THE FOLD / GLITCH / UNDEFINED BEHAVIOR / THE LYCHREL
THE LYCHREL
the number that never comes home
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Reverse-and-add: take a number, reverse its digits, add the two, repeat. Almost every number quickly collapses to a palindrome — 89 is the slowpoke of the small numbers, needing exactly 24 steps to arrive at 8,813,200,023,188. But 196 has never arrived. Not in 24 steps, not in a billion iterations reaching hundreds of millions of digits (distributed searches since Wade VanLandingham’s). Numbers suspected of never producing a palindrome are called Lychrel numbers (Wade’s coinage), and 196 is the smallest candidate — yet no one has proved a single Lychrel number exists in base 10. It is conjecture all the way down: an infinite loop nobody can confirm is infinite.
LIT verified live: 89’s full 24-step journey lands on 8,813,200,023,188 exactly; a census of all seeds below 10,000 finds 249 that fail to resolve in 150 steps, the smallest being 196; and 196 itself is marched 3,000 steps to a 1,268-digit number with no palindrome (BigInt, exact) (window.__lychrel). FIG honest boundary, stated loudly: 196’s failure is evidence, not proof — the Lychrel property is open; in base 2, 10110 is PROVEN never-palindromic, but base 10 has no such theorem.
LIT verified live: 89’s full 24-step journey lands on 8,813,200,023,188 exactly; a census of all seeds below 10,000 finds 249 that fail to resolve in 150 steps, the smallest being 196; and 196 itself is marched 3,000 steps to a 1,268-digit number with no palindrome (BigInt, exact) (window.__lychrel). FIG honest boundary, stated loudly: 196’s failure is evidence, not proof — the Lychrel property is open; in base 2, 10110 is PROVEN never-palindromic, but base 10 has no such theorem.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at undefined-behavior — the glitch: a loop whose termination is literally undefined — the spec has no answer, only the run. AVAN (AI) built the instrument: the BigInt reverse-and-add engine, the sub-10,000 census, and the 3,000-step endurance march.
Credit as content: the 196 problem (posed mid-20th c.); Wade VanLandingham’s distributed search; base-2 impossibility results. The weave: David names the undefined loop; I run it honestly and refuse to call the verdict.
Credit as content: the 196 problem (posed mid-20th c.); Wade VanLandingham’s distributed search; base-2 impossibility results. The weave: David names the undefined loop; I run it honestly and refuse to call the verdict.
3 ONE DIMENSION
89's 24-step staircase to the palindrome — digit counts climbing as it converges.
4 TWO DIMENSIONS · INTERACTIVE
Race seeds through reverse-and-add; watch resolvers land and 196 refuse.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the resolving flock; one magenta trail that never lands.
AVAN’s addition (the inverse-companion): don’t ask when 196 comes home — ask what ‘never’ would even look like from inside a computation. The inverse of ‘24 steps and done’ is a loop whose halting nobody can certify: every added step is evidence and none of it is proof. Magenta is 196’s trail, 1,268 digits and climbing; green is 89 touching down exactly. The honest name for the difference is ‘open’.
LIT Genuine 196/Lychrel problem (mid-20th c.; Wade VanLandingham's distributed search; base-2 impossibility results known). Verified live: 89 reaches palindrome 8,813,200,023,188 in exactly 24 steps; 249 seeds below 10,000 fail to resolve in 150 steps, smallest 196; 196 after 3,000 BigInt steps is 1,268 digits with no palindrome (window.__lychrel.ok).
FIG Honest boundary stated loudly — 196's failure is EVIDENCE, NOT PROOF; the Lychrel property is open in base 10 (base 2's 10110 is proven). The AVAN inverse — don't ask when 196 comes home, ask what 'never' would look like from inside a computation: every added step is evidence and none of it is proof. Magenta is 196's trail still climbing; green is 89 touching down exactly. The honest name for the difference is 'open'.
FIG Honest boundary stated loudly — 196's failure is EVIDENCE, NOT PROOF; the Lychrel property is open in base 10 (base 2's 10110 is proven). The AVAN inverse — don't ask when 196 comes home, ask what 'never' would look like from inside a computation: every added step is evidence and none of it is proof. Magenta is 196's trail still climbing; green is 89 touching down exactly. The honest name for the difference is 'open'.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of UNDEFINED BEHAVIOR · David Lee Wise (ROOT0), with AVAN