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amphora/math-intuition-20260906-403-demo-10

math-intuition-20260906-403-demo-10 3,936 mathematics problems drawn from 403 problem families, each derived from a distinct arXiv paper. Every problem is generated answer-first, so the answer is known by construction and is checked by the family's own verify() before the row is written. No row in this file is ungraded. This is the demo rung — read this before using it Each family exposes a four-rung ladder: demo, easy, medium, hard. This file samples demo, which… See the full description on the dataset page: https://huggingface.co/datasets/amphora/math-intuition-20260906-403-demo-10.

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math-intuition-20260906-403-demo-10

3,936 mathematics problems drawn from 403 problem families, each derived from a distinct arXiv paper. Every problem is generated answer-first, so the answer is known by construction and is checked by the family's own verify() before the row is written. No row in this file is ungraded.

This is the demo rung — read this before using it

Each family exposes a four-rung ladder: demo, easy, medium, hard. This file samples demo, which the source repository defines as

the smallest setting the family supports: a person must be able to solve it and check the answer on paper.

It is an illustration, not a difficulty level. The hardening oracle skips it entirely, and no family's hardness claim is measured there. Use it to see what a family looks like, to sanity-check a pipeline, or to calibrate against human solvers — not to rank models. A model scoring well here has demonstrated nothing about the generator-verifier gap, which is measured three rungs up.

Rows per family

Being the smallest supported setting, demo has the least room to vary: a problem you can solve on paper has a small space of instances by construction. 18 families cannot produce 10 distinct questions at this rung, so they contribute fewer rows rather than the file padding itself with duplicates.

rows contributed	families
10	385
9	2
8	1
7	1
6	5
4	3
3	1
2	3
1	2

No two rows within a family share a question.

Answer diversity, stated plainly

Distinct answers per family:

distinct answers	families
1	2
2	9
3	7
4	16
5	7
6	11
7	12
8	33
9	48
10	258

6 families supply 10 rows but only two distinct answers, so a solver that guesses the more common one scores about 50% on them: 1511.03623, 2206.06261, 2303.11655, 2505.18885, 2605.03727, 2605.08846. This is a property of the demo rung, not a defect that was overlooked — those families are at the ceiling of what their generators can express at hand scale.

Columns

column	meaning
`id`	`<arxiv_id>::<nn>`
`paper`	source arXiv id — the family identifier
`preset`	always `demo`
`seed`	RNG seed, always `> 10000`
`question`	the problem statement, as rendered to a solver
`answer`	the planted answer, JSON-encoded
`search_space`	size of the naive search space, where the family reports it
`params`	generator parameters, JSON-encoded
`canonical_key`	structural equivalence class — not a row identifier
`native_domain`, `computational_core`, `certificate_form`, `object_regime`, `domain_essentiality`, `reduction_kind`, `track`, `core_provenance`	family-level metadata, copied from the curated corpus rather than re-derived

canonical_key encodes the structural equivalence class of an instance, not the instance. At this rung many families admit exactly one structure, so different questions routinely share a key. Do not treat a repeated key as a repeated problem.

Two caveats on search_space: for a number of families it counts the size of the declared answer language rather than the search actually required, and for a few it does not read the instance at all. Treat it as an upper bound with a wide margin, not a difficulty score.

Composition

Native domain

domain	rows	share
combinatorics	1,861	47.3%
algebra	1,013	25.7%
unknown	394	10.0%
number_theory	252	6.4%
geometry	156	4.0%
logic	140	3.6%
optimization	120	3.0%

Computational core

core	rows	share
graph	943	24.0%
linear_algebra	648	16.5%
csp_sat	586	14.9%
polynomial_identity	479	12.2%
unknown	394	10.0%
other	264	6.7%
exact_cover	242	6.1%
subset_sum	210	5.3%
permutation	150	3.8%
telescoping	20	0.5%

The corpus is deliberately not balanced: discrete-search cores are over-represented. This reflects the source paper pool, not the sampling. Slice on computational_core before drawing conclusions about "mathematical reasoning" in general.

Loading

python

from datasets import load_dataset
ds = load_dataset("amphora/math-intuition-20260906-403-demo-10")["train"]

Plain csv works without raising the field-size limit — unlike the easy-rung release, no field here exceeds 128 KB.

Reproducibility

Deterministic. Master seed 20260905; each family's stream is seeded by sha256("20260905:<arxiv_id>"), so one family's draw never depends on another's.

Caveats

—Answers are published. A training/dev resource, not a contamination-proof holdout. For uncontaminated evaluation, generate fresh instances from the source generators with unseen seeds.
—Demo rung. Not a benchmark. See the section above.
—Unbalanced by construction. See Composition.

License

CC-BY-4.0. Problem statements are machine-generated. Source papers are cited by arXiv id in the paper column; their content remains under their own terms.