license: cc-by-4.0
task_categories:
- tabular-regression
language:
- en
pretty_name: Sum of Four Cubes Certificates
Sum of Four Cubes Certificates
This dataset contains explicit certificates for
n = x1^3 + x2^3 + x3^3 + x4^3
for every integer 0 <= n <= 1,000,000,000.
Each row has the form
123 = (x1)^3 + (x2)^3 + (x3)^3 + (x4)^3
The files are sharded by intervals of length 10,000,000, with the endpoint
1,000,000,000 appended to the last shard:
cubes-00.txt 0 <= n <= 9,999,999
cubes-01.txt 10,000,000 <= n <= 19,999,999
...
cubes-99.txt 990,000,000 <= n <= 1,000,000,000
The generation code uses a congruence-filtered generalized Pell search. For
the first successful search parameter d, it records the representation with
minimal height
H = max(|x1|, |x2|, |x3|, |x4|)
among the parity-compatible Pell representatives returned by the reference solver.
Reproduce
Generate shards with 15 worker processes:
sage -python scripts/generate_hf_dataset.py \
--start 0 --end 1000000000 \
--workers 15 \
--chunk-size 10000 \
--max-in-flight 30 \
--out-dir generated/sum4cubes \
--overwrite \
--merge-final-singleton \
--progress-every 10000000
For long runs, restart the generator from shard boundaries with --resume.
For example:
sage -python scripts/generate_hf_dataset.py \
--start 80000000 --end 129999999 \
--workers 15 \
--chunk-size 10000 \
--max-in-flight 30 \
--out-dir generated/sum4cubes \
--resume
Run a lightweight post-generation sanity check:
python3 scripts/check_generated_shards.py \
--dir generated/sum4cubes \
--start 0 --end 1000000000
The generator verifies each identity using exact integer arithmetic before writing a row. The sanity checker verifies shard coverage and exact four-cube identities for boundary rows.