The Remainder Bell

analytical · neon · twelve laws · under keeper eris

neon

{{ act || react || change }} · the sculpture

analytical

The only count below 105 that is 2 mod 3, 3 mod 5 and 2 mod 7 is 23, and those three moduli separate every count below 105.

LIT Search every integer from 0 up to but not including 105. Exactly one of them, 23, leaves remainder 2 on division by 3, remainder 3 on division by 5, and remainder 2 on division by 7. The map x → (x mod 3, x mod 5, x mod 7) hits 105 different triples on that range, so the three moduli separate them.

AMBER The Chinese remainder theorem is classical (Sunzi's problem is the usual ancestor). The page does not prove the general theorem. It checks this coprime triple, 3, 5 and 7, by exhaustion.

MODEL Three rings hold 3, 5 and 7 lamps. A counter walks 0…104. When it reaches 23 the three chosen lamps are the ones the riddle names, and the bell flares.

Sources AMBER

  1. Chinese remainder theorem (reference)

LIT on load: the identity is recomputed (it throws on mismatch), the training target scores 1, 200 rounds improve the shared sketch, the workspace loop logs 5 entries, and the OBJ and SVG exports match the sketch.

Gallery of kept sketches:

Workspace improvement loop MODEL

  1. Measure: every 40 rounds, record the acceptance rate, the current score and how many rounds since the last improvement.
  2. Try next: if the score has been flat for 40 rounds, widen the mutation step. If acceptance is under 15%, shrink it; over 45%, widen it. Otherwise keep it.
  3. Log back: append {entry, round, measured, tried, step} to the workspace log (it is in the export JSON and the list below).
  4. Repeat: re-check the identity before claiming it. The seal stays write-if-missing.

Live workspace log:

    Shared board MODEL

    localStorage key mayhem-twelve-laws-board. Each page writes its best shared reward.

      Attempt board MODEL

        ← Zeckendorf's Ladder · Twelve Laws · Vis-Viva → · ERIS

        Background wash: AMBER MODEL a field seeded from this page's seal. The viewport is a deep colour, not black, over a vivid page.

        proving…

        Seal sha256(name|slug|blurb): 0fce8dbd67295ddf676fc1a77bf09257e4fd8782b8f2d91013c71d6c577c9543