Datasets:
traj_id large_string | problem large_string | gold_answer large_string | teacher_answer large_string | is_correct bool | difficulty large_string | length_bin large_string | n_tokens int64 | thinking_paragraphs list | final_response large_string | nodes list | method large_string | exploration_share float64 | teacher large_string | annotator large_string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
deepmath-101148_4 | Determine the number of solutions to the equation \(\sin x = \frac{x}{100}\). | 63 | 63 | true | hard | long | 10,385 | [
"We need answer problem: Determine number of solutions to sin x = x/100. Need reason step by step.",
"We need count real solutions? Usually equation sin x = x/100 over real x. Need number of solutions.",
"We must analyze carefully.\n\nEquation f(x)=sin x - x/100 = 0.\nOdd function: f(-x) = -sin x + x/100 = -f(x... | Let
\[
f(x)=\sin x-\frac{x}{100}.
\]
We want the number of real solutions of \(f(x)=0\).
### 1. Symmetry and size restriction
Since
\[
f(-x)=\sin(-x)-\frac{-x}{100}=-\sin x+\frac{x}{100}=-f(x),
\]
\(f\) is odd. Therefore, solutions are symmetric about \(0\). We can count the positive solutions and then double the... | [
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"bran... | Define f=sin x−x/100, use odd symmetry, bound |x|≤100, identify 16 positive humps, apply strict concavity (f''=−sin x<0) to count 1+15×2=31 positive roots, total 63. | 0 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
deepmath-104432_0 | Given an integer \( n \geq 2 \) and a closed unit disc, find the maximum value of the product of the lengths of all \( \frac{n(n-1)}{2} \) segments determined by \( n \) points in that disc. | n^{n/2} | n^{n/2} | true | hard | long | 10,580 | [
"We need solve problem: Given integer n>=2 and closed unit disc, find maximum value of product of lengths of all n(n-1)/2 segments determined by n points in that disc. Need reason step by step and final boxed.",
"We need maximize product of pairwise distances among n points in unit disk. This is a known problem: ... | Let the \(n\) points be represented by complex numbers
\[
z_1,\dots,z_n,\qquad |z_i|\le 1.
\]
The product of the lengths of all \(\binom n2\) segments is
\[
P=\prod_{1\le i<j\le n}|z_i-z_j|.
\]
Consider the \(n\times n\) Vandermonde matrix
\[
V=\begin{pmatrix}
1&z_1&z_1^2&\cdots&z_1^{n-1}\\
1&z_2&z_2^2&\cdots&z_2^... | [
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"bra... | Represent points as complex numbers, form Vandermonde matrix, apply Hadamard's inequality to bound determinant by product of row norms ≤ n^{n/2}, show equality via regular n-gon. | 0.214 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
deepmath-57637_7 | Determine the values of \( z \in \mathbb{C} \) for which \( A_2(z) = 0 \), where \( e^{jz} = A_0(z) + j A_1(z) + j^2 A_2(z) \) and:
\[
\begin{cases}
A_0(z) = \displaystyle \sum_{n \geq 0} \frac{x^{3n}}{(3n)!} \\
A_1(z) = \displaystyle \sum_{n \geq 0} \frac{x^{3n+1}}{(3n+1)!} \\
A_2(z) = \displaystyle \sum_{n \geq 0} \f... | 0 | 0 | true | hard | long | 10,787 | [
"Let me carefully analyze this problem. We have $j = e^{i2\\pi/3}$, and we're told that:",
"$$e^{jz} = A_0(z) + jA_1(z) + j^2 A_2(z)$$",
"where $A_k(z)$ are defined as sums involving $x$. Wait, there's a notational issue here. The sums use $x$ but the functions are $A_k(z)$. Let me re-read.",
"Actually, I thi... | Looking at this problem, I need to find all $z \in \mathbb{C}$ where $A_2(z) = 0$, given the decomposition of the exponential using the primitive cube root of unity $j = e^{i2\pi/3}$.
