Datasets:
problem_id stringlengths 21 60 | condition stringclasses 6
values | generator_type stringclasses 2
values | diversity_level stringclasses 4
values | axis stringclasses 3
values | setting_key stringclasses 55
values | messages listlengths 2 2 | ground_truth stringlengths 1 154 | generator_metadata dict | verification dict | strategy dict | token_count int64 49 16.4k |
|---|---|---|---|---|---|---|---|---|---|---|---|
algebra_func_area_train_0292 | HET_1 | HET | 1 | explorative | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1|(-5x - 3) + 3| and g(x) = -1x - 2 from x = -0.3 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
"content": "Okay, so I need to ca... | 0.8 | {
"num_distinct_models": 5,
"num_distinct_families": 4,
"generator_models": [
"deepseek-ai/DeepSeek-R1-Distill-Qwen-7B",
"Skywork/Skywork-OR1-Math-7B",
"deepseek-ai/DeepSeek-R1-Distill-Llama-8B",
"microsoft/Phi-4-mini-reasoning",
"open-thoughts/OpenThinker3-7B"
],
"generator_families": [
... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "case_split",
"step_sequence": [
"setup",
"simplify",
"setup",
"case",
"solve_eq",
"case",
"solve_eq",
"case",
"simplify",
"conclude",
"setup",
"integrate",
"count",
"case",
"setup",
"integrate",
"simplify",
"integrate",
... | 4,882 |
algebra_func_area_train_0353 | HET_1 | HET | 1 | explorative | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1(3x^2 - 2x + 3) - 1, g(x) = -2|x + 1| - 3, x = -0.2, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
"content": "To f... | 2.8 | {
"num_distinct_models": 5,
"num_distinct_families": 4,
"generator_models": [
"mistralai/Mathstral-7B-v0.1",
"open-thoughts/OpenThinker3-7B",
"deepseek-ai/DeepSeek-R1-Distill-Llama-8B",
"deepseek-ai/DeepSeek-R1-Distill-Qwen-7B",
"Qwen/Qwen3-8B"
],
"generator_families": [
"mistral",
... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "coordinate_geometry",
"step_sequence": [
"setup",
"solve_eq",
"integrate",
"solve_eq",
"setup",
"integrate",
"geometry",
"integrate",
"solve_eq",
"conclude",
"solve_eq",
"conclude"
],
"contains_strategy_switch": true
} | 4,594 |
algebra_func_area_train_0532 | HET_1 | HET | 1 | explorative | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-5x^2 - 4x + 1) + 1 and g(x) = 1x + 5 between the vertical lines x = -1.2 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
... | 8.2 | {
"num_distinct_models": 4,
"num_distinct_families": 4,
"generator_models": [
"microsoft/Phi-4-mini-reasoning",
"Qwen/Qwen3-8B",
"Skywork/Skywork-OR1-Math-7B",
"open-thoughts/OpenThinker3-7B"
],
"generator_families": [
"microsoft-phi",
"qwen",
"skywork",
"openthoughts"
]
} | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "substitution",
"step_sequence": [
"setup",
"simplify",
"expand",
"simplify",
"setup",
"integrate",
"conclude",
"setup",
"solve_eq",
"factor",
"expand",
"integrate",
"solve_eq",
"conclude",
"integrate",
"expand",
"integrate",
... | 4,096 |
algebra_func_derivative_sign_train_0000 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-1(-2cos(1πx + 2) - 3)^2 + 1(-2cos(1πx + 2) - 3) + 5) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
"con... | 10 | {
"num_distinct_models": 5,
"num_distinct_families": 5,
"generator_models": [
"Skywork/Skywork-OR1-Math-7B",
"deepseek-ai/DeepSeek-R1-Distill-Qwen-7B",
"open-thoughts/OpenThinker3-7B",
"Qwen/Qwen3-8B",
"microsoft/Phi-4-mini-reasoning"
],
"generator_families": [
"skywork",
"deepseek... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "bounding",
"step_sequence": [
"setup",
"simplify",
"substitute",
"expand",
"conclude",
"substitute",
"simplify",
"conclude",
"factor",
"conclude",
"setup",
"bound",
"conclude",
"geometry",
"solve_eq",
"setup",
"geometry",
"... | 5,120 |
algebra_func_derivative_sign_train_0087 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "For the function f(x) = (-3(5(-2|(-1x + 4) - 1| + 2)^2 + 2(-2|(-1x + 4) - 1| + 2) + 5) + 1)/(-1(5(-2|(-1x + 4) - 1| + 2)^2 + 2(-2|(-1x + 4) - 1| + 2) + 5) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \... | 2 | {
"num_distinct_models": 6,
"num_distinct_families": 6,
"generator_models": [
"Qwen/Qwen3-8B",
