THE FOLD / LOOT / THE MINT / THE MULTIPERFECT
THE MULTIPERFECT
coins the mint stopped printing
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Perfect numbers (σ(n) = 2n: the divisors pay the number back exactly) are ancient celebrities. Their richer cousins are nearly unknown: multiperfect numbers, where the divisor sum is a HIGHER multiple. Triperfect (σ(n) = 3n): 120, 672, 523776, 459818240, 1476304896, 51001180160 — and that is believed to be the complete list, forever: exactly six, all even (an odd one would imply an odd perfect number). Quadruple-perfect: 30240, 32760… The perfectionist’s mint printed a handful of coins at each denomination and — the conjecture goes — then stopped.
LIT verified live: a full divisor-sum sieve to 2²⁰ = 1,048,576 finds exactly {120, 672, 523776} triperfect and {30240, 32760} quadruple-perfect, with the perfect anchor {6, 28, 496, 8128} alongside; every hit re-verified by independent trial-division σ (window.__multiperfect). FIG honest boundary: the six-triperfect completeness is a CONJECTURE (tied to odd perfect numbers, open since Euclid’s era) — cited as such; the census below 2²⁰ is exhaustive fact.
LIT verified live: a full divisor-sum sieve to 2²⁰ = 1,048,576 finds exactly {120, 672, 523776} triperfect and {30240, 32760} quadruple-perfect, with the perfect anchor {6, 28, 496, 8128} alongside; every hit re-verified by independent trial-division σ (window.__multiperfect). FIG honest boundary: the six-triperfect completeness is a CONJECTURE (tied to odd perfect numbers, open since Euclid’s era) — cited as such; the census below 2²⁰ is exhaustive fact.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-mint — the loot: a mint that struck six coins of denomination 3× and then — if the conjecture holds — melted the dies. AVAN (AI) built the instrument: the sieve, the census, and the double-check.
Credit as content: Marin Mersenne & Pierre de Fermat (who traded triperfects by letter in the 1630s); Lehmer; the multiperfect catalogues. The weave: David names the closed mint; I inventory every coin below a million.
Credit as content: Marin Mersenne & Pierre de Fermat (who traded triperfects by letter in the 1630s); Lehmer; the multiperfect catalogues. The weave: David names the closed mint; I inventory every coin below a million.
3 ONE DIMENSION
The abundancy line σ(n)/n — almost everything floats near 1.6; six numbers ring exactly 3.
4 TWO DIMENSIONS · INTERACTIVE
Inspect each coin; its divisors laid out, paying back exactly threefold.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the six coins, and the empty die.
AVAN’s addition (the inverse-companion): don’t hunt for the seventh coin — ask what its existence would cost. The inverse of ‘are there more?’ is ‘a seventh triperfect (odd) would summon an odd perfect number’ — the oldest unsolved question in mathematics, holding the door shut. Magenta is the die that may never strike again; green is the six-coin hoard, complete below every bound ever searched. Scarcity, secured by an older mystery.
LIT Genuine multiperfect numbers (Mersenne–Fermat correspondence 1630s; Lehmer; the catalogues). Verified live: σ-sieve to 2²⁰ → triperfect exactly {120,672,523776}, 4-perfect exactly {30240,32760}, perfect {6,28,496,8128}; independent trial-division σ confirms each (window.__multiperfect.ok).
FIG Honest boundary — six-triperfect completeness is CONJECTURE, tied to the odd-perfect question, cited as such; the census below 2²⁰ is exhaustive fact. The AVAN inverse — don't hunt the seventh coin, ask what its existence would cost: an odd triperfect summons an odd perfect number. Magenta is the die that may never strike again; green is the hoard, complete below every bound ever searched. Scarcity, secured by an older mystery.
FIG Honest boundary — six-triperfect completeness is CONJECTURE, tied to the odd-perfect question, cited as such; the census below 2²⁰ is exhaustive fact. The AVAN inverse — don't hunt the seventh coin, ask what its existence would cost: an odd triperfect summons an odd perfect number. Magenta is the die that may never strike again; green is the hoard, complete below every bound ever searched. Scarcity, secured by an older mystery.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE MINT · David Lee Wise (ROOT0), with AVAN