## Establishing the Key Formula
Since $j^3 = 1$ and $1 + j + j^2 = 0$, I can use the inverse discrete Fourier transform on the three r... | [
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"bra... | DFT inversion gives closed form; verify z=0 is a double zero; rule out other zeros on imaginary and positive-real axes; conclude z=0. | 0.6361 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
deepmath-106420_4 | In a right triangle \( ABC \) with hypotenuse \( AB \), a point \( P \) is marked on leg \( AC \). Let \( D \) be the foot of the perpendicular from \( A \) to line \( BP \), and \( E \) be the foot of the perpendicular from \( P \) to side \( AB \). A point \( T \) is chosen such that lines \( TA \) and \( TP \) are t... | 90^\circ | 90° | true | hard | long | 10,335 | [
"Let me work through this problem carefully.\n\nWe have a right triangle $ABC$ with hypotenuse $AB$, so $\\angle C = 90°$.",
"A point $P$ is on leg $AC$. $D$ is the foot of the perpendicular from $A$ to line $BP$. $E$ is the foot of the perpendicular from $P$ to side $AB$.",
"The circumcircle of triangle $PAB$ ... | Looking at this problem, I'll set up coordinates and work through the construction systematically.
## Setting Up Coordinates
Let $C = (0,0)$, $A = (0,a)$, $B = (b,0)$ with the right angle at $C$, and $P = (0,p)$ on leg $AC$ where $0 < p < a$.
**Circumcircle of $\triangle PAB$:** Substituting the three vertices into ... | [
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"bran... | Coordinate geometry with a specific numerical example; compute all points explicitly, then verify KO·KE=0 to show the angle is 90°. | 0.2032 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
deepmath-103096_5 | Evaluate the infinite product: \[ \prod_{n=3}^{\infty} \frac{(n^3+3n)^2}{n^6-64}. \] | \dfrac{72}{7} | \frac{72}{7} | true | hard | long | 11,533 | [
"We need solve infinite product: ∏_{n=3}^∞ ((n^3+3n)^2)/(n^6 - 64). Need reason step by step final boxed.",
"Let's analyze.\n\nTerm for n≥3: (n^3+3n)^2 / (n^6 - 64). Factor.\nn^3+3n = n(n^2+3) = n(n+√3 i? but maybe real factors? n^2+3). n^6 -64 = (n^3)^2 - 8^2? Actually 64=8^2, n^6 - 64 = (n^3-8)(n^3+8) = (n-2)(n... | Let
\[
P_N=\prod_{n=3}^{N}\frac{(n^3+3n)^2}{n^6-64}.
\]
First factor the terms. We have
\[
n^3+3n=n(n^2+3)
\]
and
\[
n^6-64=(n^3-8)(n^3+8)=(n-2)(n+2)(n^2+2n+4)(n^2-2n+4).
\]
Also,
\[
n^2+2n+4=(n+1)^2+3,\qquad n^2-2n+4=(n-1)^2+3.
\]
Thus each factor can be written as
\[
\frac{(n^3+3n)^2}{n^6-64}
=
\frac{n^2(n^2... | [
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"bran... | Factor each term into a rational part and a quadratic-shift part; telescope both separately using shift-by-1 cancellation to get 6 and 12/7. | 0.0066 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
deepmath-59985_2 | "Assume that the set of natural numbers $\\mathbb{N} = \\{0, 1, 2, \\ldots\\}$ is partitioned into $(...TRUNCATED) | 0 | 0 | true | hard | long | 10,170 | ["Let me carefully analyze this problem.\n\nWe have $\\mathbb{N} = \\{0, 1, 2, \\ldots\\}$ partition(...TRUNCATED) | "Looking at this problem, I need to determine whether for **any** partition of $\\mathbb{N}$ into $k(...TRUNCATED) | [{"branch":0,"deps":[],"flags":"","label":"SU","node_id":0,"p_end":4,"p_start":0,"path":"M"},{"branc(...TRUNCATED) | "Decompose the sum algebraically, show first term vanishes, then construct a counterexample partitio(...TRUNCATED) | 0.1824 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
