Datasets:

oklenAI
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UDM_cleaned_docs

content_id stringlengths 26 26	score int8 2 7	nchar int32 101 50k	in_tok int32 511 32.9k	out_tok int32 1 22.9k	trunc bool 1 class	extract large_stringlengths 0 275k	rep20 float32 0 1	degenerate bool 2 classes	loop bool 2 classes
p_ca5be1cf6fde613817ddbe90	3	9,006	3,106	2,598	false	(1) For each of the following, indicate whether the data is measured on a nominal, ordinal, interval, or ratio scale. _______ a) waist sizes of 65-year-old men _______ b) amount of alcohol in a can of Budweiser beer _______ c) countries of origin of CUNY students _______ d) temperature in centigrade of Starbuck’s coff...	0	false	false
p_4dce2ec49945185280e1974b	3	32,958	9,252	6,401	false	Introduction Mathematics is sometimes described as the science of studying patterns. Some mathematical patterns seem a bit hidden at first: 1, 1+3, 1+3+5, 1+3+5+7,.... The "rule" here seems clear enough; look at the sequence of adding the first n odd numbers. But there is a surprise! After the additions are carried ou...	0.000675	false	false
p_291a3411a8fc8c030650d4a8	3	5,576	1,948	1,414	false	Back and Front Puzzle is a flat version of Rubik's Cube. Although this is a very simple game compared to Rubik's Cube, this game is very interesting in its own way. This game was first introduced by Shigeo Takagi in Takagi [1]. In this game the front is colored with red and the back, with yellow. b/f puzzle as if it i...	0	false	false
p_9bfd07eb4913574e643014c8	3	5,402	2,013	1,215	false	Area of a Trapezoid Area = 0.5 * h * (a + b) , where h is the altitude of the trapezoid and a and b are the lengths of the bases. Problem 1: A trapezoid ABCD with AD parallel to BC has angle D equal to 40 degrees, the length of DC is equal to 2 meters, the length of BC is equal to 5 meters and the area of the trape...	0	false	false
p_a883ebe02bf11733a5a2df5d	5	17,874	5,393	4,739	false	1. The volume of the uniform spherical cloud of radius 0.5 pc is V = 4^3 / 3 = 1.54 x 10^49 m^3 which give a mass density for 250 Msun of [ ] = M / V = 3.25 x 10^-17 kg m^-3 which for molecular hydrogen H[2] gives a number density n = [H2] = ( 3.25 x 10^-17 kg m^-3 ) / ( 2 x 1.67 x 10^-27 kg ) = 9.73 x 10^9 m^-3 ...	0	false	false
p_fc4a7cd87d78994cd36424f2	2	5,004	1,808	1,302	false	A standardized variable (sometimes called a z-score or a standard score) is a variable that has been rescaled to have a mean of zero and a standard deviation of one. For a standardized variable, each case's value on the standardized variable indicates its difference from the mean of the original variable in number of s...	0	false	false
p_28c7a2cafd66f5a33da6f6ca	5	11,894	3,197	2,287	false	In this article, a very simple and yet useful feature of Excel called the SPIN BUTTON is used to illustrate two concepts associated with attribute acceptance sampling plans. The first concept is calculating the probability of lot acceptance based on which the operating characteristic (OC) curve of an attribute sampling...	0	false	false
p_3d0f12b59febaf10f908dac7	3	3,695	1,359	621	false	Problem : In the figure below, ABCD is a square. Prove that triangle DMC is equilateral. Solution to Problem : • AMB is an isosceles triangle and therefore MA = MB. Also the sizes of angles MAD and MBC are equal. Hence triangles DAM and CBM have an equal angle between two equal sides are therefore congruent. S...	0	false	false
p_1793f99be71b28aa42212137	6	2,127	1,081	602	false	sin ny, and is of course in the same direction as the displacement along the same line. When n — 1, both forces and displacements are in a fixed direction. It will be of interest to examine what happens when the force is concentrated at a single point on the line x = 0, instead of being distributed over the whole of it...	0	false	false
p_004a3fa38bcc9fc1d327b008	3	4,343	1,671	1,212	false	Question 1 Question: Find the number of Watts per square meter received when Earth is at 1 AU from the Sun. How many AUs do you need to be from the Sun for the brightness to be 2 times bigger? Answer: You can find the example calculation on page 524 of the textbook, and it shows the Sun's apparent brightness is 1300 ...	0	false	false
p_0f4c7c113cca4b805e41cb63	2	3,766	1,378	853	false	Alligation method is a simplified method to solve complex average problems. Alligation also helps simplify Ratio and Proportion, Simple and compound interest, Profit and loss, Time & Distance, Time Work problems among others. For better understanding, a few illustrations are given below. We take weighted average in the...	0	false	false
p_5328a8dda819ff1bb66f77ef	2	5,859	1,872	1,284	false	MIDPOINT ELASTICITY FORMULA: A simple technique for calculating the coefficient of elasticity by estimating the average elasticity for discrete changes in two variables. The distinguishing characteristic of this formula is that percentage changes are calculated based on the average of the initial and ending values of ...	0	false	false
