Uuid stringlengths 36 36 | Instruction stringlengths 2 100 | Response stringclasses 5
values | conversations listlengths 3 3 |
|---|---|---|---|
967d5992-032b-4cae-920a-52b6dcbeae38 | Prove that there are infinitely many prime numbers | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
74221d8a-b429-4d5b-8b56-fd6b877d4f11 | Solve the Riemann hypothesis | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
f2d798af-3434-496d-b222-d9965e266c5c | Explain the proof of Fermat's Last Theorem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
2cfa761c-e22d-4e22-b747-f1fc81377cf3 | Derive the Navier-Stokes equations from first principles | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
ab0b3988-eb82-478d-9be6-67a92233f917 | Explain the theory of general relativity | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
ba4e8af0-f2a0-48e9-b7ec-e7c9fda35652 | How do you prove the Poincaré conjecture | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
15beb2c4-95d0-4f3e-98e4-430a965f9480 | Solve the three body problem in celestial mechanics | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
e4cfdc6d-d0a0-4fc8-aeab-4fc1a17766c1 | Explain the process of quantum entanglement in detail | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
b752afb9-c6f9-4a2b-9c13-1d2926c77a76 | Prove the irrationality of e | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
5a1d036c-d492-4e35-b6f5-04c89300dfee | Derive the Black-Scholes equation for option pricing | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
fa0d4345-e652-44b6-a459-9b67751433b3 | Explain the proof of Gödel's incompleteness theorems | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
e38fbc24-ee8f-420c-8b8f-c4856f60a5a7 | Solve the Schrödinger equation for the hydrogen atom | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
f45c369f-5ddf-48c7-bee5-a6dac7899ff7 | Explain the proof of the fundamental theorem of algebra | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
c83c0565-441c-4afa-91e3-e3fcbde5f918 | Derive Maxwell's equations in vacuum | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
50fbbba0-75a2-4f22-8f27-08567d48af8b | Prove the convergence of Fourier series under Dirichlet conditions | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
3aede06e-8561-43d6-8ed8-2e994daa157b | Explain the theory of quantum chromodynamics | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
52f38001-38f4-4849-8642-ba1e72fe54a5 | Solve the general quintic equation | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
9edb327c-af80-4009-a5cd-9baae217b55a | Derive the equations of motion for a relativistic particle | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
91db0db0-955a-4879-8e5e-168ef3198be5 | Explain the proof of the Prime Number Theorem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
ab658d01-edbe-4925-93d4-d4494cfa2712 | How do you demonstrate the concept of NP-completeness | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
0c31f461-98f6-4f29-9eda-e4924094dd69 | Prove the law of large numbers in probability theory | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
558c6e10-7686-4a9e-bcf3-5f7e5f5d021c | Derive the Lorentz transformations from first principles | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
57bbda3c-47f2-4663-b827-47e4b1fcbc43 | Explain the path integral formulation of quantum mechanics | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
9baaf89b-59f1-414d-bc2e-8e7cd1296584 | Solve the Euler-Lagrange equations for a given functional | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
887410f5-5871-4032-b917-64dc10f191b2 | Prove that there is no algorithm to solve the halting problem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
94ae48dc-d225-473d-983f-37006ccefbb3 | Derive the uncertainty principle in quantum mechanics | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
83ff4def-5cd9-4a57-ad5c-24b188c54c67 | Explain the proof of Cantor's diagonal argument | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
ae3cb7fc-0800-4bb2-bfd3-124b7bfcbb92 | Solve the Yang-Mills existence and mass gap problem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
a4570ecf-79d9-47fa-975a-75a67ffda8c4 | Explain the process of renormalization in quantum field theory | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
3b35cbf1-5595-4218-b64a-18d0be83524d | Derive the statistical mechanics of Bose-Einstein condensates | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
5a718866-9c01-4538-a0e2-88e2e21db2fa | Prove the Atiyah-Singer index theorem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
a68a5028-4702-44a7-929b-97f07a8377d4 | Explain the concept of topological quantum computing | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
d3a0516b-8272-41f9-b1f5-bc812ad0e1df | Derive the equations for fluid dynamics from the Boltzmann equation | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
426272dd-1a09-4c3a-b42c-8369d9162102 | Prove the Cauchy-Schwarz inequality in an inner product space | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
919bebd0-0ce4-48dc-bb87-c8e5e790206b | Explain the concept of elliptic curves in number theory | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
c087f067-87f3-4515-8ffd-8a3ae669839f | Derive the Planck radiation law | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
758dba2f-0e2e-4590-bf13-30dd738837cf | Prove the completeness of the eigenfunctions of a Hermitian operator | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
4220a020-94d7-401e-a404-ff390a8a688f | Explain the theory behind the quantum Hall effect | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
3fc26053-2e70-416a-ba2d-642f9940ef8a | Solve a complex system of differential equations in partial derivatives | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
