Run the same beam search across nine different scan orders, so it lands in different regions instead of always converging to the same one. The zigzag order found a brand-new 458 board.
Reproducestochastic — won't reproduce exactly; the board is verifiable·re-verifies a stored board·Budget: ~5 min ALNS lift per build (exploratory run, not the standardized single-core bench)
Pipeline
1
beam producernot yet written up
A scan-order sweep builds many diverse boards, sampling different regions
carries: A positional corpus prior plus a swappable scan order for construction diversity
2
ALNSnot yet written up
Destroy-and-repair lifts a promising build; the committed 458 is a lifted board
3
clustering
Group results by corner arrangement to flag genuinely new basins (not a solver stage)
Complexity
Time
9 scans × 4 seeds beam builds, then 5-min ALNS lift per strong build
Space
one live beam per (scan, seed); shares PRIOR's 256×256 prior matrix
Scan order is a preprocessing choice, not a cost: the nine orders reuse the same beam machinery and the same prior.
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
~5 min ALNS lift per build (exploratory run, not the standardized single-core bench)
A beam search that always fills the board in the same order tends to discover
the same kind of board, no matter the random seed. The order you visit the
cells quietly decides which region you end up in, and across sixteen seeds,
a single scan order produced just one distinct corner-arrangement family.
GAUNTLET turns that into a tool: run the search across nine genuinely
different scan orders, and you sample genuinely different regions.
GAUNTLET forks the constructive PRIOR beam and gives it a scan order it can
swap: row, row-reversed, column, column-reversed, zigzag, zigzag-reversed,
spiral-in, spiral-out, and diagonal, nine in all. Because the order of cells
changes which partial boards survive at each step, each order explores a
different trajectory rather than crowding into one. A sweep of 9 scans × 4
seeds produced 18 distinct corner-arrangement signatures, against just
one across sixteen seeds of the single-scan beam it grew from.
Each full run produces a complete board; the strongest are then polished by a
30-minute ALNS lift. The finding is sharp: scan order is a stronger
diversity axis than the random seed. That is the lever, and it is what the
later KEYRING and PRIOR build on.
▶Interactive: the construction-order scheduleExplore →
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Step through one scan to see how the visit order steers the beam.
▶Interactive: step through the build orderExplore →
Or race the nine orders against each other, live, in your browser.
▶Interactive: race the construction strategiesExplore →
The zigzag order at seed 99, lifted, reached 458 of 480 in the corner
arrangement cp=(3,0,1,2), the first board at or above 458 ever found in that
arrangement in our database. It is at least 246 of 256 cells away from
anything we had at that level: a genuinely new basin, not another route to a
known one.
So GAUNTLET's contribution is reach rather than a record: it opened a new
region of strong boards. A second round (32 more lifts) topped out at 457
with no 461, which says the new family saturates like the others, but the
family itself was the prize.
The pipeline is three stages, and the parameters are the point.
Stage 1: diverse construction. Fork PRIOR's beam and give it a swappable
scan order over the 256 cells: row, row_rev, col, col_rev, zigzag,
zigzag_rev, spiral_in, spiral_out, diagonal, nine orders, crossed
with seeds {1, 7, 42, 99}. All share one prior (the high459 matrix) at a
low softmax temperature (0.05), so the beam is prior-guided but not
deterministic. The order changes which partial boards survive each step, so
each (scan, seed) walks a different trajectory.
Stage 2: lift. Each strong build gets an ALNS lift (prior-escape +
basic_lkh destroy/repair operators), 5 minutes per build in the sweep, longer
for the finalists.
Stage 3: cluster. Group all outputs by corner-permutation and flag the
signatures absent from the existing database. That is how the 9×4 sweep
surfaced 18 distinct corner families where sixteen seeds of a single scan
had surfaced one, the measured claim that scan order is a stronger diversity
axis than the seed.
The winning board, zigzag, seed 99, lifted, sits at cp = (3, 0, 1, 2),
Hamming distance ≥ 246/256 from anything previously at that level: a new basin
by the same corner-perm-plus-Hamming test PRIOR
uses.
just research-record-boards verifies the committed 458 board's score exactly
from its stored Bucas string. The sweep is stochastic (nine scans × four seeds,
then a polish pass), so it will not reproduce the same board; the board is the
artifact of record. The engine is the shared beam
producer run across
nine fill orders; it uses the same corpus-mined prior as
PRIOR, so the run is not
reproduced from scratch here.
Does this new family have the same rigid local structure as the others, or a
different shape? And can a longer refinement lift it past 458, the way a
fresh family sometimes has more room than a well-worn one?