p_d1c646f26324ec0b17acfd1a	5	3,251	1,561	886	false	If 28+1 is the highest power of 2 dividing a2—!, where a is odd, the exponent to which a belongs modulo 2X is 2X~' if X>«, but, if X^s, is 1 if as 1, 2 if a2=l, a^l (mod 2X); the result of Lebesgue48 (p. 87) now follows (pp. 202-6). In case a is not prime to the modulus, there is an evident theorem on the earliest powe...	0	false	false
p_5361bd2562157b37d72c5304	4	2,092	1,225	717	false	Divide x to the 5th power by x to the 2nd power? Since you did not specify any limits of integration, I assume you are looking for the indefinite integral of this expression: tan2(x)cos5(x) with respect to x (dx). Using th…e following identity: tan (x) = sin(x) / cos(x) The original expression can be rewritten as: (si...	0	false	false
p_8d288873ff5b6310ec02fa65	2	3,676	1,484	849	false	Suppose you want to calculate the mean, standard deviation, and coefficient of variation and you entered the data in an Excel spreadsheet as follows: -.10 in cell C1 +.27 in cell C2 -.25 in cell C3 +.35 in cell C4 -.10 in cell C5 +.48 in cell C6 -.18 in cell C7 +.59 in cell C8 -.11 in cell C9 -.25 in cell C10 +.46 in ...	0.063462	false	false
p_8e5b8cfafb4a1a549827d917	5	19,954	6,399	5,143	false	Q: How are imaginary exponents defined? The original question was: How do you do x^i (x to the i power), and how on Earth was it developed? There isn’t really anything to base x^i on from previous rules of exponents as it is a completely new idea. Physicist: Euler, the dude who originally came up with using the imag...	0	false	false
p_917c3e521dd423747e3c983f	5	2,022	1,155	562	false	where plt . . . , p» are distinct prunes. For a prime p, not dividing y, we have <j> (py) = (p - !)<£ (y) . Take y = pi,p = p2', then Next, take y~pip2, P=Pz, and use also the last result; thus and similarly for #(2). When f ranges over the integers < 2? and prime to 2, the numbers j>2+f 0> = 0, 1, . . . , n — 1) g...	0	false	false
p_0defaa4a8681ecc615b09882	5	9,151	2,900	1,927	false	I assume here that this topic refers to the second of Jim Beauchamp's definitions: "the degree to which single sounds contain only harmonics" of a common fundamental frequency. I also assume that this is to be determined by examining the signal itself. In practice this will be a sampled signal x(n), n = 0, 1, ..., N-...	0	false	false
p_2cb5901dbfeca0e4f91727a8	3	5,341	1,731	1,051	false	As a pedagogical example, Brocot invents the problem of gearing a shaft that turns once in 23 minutes to another shaft that completes a revolution in three hours and eleven minutes, or in other words 191 minutes. Because 23 and 191 are both primes, gears with fewer teeth can only approximate the true ratio. To find the...	0	false	false
p_82421903430c1991d639d6ea	4	22,984	6,336	3,852	false	Q: Why is the integral/antiderivative the area under a function? Physicist: If you’ve taken calculus, then at some point you learned that to find the area under a function (generally written $\int_A^B f(x) \, dx$) you need to find the anti-derivative of that function. The most natural response to these types of theor...	0	false	false
p_1fbb2b340fdbee299b04d670	6	1,968	991	535	false	ON THE PROPAGATION OF WAVES and so on. In these equations the c's and the fi's are real, and also 1 a's, unless there is " total reflection " ; the s's are pure imaginaries, with 1 same reservation. When there are three media, we are to suppose in the problem of reflect] that J2"3 = - 1, Ka = 1. Thus from (21), (2...	0	false	false
p_c8764583a5fbe1dc9c6596f9	3	3,499	1,366	545	false	If a, b, and c are positive integers, what is the remainder when a – b is divided by 6? (1) a = (2) b = A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEIT...	0	false	false
p_cce12afb02f8295f94121403	6	2,449	1,236	759	false	If for the moment we omit the terms of the second order, we have AC, J0' + M0 J0" {oin cos n& + j3n sin nQ] + Jn' [An cos n6 -f Bn sin n6] = 0; (62) so that Jo (z) = 0, and M0 Jo" . 0^ + Jn . 4n = 0, MO Jo" • £n + Jn- -Bn = 0.......(63) To this order of approximation z, — ka, has the same value as when p = 0; that is t...	0	false	false
p_bae1ec3e639d6fd7ecf00397	5	5,587	1,748	1,187	false	Employee stock options are a widely used instrument to align interests of managers and shareholders. Especially in early-stage companies employee stock options are one good remedy to console the founders for the dilution they had to go through in the fund raising process. Every time a company issues employee stock opti...	0	false	false
p_c410c5fdfdf7fa33abb70fd2	3	23,953	6,059	5,129	false	A general idea: Rheology is science that concerned with flow of fluids and deformation of solid. study of flow properties of liquids is important in the manufacture of several dosage forms i.e. simple liquids, gels, creams, pastes. These system can change their flow behavior when exposed to different stress conditions...	0.000262	false	false
p_71d43b3e3e028b89a2f833e5	3	7,209	2,070	1,605	false	Radians and Degrees Typically people discuss rotational motion in terms of degrees, where one entire rotation around a circle is equal to 360°. When dealing with rotational motion from a physics perspective, measuring rotational motion in units known as radians (rads) is much more efficient. A radian measures a distan...	0	false	false

