uuid string | question string | response_reasoning string | response_content string | correctness bool | _uuid_index int64 | trajectory_source string | _trajectory_matched bool | raw_messages list | qwen_text string | num_qwen_tokens int64 |
|---|---|---|---|---|---|---|---|---|---|---|
classified-0 | The graph of $y = \frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are quadratic. (Assume that the grid lines are at integers.)
[asy]
unitsize(0.6 cm);
real func (real x) {
return (2*(x - 1)/(x + 2));
}
int i;
for (i = -8; i <= 8; ++i) {
draw((i,-8)--(i,8),gray(0.7));
draw((-8,i)--(8,i),gray(0.7));... | Okay, so I need to find p(3)/q(3) where p(x) and q(x) are quadratic polynomials, and the graph of y = p(x)/q(x) is given. The horizontal asymptote is y = 2, and the only vertical asymptote is x = -2. Let me start by recalling some things about rational functions.
First, vertical asymptotes occur where the denominator ... | To solve the problem, we are given that the graph of the rational function
$$
y = \frac{p(x)}{q(x)}
$$
is shown, where $ p(x) $ and $ q(x) $ are both **quadratic** polynomials. The key features of the graph are:
- A **horizontal asymptote** at $ y = 2 $.
- A **vertical asymptote** at $ x = -2 $.
- A **hole** at $ ... | false | 0 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [
{
"content": "The graph of $y = \\frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are quadratic. (Assume that the grid lines are at integers.)\n\n[asy]\nunitsize(0.6 cm);\n\nreal func (real x) {\n return (2*(x - 1)/(x + 2));\n}\n\nint i;\n\nfor (i = -8; i <= 8; ++i) {\n draw((i,-8)--(i,8),gray(0.7)... | <|im_start|>user
The graph of $y = \frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are quadratic. (Assume that the grid lines are at integers.)
[asy]
unitsize(0.6 cm);
real func (real x) {
return (2*(x - 1)/(x + 2));
}
int i;
for (i = -8; i <= 8; ++i) {
draw((i,-8)--(i,8),gray(0.7));
draw((-8,i)--... | 5,607 |
classified-1 | 157. Secret Code. Two conspirators had a secret code. Sometimes their correspondence contained simple arithmetic operations that looked completely innocent. However, in the code, each of the ten digits represented its own letter of the alphabet. Once, a sum was encountered which, after substituting the corresponding le... | Okay, so I need to solve this cryptarithmetic puzzle. Let me start by writing down the problem again to make sure I have it right. The sum is:
```
F L Y
F O R
Y O U R
----------
L I F E
```
And we know that I is 1 and O is 0. So, I can substitute those values in. Let me note that down:
I = 1, O = 0.
So, the let... | To solve the cryptarithmetic puzzle:
$$
\begin{gathered}
F\ L\ Y \\
F\ O\ R \\
Y\ O\ U\ R \\
\hline
L\ I\ F\ E \\
\end{gathered}
$$
we are told that:
- $ I = 1 $
- $ O = 0 $
Each letter represents a unique digit from 0 to 9, and we must deduce the digit values for the other letters $ F, L, Y, R, U, E $ such that th... | false | 1 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [
{
"content": "157. Secret Code. Two conspirators had a secret code. Sometimes their correspondence contained simple arithmetic operations that looked completely innocent. However, in the code, each of the ten digits represented its own letter of the alphabet. Once, a sum was encountered which, after substitutin... | <|im_start|>user
157. Secret Code. Two conspirators had a secret code. Sometimes their correspondence contained simple arithmetic operations that looked completely innocent. However, in the code, each of the ten digits represented its own letter of the alphabet. Once, a sum was encountered which, after substituting the... | 5,818 |
