お八つ), every Japanese snack-time, is the sheep-hour's eight bells (~2 pm); USHIMITSU (丑三つ時), the ox's third quarter (~2:00–2:30 am), is the ghost hour of every kaidan; and 正午 means noon because noon is the HORSE's hour. THE UNEQUAL REALITY DISCLOSED: true Edo practice stretched daylight's six toki with the seasons, and the wadokei — clocks with MOVABLE NUMERALS — bent machinery to elastic time, horology's most wonderful dead end; the fixed table served is the standard convention, the elasticity named. Japanese becomes twenty-four. Pure compute, no LLM.

Cost: 1 TIAN Points per call. tRPC procedure edoClock.toki.