Tekufot & Tal u-Matar (Halachic Seasons) (哈拉哈四季)

THE TEKUFOT OF SHMUEL — the halachic seasons: Shmuel's year is EXACTLY 365¼ days (the Julian year by construction), so his four season-points sit on FIXED Julian dates forever, drifting through the civil calendar one day per uncorrected century. TWO FAMOUS CONSEQUENCES SERVED: Birkat Hachama (Tekufat Nisan returning to Tuesday 18:00 every 28 years — 8 April 2009, next 2037 — cross-locked at load to the shmita engine's published series) and TAL U-MATAR, the diaspora rain-prayer start whose rule every siddur prints: 'Maariv of December 4th; December 5th before a civil leap year.' THIS ENGINE DERIVES THAT RULE RATHER THAN RECITING IT — the 6-hour year-cycle plus the nightfall rule makes the alternation FALL OUT, proven against the printed rule for every year 2020–2029 at load — and asserts the CENTURY DRIFT: from 2101 the Julian slide (the same +13→+14 gap the Revised Julian engine proves) moves it to December 5th/6th, the reprint every siddur eventually faces. Julian fixity asserted through the shared machinery (Tekufat Tishrei = Julian 24 September); Israel's different rule (7 Marcheshvan) named, never blended; the tekufah water-folklore labeled folklore; NOT A PSAK stated. Kabbalistic becomes eight systems. Pure compute, no LLM.

Cost: 1 TIAN Points per call. tRPC procedure tekufot.year.