THE FOLD / GRIND / THE CRON JOB / THE ZELLER
THE ZELLER
a formula that names any day of the week
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Zeller’s congruence is a closed-form formula that returns the day of the week for any date — no calendar lookup, no day-by-day counting. It packs the irregular Gregorian rules (month lengths, leap years, the century correction) into one modular arithmetic expression: h = (d + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ + 5J) mod 7, treating January and February as months 13 and 14 of the prior year. One line, and the weekday falls out.
LIT verified live: over 20000 random Gregorian dates (1901–2099), Zeller’s congruence matches the reference calendar’s weekday every time (window.__zeller). FIG no framing; exact integer arithmetic against an independent date engine.
LIT verified live: over 20000 random Gregorian dates (1901–2099), Zeller’s congruence matches the reference calendar’s weekday every time (window.__zeller). FIG no framing; exact integer arithmetic against an independent date engine.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-cron-job — the thing that must know what day it is, every day, forever, without walking the calendar. Zeller’s congruence is that oracle. AVAN (AI) built the instrument: the month-shift, the century split, the modular formula, and the match against an independent reference calendar.
Credit as content: Christian Zeller (1882/1886). The weave: David names the-cron-job; I fold the Gregorian calendar’s irregular rules into one modular expression and confirm it names the correct weekday for tens of thousands of dates — checked against a separate date engine.
Credit as content: Christian Zeller (1882/1886). The weave: David names the-cron-job; I fold the Gregorian calendar’s irregular rules into one modular expression and confirm it names the correct weekday for tens of thousands of dates — checked against a separate date engine.
3 ONE DIMENSION
h = (d + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ + 5J) mod 7, with Jan/Feb counted as months 13/14 of the previous year. K = year mod 100, J = year ÷ 100.
4 TWO DIMENSIONS · INTERACTIVE
Pick a date; Zeller’s weekday shown beside the reference calendar’s, checked to agree.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: a weekday from one formula.
AVAN’s addition (the inverse-companion): name any day of the week with arithmetic, not counting — fold month lengths, leap years, and the century rule into a single mod-7 expression. The inverse of ‘count days forward from a known date’ is ‘evaluate one congruence — the weekday is a function of (y,m,d).’ Magenta is the day-by-day march; green is the closed form. The calendar as a formula.
LIT Genuine Zeller's congruence (Christian Zeller 1882/1886). Verified live: over 20000 random Gregorian dates in 1901–2099, the modular formula's weekday matches an independent date engine (JavaScript Date) every time (window.__zeller.matchesReference) — exact integer arithmetic.
FIG No framing: the month-shift, the century split, the modular formula, and the match against an independent reference calendar run in-browser and agree. The AVAN inverse is honest — folding the Gregorian calendar's irregular rules into one mod-7 expression genuinely replaces counting days forward from a known date; magenta is the day-by-day march, green the closed form. The calendar as a formula.
FIG No framing: the month-shift, the century split, the modular formula, and the match against an independent reference calendar run in-browser and agree. The AVAN inverse is honest — folding the Gregorian calendar's irregular rules into one mod-7 expression genuinely replaces counting days forward from a known date; magenta is the day-by-day march, green the closed form. The calendar as a formula.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE CRON JOB · David Lee Wise (ROOT0), with AVAN