LEVELS_4_5.md

# ModeBench Levels 4 and 5

Ten configs extending the ModeBench release with two harder difficulty levels,
five domains each, in the same row surface as Levels 1-3: `problem`, `answer`
(an executable specification carrying its own `verifier`), and
`answer_mode_count`.

## Admission status

**Level 5 is admitted.** All five domains cleared held-out confirmation against
128 fresh rows each, 4096 attempts per domain, replayed through the original
graders, with worst margins of 0.43 to 0.92 of tolerance. Level 5 carries the
same warrant as Levels 1-3.

**Level 4 cleared four of five and is not admitted.** Countdown, graph colouring,
pantry and python factors are difficulty-matched at 0.20, 0.34, 0.81 and 0.32 of
tolerance. MathIR missed its pass@1 gate at 1.07 of tolerance: it measured 0.0864
against a 0.0437 target on a 0.04 tolerance. A Level 4 MathIR result should not be
reported as difficulty-matched; the other four Level 4 domains may be.

The Level 4 MathIR dataset is sound and verified — the target is what is out of
reach. It pairs pass@1 0.0437 with pass@8 0.2402, a heterogeneity gap of 0.060,
while every 7B MathIR construction measured runs a gap of 0.169 to 0.398:
success concentrates on few prompts, so raising pass@8 into its band drives
pass@1 through its ceiling and the two gates cannot be satisfied together.
Three difficulty mechanisms were measured — family choice, binding magnitude and
denominator structure — and all fail the same way. The same law is
difficulty-matched at 14B and ships in Level 5.

## Splits

| level | domains | train | dev | eval |
| --- | --- | --- | --- | --- |
| 4 | 5 | 384 | 128 | 128 |
| 5 | 5 | 384 | 128 | 128 |

Every split was verified against the row digest frozen in its dataset identity,
then round-tripped through Parquet and re-read to confirm rows, feature types
and column order are unchanged.

## Configs

- `level4_countdown` — difficulty-matched: yes, status `heldout_confirmed_difficulty_matched`
- `level4_graph_coloring` — difficulty-matched: yes, status `heldout_confirmed_difficulty_matched`
- `level4_mathir` — difficulty-matched: **no**, status `heldout_confirmed_not_difficulty_matched`
- `level4_pantry_plan` — difficulty-matched: yes, status `heldout_confirmed_difficulty_matched`
- `level4_python_factors` — difficulty-matched: yes, status `heldout_confirmed_difficulty_matched`
- `level5_countdown` — difficulty-matched: yes, status `admitted_difficulty_matched`
- `level5_graph_coloring` — difficulty-matched: yes, status `admitted_difficulty_matched`
- `level5_mathir` — difficulty-matched: yes, status `admitted_difficulty_matched`
- `level5_pantry_plan` — difficulty-matched: yes, status `admitted_difficulty_matched`
- `level5_python_factors` — difficulty-matched: yes, status `admitted_difficulty_matched`