classified-2 | "A group with 7 young men and 7 young women was divided into pairs randomly. Find the probability th(...TRUNCATED) | "Okay, so I need to find the probability that when a group of 7 young men and 7 young women is divid(...TRUNCATED) | "To find the probability that **at least one pair consists of two women** when 7 young men and 7 you(...TRUNCATED) | false | 2 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [{"content":"A group with 7 young men and 7 young women was divided into pairs randomly. Find the pr(...TRUNCATED) | "<|im_start|>user\nA group with 7 young men and 7 young women was divided into pairs randomly. Find (...TRUNCATED) | 6,008 |
classified-3 | "Celine has 240 feet of fencing. She needs to enclose a rectangular area such that the area is eight(...TRUNCATED) | "Okay, so Celine has 240 feet of fencing, and she wants to enclose a rectangular area. The problem s(...TRUNCATED) | "To solve the problem, we are given that Celine has **240 feet of fencing** and wants to enclose a *(...TRUNCATED) | false | 3 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [{"content":"Celine has 240 feet of fencing. She needs to enclose a rectangular area such that the a(...TRUNCATED) | "<|im_start|>user\nCeline has 240 feet of fencing. She needs to enclose a rectangular area such that(...TRUNCATED) | 7,433 |
classified-4 | "8. Let the complex numbers be $z_{1}=-3-\\sqrt{3} \\mathrm{i}, z_{2}=\\sqrt{3}+\\mathrm{i}, z=\\sqr(...TRUNCATED) | "Okay, so I need to find the minimum value of |z - z₁| + |z - z₂| where z is given as √3 sinθ(...TRUNCATED) | "To determine the **minimum value of** \n$$\n|z - z_1| + |z - z_2|\n$$ \nwhere \n$$\nz_1 = -3 - \(...TRUNCATED) | false | 4 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [{"content":"8. Let the complex numbers be $z_{1}=-3-\\sqrt{3} \\mathrm{i}, z_{2}=\\sqrt{3}+\\mathrm(...TRUNCATED) | "<|im_start|>user\n8. Let the complex numbers be $z_{1}=-3-\\sqrt{3} \\mathrm{i}, z_{2}=\\sqrt{3}+\\(...TRUNCATED) | 7,687 |
classified-5 | "There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house (...TRUNCATED) | "Okay, let's try to solve this logic puzzle. There are 5 houses with different people, each having u(...TRUNCATED) | "To determine the **CarModel** for **Peter**, we systematically analyzed the clues and built a consi(...TRUNCATED) | false | 5 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [{"content":"There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street.(...TRUNCATED) | "<|im_start|>user\nThere are 5 houses, numbered 1 to 5 from left to right, as seen from across the s(...TRUNCATED) | 7,221 |
classified-6 | "17. At 6:20:25, a certain electronic watch displays 6:20:25. How many times within the hour from 5:(...TRUNCATED) | "<Parallel>\n<Outlines>\n<Trial>1: Fix the hour as 5 and impose the distinct-digit constraint agains(...TRUNCATED) | "To determine how many times between **5:00 and 6:00** an electronic watch displays a time with **fi(...TRUNCATED) | false | 6 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [{"content":"17. At 6:20:25, a certain electronic watch displays 6:20:25. How many times within the (...TRUNCATED) | "<|im_start|>user\n17. At 6:20:25, a certain electronic watch displays 6:20:25. How many times withi(...TRUNCATED) | 10,529 |
classified-7 | "What is the result of adding 0.45 to 52.7 and then subtracting 0.25? Let's think step by step and o(...TRUNCATED) | "Okay, let me try to figure out this math problem. So the question is, what is the result of adding (...TRUNCATED) | "To solve the problem of adding 0.45 to 52.7 and then subtracting 0.25, we can break it down into tw(...TRUNCATED) | false | 7 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [{"content":"What is the result of adding 0.45 to 52.7 and then subtracting 0.25? Let's think step b(...TRUNCATED) | "<|im_start|>user\nWhat is the result of adding 0.45 to 52.7 and then subtracting 0.25? Let's think (...TRUNCATED) | 1,227 |
