analysis/SAMPLING_AUDIT.md

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']