Reproduceseeded — reproduces with the given seed·reruns the search (See below)·Budget: ~300 s × 8 finishers (exploratory run, not the standardized single-core bench)
Pipeline
1
restart tournament
Flood hundreds of short probes from random seeds, rank by perfect-prefix depth, ratchet-pin the deepest and probe beyond it
2
exact tail
From the deepest banked prefixes, a 14-cell exact finisher converts an opening into a full board
Complexity
Time
round 1: hundreds of 5 s probes; finish: 300 s × 8 exact-tail-14 runs from the deepest prefixes
Space
keeps only the banked prefixes and their live continuations between rounds
Successive halving: total effort is roughly constant per round, but each round spends it on fewer, deeper survivors, so the cost concentrates where it pays.
Hardware & run
Native runCPU only
0.67core-hours
Cores
8
RAM
16 GiB
GPUs
0
CPU
Apple M1
Machine
MacBook (Apple M1, 8 cores)
Budget
~300 s × 8 finishers (exploratory run, not the standardized single-core bench)
Most of a long search is wasted on starts that were doomed early. LADDER
spends almost nothing to find out which beginnings are worth pursuing. It runs
a flood of very short probes, keeps the few that got deepest, and only then
pays for longer runs, on those alone. It's tournament selection for search
starts.
Round one is hundreds of five-second probes from different random seeds, each
trying to lay down a long run of perfectly-matched cells. Keep the deepest
prefixes, and throw out ones that are near-duplicates of each other so the
survivors stay diverse.
Promote those to a longer round with tighter quality gates, then promote the
best of those to a full-length run. Each rung spends more time on fewer,
better candidates, the way successive-halving tournaments allocate effort to
the contenders that keep winning.
▶Interactive: the rung-by-rung progressionExplore →
LADDER produced a 451 board obeying all five official clues, with no guidance
from any known record, the first time the project escaped the band of 444 to
450 that unguided search kept landing in. The finishes are determined by their
prefix: once a strong enough opening is banked, the rest follows. A longer run
later touched 452, one edge more, though 451 is the board committed and
reproducible here.
It also mapped the limits: the supply of perfect openings runs out, and beyond
a point the rungs all converge to the same ceiling. So LADDER is a good way to
find the best start, not a way past the structural walls that stop every
method near the top.
The ladder is a recursive successive-halving tournament over search starts,
scored by prefix depth.
Round one: flood. Hundreds of 5-second probes from different seeds, each
laying down as long a run of perfectly-matched cells as it can. Rank by the
depth of that perfect prefix; keep the deepest, and drop near-duplicates
(prefixes too similar to a survivor) so the kept set stays diverse.
Ratchet. Each subsequent round pins the previous round's deepest banked
prefix (a depth-15 pin in the recorded run) and probes beyond it, pushing
the perfect-prefix frontier one notch further. The recursion stops when a
round gains fewer than four cells of depth, the supply of deeper openings has
run dry.
Finish. From the three deepest distinct prefixes, run long exact-tail-14
rungs (300 s × 8 seeds each) to convert the banked opening into a full board.
The finding is that the finish is determined by the prefix: once a deep enough
perfect opening is banked, the endgame follows. That is why concentrating
compute on finding the best start, rather than spreading it across full runs,
escaped the 444–450 band unguided search kept landing in. A longer finishing
round later touched 452; the committed, reproducible board here is the 451.
Seeded; the probe-and-promote structure reproduces the behaviour reliably
though the exact board depends on seeds. The committed 451 board is checkable in
the viewer. The climb needs no corpus, frame, or witness, it runs from the
puzzle alone, so a runnable backing directory for it is planned alongside the
other from-scratch experiments.
What's the real ceiling of prefix-first selection given more compute on the
early rungs? Could the diversity rule be smarter about which near-duplicates
to keep? And does combining the deepest prefixes from different families beat
promoting within one?