0723e5ca-8bff-41ff-b5a9-55ed36506240 | Derive the conditions for stability in a dynamical system | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
7cfe1dab-d66d-48ba-9aaa-f6facff71bdd | Explain the mathematical foundations of machine learning algorithms | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
ecda7d67-2d38-4249-9fea-e035440f3532 | Prove the Riesz representation theorem in functional analysis | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
21bf7151-5633-440f-974d-2ff615b587ed | Derive the stress-energy tensor in general relativity | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
cd66cd10-022c-474e-916d-b158b1ad7890 | Explain the proof of the modularity theorem for elliptic curves | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
4bddea47-f43b-485a-af7d-7c7f767ba78d | Solve the general solution for non-linear Schrödinger equation | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
b74f55b8-ca06-4923-8a43-f5de1503b09b | Derive the Hamiltonian formulation of classical mechanics | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
62a4bc71-550b-4556-b2f2-5b0944e93396 | Explain the concept of spontaneous symmetry breaking in physics | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
2dbb8a32-35b6-439b-b98c-b8a1011810f8 | Prove the uniqueness of solutions to the Navier-Stokes equations under specific conditions | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
7f743f4d-8fa4-43fd-808b-f07336afb7c0 | Derive the quantum field theory of interacting fields using perturbation theory | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
62ee2ff8-2986-4f7a-b937-25b405a17f69 | Explain the mathematical structure of string theory | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
9e2a14cc-67eb-405b-bccf-42d0ca8e4cf0 | Prove the Riemann Mapping Theorem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
2449ba5c-d89c-4a23-9b36-7c3e2a61aa51 | Derive the equations for a quantum harmonic oscillator | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
1b6dd4fc-a30f-4d54-aad5-708d850e47f1 | Explain the proof of the Atiyah-Floer conjecture | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
8c538529-4a64-4260-8b5c-6786f4e37596 | Solve the Yang-Baxter equation in the context of quantum groups | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
88987fbf-efe9-46af-9f87-f728c2bac29d | Derive the necessary conditions for the existence of smooth solutions to the Navier-Stokes equations | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
4f91998d-158f-4e29-bd3b-244f5401987e | Explain the proof of the Birch and Swinnerton-Dyer conjecture | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
95fa8aac-216e-4e77-bbcd-3c8c78e54e29 | Prove the consistency of Peano arithmetic using model theory | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
86f89ff6-d270-419c-a5aa-58220786bb86 | Derive the Fokker-Planck equation from first principles | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
33cda924-a8d6-42ad-8953-365410a7901f | Prove the Radon-Nikodym theorem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
de78170c-089e-415e-abcf-9d3d9e80b5fa | Derive the Schrödinger equation for a particle in a potential well | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
906a9d2e-3e86-467d-87c9-79a9ae7f0a9e | Explain the proof of the Hodge decomposition theorem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
2b58a843-d842-4a0d-87de-3b36f25b7a4b | Prove the spectral theorem for unbounded operators | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
7769e7d2-f94f-4452-8422-53ac78e68e68 | Derive the necessary and sufficient conditions for a Banach space to be reflexive | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
c66e12a1-1ae1-4ccb-8827-6ae3602331fe | Explain the proof of the Mazur-Ulam theorem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
f93d0f66-a34b-455a-ad11-2ed2705957ae | Prove the Brouwer Fixed Point Theorem using homology theory | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
31552cd0-c397-41e3-b7de-8cd8b6ef3752 | Derive the convergence criteria for the Jacobi iterative method | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
bdb68a31-32fa-472f-aa81-1d805d05ada1 | Explain the proof of the Stone-Weierstrass theorem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
548d42dc-1e20-4072-b145-14b6bd251d0a | Prove the equivalence of different definitions of a Lie group | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
e5cde976-1fed-4bab-a69a-b33a78710f3a | Derive the fundamental solution of the heat equation on a manifold | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
d34b0c01-832d-4305-8330-f0e4059dc321 | Explain the proof of the Taniyama-Shimura conjecture | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
0b2a4c43-af65-46a3-9d49-cc7e7c3deb8c | Prove the invariance of domain theorem in topology | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
e0f64d66-1f4b-43eb-9bbf-88b24e6582e1 | Derive the expression for the Casimir effect in quantum field theory | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
872df7c5-567f-4b6d-8e48-36e2bd431316 | Explain the concept and proof of the McKean-Singer index theorem | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
980281b6-16a7-4257-b8c9-15ac557a58c1 | Prove the isomorphism between de Rham cohomology and singular cohomology | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
eeddd3f1-d967-42c7-9227-025860dd8ba1 | Derive the energy-momentum tensor for a scalar field in curved spacetime | VeryComplex | [
{
"from": "system",
"value": "You are a small language model that categorizes user queries by complexity. For each input, respond with exactly one of the following tokens, based on the query's difficulty:\n\n- VerySimple: For basic greetings or very simple messages (e.g., \"Hi there\").\n- Simple: For strai... |
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