← Range ArcadeWORLD Nº 055 · CALL THE EDGE, THEN STOP
◐ edge fortuneKNOW WHAT THE CARRY DECIDES. KNOW WHERE IT STOPS DECIDING.

GENERATION ONE QUINTILLION. NO SIMULATION. STILL KNOWN.

The carry decides
exactly this many bits.

Read g+1 in binary. However many low bits carried, that is v, and v alone fixes the first bits of the edge:
a run of ones, a zero, a plateau. Call them, then stop before the first bit nobody can know from v.

THE EDGEFORTUNE 1 / 8
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Eight fortunes
at the edge of the cone.

Each fortune is a generation g, far too large to simulate. Call the edge bits from the outside in: lit or dark.
Five points a known bit, fifteen for stopping exactly where the law runs out, and a slip ends the fortune.

0 POINTS1 LIT · 0 DARK · ENTER STOPTELL ME THE EDGE

prefixlaw: bit b of the edge has period 2^p(b) from generation zero, so v2(g+1) = v pins every bit with p(b) ≤ v+1, and the next one genuinely varies.

OTHER GENERATIONS

Words choose which generations the fortune teller reads.

THE FORTUNE TELLER'S LADDER

What v2(g+1) knows, and what it cannot.

Every bit of rule 30's light-cone edge is exactly periodic with a period that is a power of two, from generation zero. So which bits are fixed by g+1's carry is a matter of divisibility: if 2^v divides g+1, every bit with p(b) ≤ v+1 is pinned, and the bit after that takes both values as the odd part of g+1 changes.

The pinned prefix is always a run of ones (the edge run, A094604), then a zero, then a short plateau pattern that depends only on v. The ladder in the first level shows the run and the whole pinned prefix per rung; later levels ask you to read v off the counter and remember.

Calling past the pinned bits is gambling: the game looks each bit up honestly, and a lucky call scores two, but a slip ends the fortune. The encore asks for the centre column at a small generation, where no lookup exists at all; the game has to simulate, and so would anyone.

EIGHT FORTUNES READ

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You knew
where knowledge ends.

A FORTUNE FOR A FRIEND

Read these edges with me.