classified-8 | "Two circles touch each other internally at point \\( M \\). Let \\( AB \\) be a chord of the larger(...TRUNCATED) | "Okay, so I need to prove that MT is the angle bisector of angle AMB. Let me start by visualizing th(...TRUNCATED) | "To prove that **$ MT $** is the **angle bisector** of **$\\angle AMB$**, we begin by analyzing the (...TRUNCATED) | false | 8 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [{"content":"Two circles touch each other internally at point \\( M \\). Let \\( AB \\) be a chord o(...TRUNCATED) | "<|im_start|>user\nTwo circles touch each other internally at point \\( M \\). Let \\( AB \\) be a c(...TRUNCATED) | 12,575 |
classified-9 | "Let the parabola \\( C: y^2 = 2x \\) have its directrix intersect the \\( x \\)-axis at point \\( A(...TRUNCATED) | "<Parallel>\n<Outlines>\n<Subtask>1: Compare the parabola to the standard right-opening form to dete(...TRUNCATED) | "To find the area of triangle $ \\triangle KMN $, we begin by analyzing the geometric setup involvin(...TRUNCATED) | false | 9 | E:\AReaL-zzy-add-trial\pipeline\work\train_classified.jsonl | false | [{"content":"Let the parabola \\( C: y^2 = 2x \\) have its directrix intersect the \\( x \\)-axis at(...TRUNCATED) | "<|im_start|>user\nLet the parabola \\( C: y^2 = 2x \\) have its directrix intersect the \\( x \\)-a(...TRUNCATED) | 5,693 |
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Parason: Subtask- and Trial-Parallel Reasoning Data
Training data for Parason, which turns long sequential reasoning traces into executable parallel programs. Three subsets, one per training stage.
| Subfolder | Stage | Contents |
|---|---|---|
sft-8x |
SFT (main) | Parallel trajectories with <Subtask> / <Trial> branches, Trial stages expanded 8x — extra branches sampled with Qwen3-8B, their <Trial> goals written by Gemini-3-Flash |
sft-1x |
SFT (baseline) | The unexpanded parallel trajectories: 964 annotated Qwen3-8B traces released by ThreadWeaver, each parallel stage labeled Subtask or Trial by Gemini-3-Flash |
rl |
PA-GRPO | RL prompt set — Polaris-53k (~53,000 complex reasoning problems), used unmodified |
Each subfolder holds a single train.parquet; there is no validation split. The two SFT sets are
matched in effective token budget (8 epochs over sft-1x ≈ 1 epoch over sft-8x).
Trajectory format
The SFT trajectories mark two distinct forms of parallelism:
<Subtask>— AND-branches. The problem splits into independent sub-goals, each producing a required result. Shortens the critical path.<Trial>— OR-branches. Competing speculative attempts test different hypotheses; all outputs are concatenated back into the reasoning history. Widens search.
<think>
[Initial problem analysis and setup]
<Parallel>
<Outlines>
<Trial> 1: [First hypothesis to test]
<Trial> 2: [Second hypothesis to test]
<Subtask> 3: [An independent sub-goal whose result is required]
</Outlines>
<Thread>
1: [Detailed reasoning for the first branch...]
</Thread>
<Thread>
2: [Detailed reasoning for the second branch...]
</Thread>
<Thread>
3: [Detailed reasoning for the third branch...]
</Thread>
</Parallel>
</think>
[Final answer in \boxed{} format]
Reserved tags, added as special tokens before training:
<Think> </Think> <Parallel> </Parallel> <Outlines> </Outlines> <Outline> </Outline>
<Trial> </Trial> <Subtask> </Subtask> <Thread> </Thread> <Conclusion> </Conclusion>
Schema
sft-8x, sft-1x
| Field | Type | Description |
|---|---|---|
uuid |
string |
Source-trace identifier |
question |
string |
Problem statement |
response_reasoning |
string |
Trajectory body — the <think> contents, containing the <Parallel> blocks |
response_content |
string |
Post-</think> final answer, ending in \boxed{...} |
correctness |
bool |
Whether the source trace was graded correct |
raw_messages |
list[dict] |
[{"role": "user", ...}, {"role": "assistant", ...}] |
qwen_text |
string |
The training field. Full trace with the Qwen3 chat template applied |
num_qwen_tokens |
int |
Token count of qwen_text under the Qwen3-8B tokenizer |
rl — standard veRL prompt format: prompt
(list[dict]), data_source, ability, reward_model ({"style": "rule", "ground_truth": ...}),
extra_info.
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