| <!-- Copied verbatim from analysis/out/SAMPLING_AUDIT.md in the project repo, |
| generated by analysis/scripts/audit_sampling.py. Regenerating it against |
| the released problems parquet reproduces this file byte-identically |
| (verified 2026-09-30). Shipped in v1.1.0 because the dataset card cites it |
| for the six excluded SciBench problem_uids and for the Omni-MATH |
| representativeness tests; a card that cites a file a consumer cannot open |
| is not a citation. --> |
| |
| # Sampling and denominator audit |
|
|
| Generated by `analysis/scripts/audit_sampling.py`. Every figure below is |
| re-derived from the released problems parquet; the sample is re-drawn |
| through `runner.load_problems`, the same function the campaign used. |
|
|
| ## 1. OmniMath2: 4,181 available -> 1,600 run |
|
|
| - full matched pool: **4181** |
| - scientific run: **1600** (38.3%) |
| - seed: **20270101**, drawn by `runner.load_problems(n=1600, seed=20270101)` |
| - manifest: `experiments/manifest_omnimath2_n1600.json` |
|
|
| **Procedure** (verbatim from `runner.py:load_problems`): filter to the |
| benchmark, require `problem_text` and `answer` non-null, sort by |
| `problem_uid` with a stable mergesort, shuffle the index with |
| `random.Random(seed)`, take the first n, re-sort. Deterministic and |
| independent of row order in the parquet. |
|
|
| **It is a uniform random sample of the whole pool — not a tier-specific, |
| difficulty-stratified, or otherwise purposive subset.** |
|
|
| ## 2. Is difficulty/tier metadata available? |
|
|
| - `difficulty_tier`: non-null **0/4181**, distinct 0 |
| - `question_type`: non-null **0/4181**, distinct 0 |
| - `difficulty_score`: non-null **4181/4181**, distinct 27 |
| - `subset`: non-null **4181/4181**, distinct 64 |
|
|
| `difficulty_tier` and `question_type` are **entirely null** for this |
| benchmark, so no tier table is possible on those fields. `difficulty_score` |
| is fully populated and is used below as the difficulty axis. |
|
|
| ## 3. Representativeness: full 4,181 vs selected 1,600 |
|
|
| ### 3a. difficulty_score |
| |
| | statistic | full 4,181 | selected 1,600 | delta | |
| |---|---:|---:|---:| |
| | mean | 4.9444 | 4.9524 | +0.0080 | |
| | std | 1.9061 | 1.9882 | +0.0821 | |
| | min | 1.0000 | 1.0000 | +0.0000 | |
| | 25th pct | 4.0000 | 4.0000 | +0.0000 | |
| | median | 5.0000 | 5.0000 | +0.0000 | |
| | 75th pct | 6.0000 | 6.0000 | +0.0000 | |
| | max | 9.5000 | 9.5000 | +0.0000 | |
| |
| Two-sample Kolmogorov-Smirnov: **D=0.0251, p=0.449** |
| (a large p means the selected sample is *not* distinguishable from the pool) |
| |
| ### 3b. difficulty_score, binned |
|
|
| | score | full 4,181 | share | selected 1,600 | share | delta | |
| |---|---:|---:|---:|---:|---:| |
| | 1.0 | 116 | 0.028 | 49 | 0.031 | +0.003 | |
| | 1.5 | 194 | 0.046 | 84 | 0.052 | +0.006 | |
| | 2.0 | 151 | 0.036 | 60 | 0.037 | +0.001 | |
| | 2.25 | 4 | 0.001 | 3 | 0.002 | +0.001 | |
| | 2.5 | 168 | 0.040 | 74 | 0.046 | +0.006 | |
| | 3.0 | 20 | 0.005 | 5 | 0.003 | -0.002 | |
| | 3.5 | 189 | 0.045 | 68 | 0.043 | -0.003 | |
| | 3.75 | 3 | 0.001 | 0 | 0.000 | -0.001 | |
| | 4.0 | 530 | 0.127 | 198 | 0.124 | -0.003 | |
| | 4.25 | 3 | 0.001 | 1 | 0.001 | -0.000 | |
| | 4.375 | 1 | 0.000 | 1 | 0.001 | +0.000 | |
| | 4.5 | 380 | 0.091 | 149 | 0.093 | +0.002 | |
| | 4.75 | 12 | 0.003 | 1 | 0.001 | -0.002 | |
| | 5.0 | 848 | 0.203 | 295 | 0.184 | -0.018 | |
| | 5.25 | 218 | 0.052 | 69 | 0.043 | -0.009 | |
| | 5.5 | 153 | 0.037 | 47 | 0.029 | -0.007 | |
| | 6.0 | 241 | 0.058 | 101 | 0.063 | +0.005 | |
| | 6.25 | 7 | 0.002 | 2 | 0.001 | -0.000 | |
| | 6.5 | 96 | 0.023 | 32 | 0.020 | -0.003 | |