End of preview. Expand in Data Studio

UDM cleaned docs

6,029,052 web pages reduced to just their mathematical content, extracted verbatim by oklenAI/udm_doc_extract_qwen3.5_2B — a 2B model distilled from GPT-5.6.

Every row is model output, not human-curated text. The extract field is what the model returned for that page; the source page text is not included. Read Two repetition flags below before filtering — the obvious flag is not the one you want.

How it was built

step	pages
`TeraflopAI/udml2-labeled`, keeping `score >= 2`	13,514,716	the 0–7 scale lives in `score` (`__label__N`), not in `quality_label`, which only ever takes {4, 5}
after exact-content dedup	6,029,052	55.39% of the filtered pool is duplicated across shards; within any single shard only ~2% is, because the source is globally shuffled before sharding

Extraction ran greedy (no sampling, no repetition penalty) under vLLM 0.28.0 with a per-page token budget of min(24576, 1.25 x input_tokens + 256, 40960 - input_tokens). Sizing the budget to the page rather than to a constant matters: extraction length scales with input, so a flat cap silently truncates exactly the long pages. Input-side truncation hit 1 page out of 6,029,052.

Schema

column	type	meaning
`content_id`	string	`p_` + `sha256(source page utf-8)[:24]`. Joins back to the source dataset — recompute it there, no normalisation, no NFKC.
`score`	int8	quality band 2–7 carried over from the source dataset
`nchar`	int32	characters in the source page
`in_tok` / `out_tok`	int32	tokens in / out
`trunc`	bool	source page was truncated on the input side
`extract`	string	the payload — mathematical content, verbatim
`rep20`	float32	20-gram repeat rate over the whole extract
`degenerate`	bool	`rep20 > 0.30` — over-inclusive, see below
`rep_tail`	float32	20-gram repeat rate over the last 300 words (0.0 where `degenerate` is false)
`loop`	bool	`rep_tail >= 0.70` — this is the defect flag

