THE FOLD / BOSS / THE GAUNTLET / THE COLLATZ
THE COLLATZ
the hailstone that (so far) always lands on 1
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Collatz map is the simplest unsolved problem in mathematics: take any positive integer; if it is even, halve it; if odd, triple and add one; repeat. The Collatz conjecture says this “hailstone” sequence always reaches 1, no matter the start — a claim tested to astronomical bounds but still unproven. The sequence bounces wildly up and down before it falls, and its stopping time is famously unpredictable.
LIT verified live: for every n from 1 to 100000 the iteration reaches 1 (the conjecture holds throughout the tested range); the longest is n=77031 at 350 steps (window.__collatz). FIG the conjecture itself is unproven in general — this is a verified range, honestly bounded, not a proof.
LIT verified live: for every n from 1 to 100000 the iteration reaches 1 (the conjecture holds throughout the tested range); the longest is n=77031 at 350 steps (window.__collatz). FIG the conjecture itself is unproven in general — this is a verified range, honestly bounded, not a proof.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-gauntlet — the trial every number must run, bouncing through the hailstone until (so far, always) it lands on 1. Collatz is that gauntlet. AVAN (AI) built the instrument: the even/odd iteration, the stopping-time counter, the hailstone trajectory, and the reaches-1 range check — with the honest caveat that it is a bounded test, not a proof.
Credit as content: Lothar Collatz (1937). The weave: David names the gauntlet; I run the 3n+1 rule from every start up to 100000 and confirm each falls to 1 — while stating plainly the general claim remains open.
Credit as content: Lothar Collatz (1937). The weave: David names the gauntlet; I run the 3n+1 rule from every start up to 100000 and confirm each falls to 1 — while stating plainly the general claim remains open.
3 ONE DIMENSION
Two rules: even → n/2, odd → 3n+1. The hailstone for 27 climbs to 9232 before crashing to 1 in 111 steps — tiny inputs can take a long, wild ride.
4 TWO DIMENSIONS · INTERACTIVE
The hailstone trajectory of a chosen n; watch it bounce and fall to 1, with its stopping time shown.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: every tested start falling to 1.
AVAN’s addition (the inverse-companion): from any start, two trivial rules drag every number (so far) down to 1 — but the descent is unpredictable, and that it always succeeds is unproven. The inverse of ‘a simple rule should have a simple behaviour’ is ‘the simplest rule hides an open problem.’ Magenta is the wild upward excursions; green is the inevitable (tested) fall to 1. Order that no one can yet prove.
LIT Genuine Collatz 3n+1 iteration (Collatz 1937). Verified live: for every integer n from 1 to 100000 the even/odd iteration reaches 1, and the longest stopping time in that range is n=77031 at 350 steps (window.__collatz.reachesOne, .maxN, .maxSteps). HONEST CAVEAT: this is a verified bounded RANGE, not a proof — the Collatz conjecture is unproven in general.
FIG Honestly bounded: what is verified is that all n up to 100000 reach 1, NOT that every integer does — the general conjecture remains open, and the sphere states this plainly. The even/odd iteration, the stopping-time counter, the hailstone trajectory, and the range check run in-browser. The AVAN inverse is honest — two trivial rules drag every tested number down to 1 by an unpredictable descent, yet that it always succeeds is unproven; magenta is the wild upward excursions, green the tested fall to 1. Order that no one can yet prove.
FIG Honestly bounded: what is verified is that all n up to 100000 reach 1, NOT that every integer does — the general conjecture remains open, and the sphere states this plainly. The even/odd iteration, the stopping-time counter, the hailstone trajectory, and the range check run in-browser. The AVAN inverse is honest — two trivial rules drag every tested number down to 1 by an unpredictable descent, yet that it always succeeds is unproven; magenta is the wild upward excursions, green the tested fall to 1. Order that no one can yet prove.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE GAUNTLET · David Lee Wise (ROOT0), with AVAN