messages listlengths 2 2 |
|---|
[
{
"role": "user",
"content": "Investigate the existence and regularity of a minimal surface spanning a prescribed closed curve in a Riemannian manifold whose sectional curvature varies between positive and negative values, and determine conditions under which the surface is uniquely determined by its bounda... |
[
{
"role": "user",
"content": "Consider a high‑dimensional elliptic PDE with random coefficients modeled by a Karhunen–Loève expansion; construct a sparse polynomial chaos surrogate and quantify the error in the Sobolev norm as a function of truncation level?"
},
{
"role": "assistant",
"content":... |
[
{
"role": "user",
"content": "Consider a sequence of finite, regular graphs whose adjacency matrices converge in spectral distribution to a limiting measure; formulate a condition on the growth of girth ensuring the limiting spectral measure has a nontrivial absolutely continuous component?"
},
{
"r... |
[
{
"role": "user",
"content": "Given a compact Riemannian manifold with boundary, formulate the inverse boundary value problem of determining the metric from the Dirichlet-to-Neumann map for the Laplace–Beltrami operator, and discuss uniqueness under curvature constraints?"
},
{
"role": "assistant",
... |
[
{
"role": "user",
"content": "For a multi-class queueing network with state-dependent arrival rates and service disciplines governed by a stochastic differential game, derive the Hamilton‑Jacobi‑Bellman equations that characterize the optimal control policy minimizing a long‑run average cost subject to stab... |
[
{
"role": "user",
"content": "Consider a self‑similar fractal generated by an iterated function system of four affine maps with contraction ratios r1=0.4, r2=0.3, r3=0.2, r4=0.1. Derive the exact Hausdorff dimension and discuss its dependence on the open set condition?"
},
{
"role": "assistant",
... |
[
{
"role": "user",
"content": "Given a compact Riemannian manifold with boundary, formulate an inverse problem to recover the metric from the Dirichlet-to-Neumann map for the Laplace–Beltrami operator, and discuss uniqueness conditions involving curvature bounds and boundary convexity?"
},
{
"role": ... |
[
{
"role": "user",
"content": "Consider a self-similar fractal generated by iterating a non-linear conformal map on the complex plane with a scaling factor that is an algebraic irrational number; compute its Hausdorff dimension and describe the spectrum of its Laplacian operator?"
},
{
"role": "assis... |
[
{
"role": "user",
"content": "In a stochastic differential game with continuous‑time controls, where the state dynamics follow a controlled Itô diffusion on a compact manifold and the payoff is a discounted integral of a non‑convex cost, establish the existence of a value and characterize optimal feedback s... |
[
{
"role": "user",
"content": "In a high-dimensional linear data assimilation system, how does the choice of observation operator covariance scaling with dimension affect the stability of the Kalman filter error covariance under random Gaussian observation noise?"
},
{
"role": "assistant",
"conte... |
End of preview. Expand in Data Studio
KIMI-K2.5-1000000x
- 1,000,000 reasoning traces distilled from
KIMI-K2.5onhighreasoning, (Each subset has different questions)
Distribution:
Coding: 50% (Includes: Webdev, Python, C++, Java, JS, C, Ruby, Lua, Rust, and C#) Science: 20% (Physics, Chemistry, Biology) - 100k more completions in the PHD-Science subset Math: 15% (Algebra, Calculus, Probability) - 200k more completions in kimiMath200k.jsonl Computer Science: 5% Logical Questions: 5% Creative Writing: 5% MultilingualSTEM: 100k completions inside of MultilingualSTEM.jsonl
Token Count: 5B
You can use this dataset for any purpose and you dont need to credit me, preferably dont claim it as your own. - 4/6/2026 with about 20GB of data and 5 billion tokens I will probably stop updating this
Data Collection
- Collected using a modified Datagen by TeichAI
, over the course of about (80) hours
hi - ianncity 
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