deepmath-108194_2 | "Consider a polynomial \\( P(x,y,z) \\) in three variables with integer coefficients such that for a(...TRUNCATED) | 2 | 2 | true | hard | long | 10,221 | ["Let me work through this problem carefully.\n\nWe need to find a polynomial $P(x,y,z)$ with intege(...TRUNCATED) | "Looking at this problem, I need to find the largest $r$ such that $m^r \\mid P(n,n+m,n+2m)$ for ALL(...TRUNCATED) | [{"branch":0,"deps":[],"flags":"","label":"SU","node_id":0,"p_end":5,"p_start":0,"path":"M"},{"branc(...TRUNCATED) | "Change variables to u=x-y, v=y-z; use IFT to show degree-1 part vanishes (giving m² divisibility),(...TRUNCATED) | 0.2256 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
deepmath-106656_5 | "Find the greatest possible integer $n \\geq 3$ such that there exist $n$ positive integers $a_1, a_(...TRUNCATED) | 4 | 4 | true | hard | long | 11,667 | ["Let me think about this problem carefully.\n\nWe need to find the greatest $n \\geq 3$ such that t(...TRUNCATED) | "Looking at this problem, I need to find the maximum $n$ where $n$ positive integers (each $< 5000$)(...TRUNCATED) | [{"branch":0,"deps":[],"flags":"","label":"SU","node_id":0,"p_end":1,"p_start":0,"path":"M"},{"branc(...TRUNCATED) | "Assign one prime per pair; bound n via max prime factors per number; rule out n≥5 by product ineq(...TRUNCATED) | 0.2217 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
deepmath-63149_7 | "Let $V$ be a finite-dimensional complex vector space and $G \\subset GL(V)$ be a finite group. Cons(...TRUNCATED) | 2 | "\\operatorname{codim}_{V/G}\\operatorname{Sing}(V/G)\\ge 2\n\\text{ (with empty singular locus/smoo(...TRUNCATED) | true | hard | long | 10,544 | ["We need answer math. Need analyze fully. Problem: Let V finite-dimensional complex vector space an(...TRUNCATED) | "Let \\(X=V/G\\). Then\n\n\\[\nX=\\operatorname{Spec}\\mathbb C[V]^G,\n\\]\n\nwhere \\(V\\) has comp(...TRUNCATED) | [{"branch":0,"deps":[],"flags":"","label":"SU","node_id":0,"p_end":0,"p_start":0,"path":"M"},{"branc(...TRUNCATED) | "Show C[V]^G is normal (invariants of normal ring under finite group), then apply Serre R1 to conclu(...TRUNCATED) | 0 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
deepmath-106972_3 | "Find the largest real number \\(\\lambda\\) such that for the polynomial \\(f(x) = x^3 + ax^2 + bx (...TRUNCATED) | -\dfrac{1}{27} | -\dfrac{1}{27} | true | hard | long | 11,602 | ["Let me work through this problem carefully.\n\nWe have $f(x) = x^3 + ax^2 + bx + c$ with all roots(...TRUNCATED) | "# Finding the Largest $\\lambda$\n\n## Setting Up the Problem\n\nLet the non-negative roots be $r_1(...TRUNCATED) | [{"branch":0,"deps":[],"flags":"","label":"SU","node_id":0,"p_end":9,"p_start":0,"path":"M"},{"branc(...TRUNCATED) | "Normalize via x=ts, u_i=r_i/s; minimize over u_i using Lagrange multipliers and boundary analysis; (...TRUNCATED) | 0.1484 | Qwen3.8-27B (thinking) | Qwen3.8-27B-FP8 (thinking), TraceAtlas v4 |
ThoughtAtlas-1K: 1,000 Long Reasoning Traces, Mapped
ThoughtAtlas is a set of long chain-of-thought traces with paragraph-level structure labels. Each trace comes from Qwen3.8-27B in thinking mode (an open model on par with Claude Opus 4.6 — e.g. 75 vs 73/100 on coding in OpenCode's comparison) on a competition-style math problem, and every paragraph of its thinking is labeled with the path it belongs to — the reasoning the final answer is built on, a path that was tried and dropped, or work done after the answer was already settled — and what the model is doing (setup, plan, recall, compute, explore, verify, monitor, consolidate, answer).