| | 6.75 | 1 | 0.000 | 0 | 0.000 | -0.000 | |
| | 7.0 | 357 | 0.085 | 167 | 0.104 | +0.019 | |
| | 7.5 | 70 | 0.017 | 21 | 0.013 | -0.004 | |
| | 8.0 | 244 | 0.058 | 98 | 0.061 | +0.003 | |
| | 8.25 | 1 | 0.000 | 0 | 0.000 | -0.000 | |
| | 8.5 | 13 | 0.003 | 6 | 0.004 | +0.001 | |
| | 9.0 | 146 | 0.035 | 62 | 0.039 | +0.004 | |
| | 9.5 | 15 | 0.004 | 7 | 0.004 | +0.001 | |
|
|
| ### 3c. subset (source competition) |
|
|
| | subset | full | share | selected | share | delta | |
| |---|---:|---:|---:|---:|---:| |
| | HMMT_2 | 1321 | 0.316 | 494 | 0.309 | -0.007 | |
| | HMMT_11 | 860 | 0.206 | 289 | 0.181 | -0.025 | |
| | fermat | 224 | 0.054 | 96 | 0.060 | +0.006 | |
| | pascal | 223 | 0.053 | 79 | 0.049 | -0.004 | |
| | cayley | 190 | 0.045 | 92 | 0.058 | +0.012 | |
| | imo_shortlist | 176 | 0.042 | 71 | 0.044 | +0.002 | |
| | usamo | 112 | 0.027 | 53 | 0.033 | +0.006 | |
| | putnam | 100 | 0.024 | 41 | 0.026 | +0.002 | |
| | china_team_selection_test | 96 | 0.023 | 41 | 0.026 | +0.003 | |
| | imo | 71 | 0.017 | 31 | 0.019 | +0.002 | |
| | imc | 66 | 0.016 | 30 | 0.019 | +0.003 | |
| | apmoapmo_sol | 57 | 0.014 | 26 | 0.016 | +0.003 | |
| | ToT | 54 | 0.013 | 17 | 0.011 | -0.002 | |
| | baltic_way | 45 | 0.011 | 19 | 0.012 | +0.001 | |
| | imo_longlists | 41 | 0.010 | 17 | 0.011 | +0.001 | |
| |
| _(top 15 of 64 subsets)_ |
|
|
| Chi-square on subset x selected: **chi2=58.3, dof=46, p=0.106** |
|
|
| ## 4. SciBench denominators: 692 upstream -> 580 released -> 574 matched |
|
|
| - upstream SciBench (published): **692** |
| - present in the released problems table: **580** |
| - carrying the `text_only` slice, i.e. the matched scientific run: **574** |
| - **run in this campaign: 574 problems x 2 actors x 2 arms = 2,296 trajectories** |
|
|
| ### Where the 692 - 580 = 112 go |
|
|
| **NOT RECOVERABLE FROM THIS RELEASE, and I will not guess.** The released |
| problems table contains only rows that survived the upstream build, so the |
| 112 excluded items are absent from it entirely and carry no reason code |
| here. A first draft of this audit asserted they were figure/table/tool |
| items plus collisions; that was an inference presented as a measurement |
| and has been removed. |
|
|
| What the release *does* record, for the 580 rows that are present: |
|
|
| | collision_status | n | |
| |---|---:| |
| | unique | 574 | |
| | conflicting_source_id_disambiguated | 6 | |
|
|
| Note the 6 `conflicting_source_id_disambiguated` rows are **not** the same |
| 6 rows that lack the text-only slice — they are disjoint sets, so the two |
| subtractions below are independent, not the same six items counted twice. |
|
|
| To establish the 112 one would have to diff the upstream SciBench release |
| against this table. That is tracked as a P2 item; it does not affect any |
| denominator this paper reports, because the paper's denominator is the 574 |
| it actually ran. |
|
|
| ### Where the 580 - 574 = 6 go |
|
|
| 6 released rows lack the `text_only` slice and are therefore |
| outside the matched denominator: |
|
|
| | problem_uid | slices | |
| |---|---| |
| | `scibench:calculus:8.1.39` | ["full"] | |
| | `scibench:class:Problem 2.20` | ["full"] | |
| | `scibench:fund:Question 21.65` | ["full"] | |
| | `scibench:fund:Question 21.67` | ["full"] | |
| | `scibench:fund:Question 23.41` | ["full"] | |
| | `scibench:thermo:6.12` | ["full"] | |
| |
| **`574 matched` is not `574 total benchmark`.** The upstream benchmark has |
| 692 items; 580 reach the release; 574 carry the text-only slice this |
| project's protocol can run. All 574 were run — no sub-sampling. |
| |
| - license: ['MIT'] |
| - training policy: ['evaluation_only_recommended'] |
| |
| |
