Spreadsheets covering every problem in this repository. Click a file on GitHub and it appears as a table with a search box. GitHub cannot sort columns, so each family file is already sorted by gap, smallest first: the problems closest to being settled are at the top. For real sorting and filtering, open the raw file in any spreadsheet program.
One row per problem. The columns tell you where the problem came from, whether we can check an answer to it, and how close it is to being solved.
A script writes these files by reading the problem records. Every number is either copied straight out of a problem's record, or is one bound subtracted from another. Nothing is guessed or rated. So if a number here looks wrong, the problem's record is wrong, not the table.
Rebuild them with python3 scripts/build_browse_tables.py. Do not edit them by hand,
because the script overwrites them.
Every row says which kind it is, because the three are not interchangeable.
A task is a reviewed conjecture in problems/benchmark/ with its own checker. A
database row is one instance of a family in problems/benchmark/families/, where
thousands of instances share a single checker. A discovery row is a sourced
pointer in problems/extended-catalog/ that has no checker of its own.
all.csv lists all 15,607 problems of all three kinds. It only has
columns that mean the same thing for every kind, so it has no gap column. It is
over a megabyte, so GitHub may decline to show it as a table. The smaller files
below are the ones to browse.
kind-conjecture.csv and
kind-catalog.csv each list one kind.
The remaining files each cover one family and add the gap for that
family. The unit is part of the column name, e.g. gap_blocks. Family rows have no kind file, because the per-family files below cover them
and carry more.
The gap needs its own files because it is measured in different units for different families. For linear codes a gap of 2 means 2 units of Hamming distance. For constant weight codes a gap of 179 means 179 codewords. If both sat in one column you could sort them together, and the order would tell you nothing. GitHub also sorts one column at a time, so it cannot group by family first. Within one family file every row uses the same unit, so sorting by gap works.
| Column | Meaning |
|---|---|
id |
name of the problem, unique across the database |
source |
which published collection it came from |
family |
problems that share one answer format and one checker |
shape |
what you submit, either a better record or an example object |
has_verifier |
whether a checker is written, not whether one is possible |
best_known |
the current record you have to beat |
gap_* |
how far apart the best answer and the best proved limit are |
The gap is the distance between the best answer anyone has published and the best limit anyone has proved. A gap of 1 means one step from solved.
The gap is not a difficulty score. A wide gap can mean the problem is far from solved. It can also mean nobody has found a good way to prove a limit yet. Constant weight codes have a median gap of 91 percent of the record for the second reason, and that source says its own limits are weak.
Two families have no gap column at all. A difference set either exists or it does not, so there are no bounds to narrow.
There is no difficulty rating and no importance score. Both would need a judgement call, and these files only hold numbers copied from the database.