Good chain-of-thought data is scarce, and what exists is plain text: you can see that a model thought for ten thousand tokens, but not which of them the answer rests on. ThoughtAtlas draws that map.
The labeling procedure was cross-checked against an independent annotator, GPT-6.1 Sol, before being used at scale (see Quality check below).
- Project page: https://seafill.info/ThoughtAtlas
- Blog: https://seafill.info/ThoughtAtlas/blog/
- Browse all 1,000 traces online: https://seafill.info/ThoughtAtlas/
Contents
1,000 traces, all with a correct final answer, from medium (632) and hard (368) problems, covering short, medium and long reasoning.
| Field | Content |
|---|---|
traj_id |
Trace id (<problem id>_<sample index>) |
problem, gold_answer |
Math problem and reference answer |
teacher_answer, is_correct |
Answer extracted from the teacher's response, and whether it matches |
difficulty, length_bin, n_tokens |
Problem difficulty (by teacher accuracy over 8 samples), trace length bin, token count |
thinking_paragraphs |
The teacher's full thinking, split into paragraphs |
final_response |
The response written after thinking |
nodes |
List of nodes: p_start, p_end (paragraph span), label (function), path, deps (earlier nodes used), branch, flags |
method |
One-line summary of the approach on the main path |
exploration_share |
Fraction of the thinking (by characters) on dropped paths (A + D) |
Paths: M main path (what the final derivation uses, plus setup/restating/planning before the answer) · A explicitly
abandoned (given up, or a wrong computation later redone) · D dead end (explored before the answer but never used) ·
P post-answer (re-checks, alternative proofs, write-up planning after the answer was first reached).
Function labels: SU setup · PL plan · RC recall · CP compute · EX explore · VF verify · MB monitor (doubt,
noticing an error, deciding to go back) · CS consolidate · AN answer. Flags: E math error · R redundant · L
mentions hidden settings or meta instructions.
How it was made
Problems come from NuminaMath-1.5 and DeepMath-103K, deduplicated and decontaminated against common math benchmarks. Traces were generated with Qwen3.8-27B (thinking mode, temperature 1.0, 16k-token cap) and graded with math-verify. Labels were produced by Qwen3.8-27B-FP8 in thinking mode at temperature 0: short traces (≤ 50 paragraphs) in one pass; long traces are first outlined as a whole (where the answer is reached, which paragraphs it relies on, a segment-level map) and then labeled in 40-paragraph chunks with that map in view, followed by consistency checks.
Quality check. Before labeling at scale, the labels were checked against an independent reference: GPT-6.1 Sol annotated 100 pilot traces with the same scheme. Of four versions of the labeling procedure, the one used here agreed best with the reference — paragraph-level F1 of 0.73 on which steps were dropped before the answer (0.86 on short traces, about 0.67 on medium and long ones). Part of the remaining gap is genuine ambiguity. Only then were these traces labeled.
All labels are model annotations, not human annotations. Paths are the most reliable part; the split between A and D
and the function labels are best treated as approximate.
Load
from datasets import load_dataset
ds = load_dataset("SeaFill2025/ThoughtAtlas-1K", split="train")
Citation
@misc{li2026thoughtatlas1k,
title = {ThoughtAtlas-1K: 1,000 Long Reasoning Traces, Mapped},
author = {Li, Hongyang and Hong, Kyungmin and Li, Xiao and
Wu, Caesar and Bouvry, Pascal and
{SeaFill Open-Source Team}},
year = {2026},
month = oct,
publisher = {Hugging Face},
howpublished = {\url{https://huggingface.co/datasets/SeaFill2025/ThoughtAtlas-1K}},
note = {Project page: \url{https://seafill.info/ThoughtAtlas/blog/}}
}
SeaFill Open-Source Team · University of Luxembourg
Formerly released as "TraceAtlas" and "ThoughtAtlas"; renamed to ThoughtAtlas-1K on 2026-10-09. Old links redirect here. Not related to the compiler tool TraceAtlas, nor to harsh-kumar9/thought-atlas (sentence-level behavior labels from an LLM judge); ThoughtAtlas-1K labels each paragraph by its role on the path to the answer.
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