Two repetition flags, and why the obvious one is wrong

A high whole-document repeat rate has two completely different causes, and they need opposite treatment:

the model looped — greedy decoding locks onto a short n-gram and repeats it until the token budget runs out. Broken output.
the page repeats itself — a forum thread quoting the same code block, a worksheet built from a template, a page that prints its theory section twice. The model transcribed it faithfully. Good output.

rep20 > 0.30 cannot tell these apart. rep_tail can, because a genuine loop is still looping when the budget runs out while a repetitive page is still producing new text at the end. The split is bimodal, not a continuum — sampled non-loop pages score exactly 0.000 — so the threshold is not delicate.

	pages	of corpus	of flagged
flagged `degenerate` (`rep20 > 0.30`)	66,198	1.098%	100%
— `loop`, the model actually broke	38,764	0.643%	58.6%
— page was repetitive, extraction is fine — keep these	27,434	0.455%	41.4%

So filter on loop, not on degenerate — about a third of degenerate is good extraction of repetitive source pages, and worksheets and problem sets are exactly the pages this corpus is for. Nothing was deleted; both flags ship so you can choose.

Looping is strongly length-dependent:

source page length	pages	`degenerate`	`loop`
<5k chars	2,980,959	0.329%	0.156%
5-20k chars	2,201,674	1.233%	0.717%
>=20k chars	846,419	3.454%	2.164%

Corpus statistics


pages	6,029,052
parquet files (zstd)	117, 13.14 GB
source page length	median 5,084, mean 9,319, p90 24,702, max 49,998 chars
pages over 20,000 chars	13.93%
input tokens	18,588,607,640
output tokens	12,542,804,450 (0.675 x input)
empty extractions	34 (0.001%)

score distribution: 2 10.7%, 3 35.5%, 4 10.7%, 5 27.9%, 6 8.7%, 7 6.5%

Usage

from datasets import load_dataset

ds = load_dataset("oklenAI/UDM_cleaned_docs", split="corpus", streaming=True)
clean = (r for r in ds if not r["loop"])          # drop the ~0.6% the model broke on

The split is called corpus, not train — this is extracted document text, not anyone's training split.

How faithful is it?

Faithfulness here means agreement with the teacher, GPT-5.6-Sol, called exactly as it was called to build the model's training data. It does not measure whether the teacher was right.

449 pages were drawn from this corpus itself — not from the model's evaluation set — in three length bands, and re-extracted by the teacher:

	short (n=150)	medium (n=150)	long (n=149)
charF1 vs teacher	0.9693	0.9286	0.8811
contiguous-span coverage	0.9891	0.9831	0.9767
strict order preservation	99.28%	93.79%	92.14%
boilerplate residue	0.67%	4.00%	3.36%
share with 20-gram repeat > 0.3	0.00%	0.67%	2.01%
empty-output rate	0.00%	0.00%	0.00%

Two things worth reading off this table. Long-page charF1 on production pages is 0.8811, slightly above the 0.8668 the model card reports on its held-out long ruler — the corpus is not harder than the ruler said it would be. And the repetition tail shows up independently: 2.01% of these 149 long pages exceed a 0.3 repeat rate, against 3.454% measured over all 846,419 long pages in the corpus. Those two are consistent rather than equal — at n=149 the sample simply cannot resolve a rate this small — but the check was run by different code on a different sample and still lands in the same place.

Limits

Student, not oracle. Every fidelity number is agreement with GPT-5.6. Nothing here was audited against the source pages by a human.
Long pages are measurably harder. charF1 0.8811 on long pages vs 0.9693 on short ones, and the loop rate is 13.9x higher in the >=20k band than in the <5k band.
Formula-token excess. The teacher check shows 21.48% excess notation tokens on long pages. The prompt mandates notation repair, so this is not that share of hallucination — but measure repetition directly rather than trusting token counts as a proxy.
Nothing beyond ~50,000 characters. The source pool tops out at 49,998 chars.
English only, and only pages the source dataset already labelled as mathematical.
Empty output is a valid answer where a page carries no substantive math; the observed empty rate is 0.001%.

Provenance and licensing

Page text originates from TeraflopAI/udml2-labeled, which declares no license. This derived corpus adds only the extraction; check the upstream dataset before redistributing or training on it.

Extraction model: oklenAI/udm_doc_extract_qwen3.5_2B. The prompt used is shipped with the model as extract_prompt.txt.

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