"deepseek-ai/DeepSeek-R1-Distill-Llama-8B",
"open-thoughts/OpenThinker3-7B",
"microsoft/Phi-4-mini-reasoning",
"Skywork/Skywork-OR1-Math-7B",
"mistralai/Mathstral-7B-v0.1"
],
"generator_famil... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "substitution",
"step_sequence": [
"setup",
"differentiate",
"setup",
"expand",
"simplify",
"conclude",
"simplify",
"substitute",
"conclude",
"substitute",
"conclude",
"factor",
"setup",
"conclude",
"bound",
"conclude",
"differe... | 5,284 |
algebra_func_derivative_sign_train_0132 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(3|(-3x + 3)| - 1)^2 + 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
"content": "Okay, so I have this prob... | 2 | {
"num_distinct_models": 4,
"num_distinct_families": 4,
"generator_models": [
"deepseek-ai/DeepSeek-R1-Distill-Llama-8B",
"open-thoughts/OpenThinker3-7B",
"microsoft/Phi-4-mini-reasoning",
"mistralai/Mathstral-7B-v0.1"
],
"generator_families": [
"deepseek",
"openthoughts",
"microso... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "complex_numbers",
"step_sequence": [
"setup",
"differentiate",
"simplify",
"substitute",
"differentiate",
"substitute",
"differentiate",
"setup",
"conclude",
"bound",
"conclude",
"case",
"setup",
"case",
"modular",
"conclude",
... | 3,159 |
algebra_func_derivative_sign_train_0224 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5((-3(-3|(-5x^2 - 1x) + 3|) + 3)/(2(-3|(-5x^2 - 1x) + 3|) + 2)) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
"content": "Oka... | 2 | {
"num_distinct_models": 5,
"num_distinct_families": 4,
"generator_models": [
"Skywork/Skywork-OR1-Math-7B",
"mistralai/Mathstral-7B-v0.1",
"deepseek-ai/DeepSeek-R1-Distill-Llama-8B",
"microsoft/Phi-4-mini-reasoning",
"deepseek-ai/DeepSeek-R1-Distill-Qwen-7B"
],
"generator_families": [
... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "bounding",
"step_sequence": [
"differentiate",
"setup",
"differentiate",
"simplify",
"setup",
"differentiate",
"bound",
"setup",
"differentiate",
"substitute",
"solve_eq",
"setup",
"solve_eq",
"conclude",
"setup",
"conclude",
"... | 4,826 |
algebra_func_derivative_sign_train_0271 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(-5((3x + 2)/(3x + 3)) + 5) + 3| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to tackl... | 2 | {
"num_distinct_models": 4,
"num_distinct_families": 4,
"generator_models": [
"Qwen/Qwen3-8B",
"open-thoughts/OpenThinker3-7B",
"deepseek-ai/DeepSeek-R1-Distill-Qwen-7B",
"mistralai/Mathstral-7B-v0.1"
],
"generator_families": [
"qwen",
"openthoughts",
"deepseek",
"mistral"
]
... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "substitution",
"step_sequence": [
"setup",
"differentiate",
"setup",
"simplify",
"factor",
"simplify",
"conclude",
"simplify",
"conclude",
"factor",
"setup",
"count",
"setup",
"substitute",
"setup",
"solve_eq",
"differentiate",... | 3,795 |
algebra_func_derivative_sign_train_0277 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-1((-1(-1|x - 2| + 2) + 2)/(-3(-1|x - 2| + 2) + 4)) + 2)^2 + 1(-1((-1(-1|x - 2| + 2) + 2)/(-3(-1|x - 2| + 2) + 4)) + 2) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format... | 2 | {
"num_distinct_models": 5,
"num_distinct_families": 5,
"generator_models": [
"Qwen/Qwen3-8B",
"deepseek-ai/DeepSeek-R1-Distill-Qwen-7B",
"Skywork/Skywork-OR1-Math-7B",
"open-thoughts/OpenThinker3-7B",
"mistralai/Mathstral-7B-v0.1"
],
"generator_families": [
"qwen",
"deepseek",
... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "monotonicity",
"step_sequence": [
"bound",
"setup",
"case",
"simplify",
"setup",
"substitute",
"simplify",
"conclude",
"bound",
"setup",
"simplify",
"setup",
"differentiate",
"conclude",
"setup",
"conclude",
"setup",
"diffe... | 5,028 |
algebra_func_derivative_sign_train_0292 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "For the function f(x) = -1|(-4x^2 + 2x + 5) + 1| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
"content": "Alright, so I have this problem wher... | 2 | {
"num_distinct_models": 4,
"num_distinct_families": 4,
"generator_models": [
"Skywork/Skywork-OR1-Math-7B",
"Qwen/Qwen3-8B",
"microsoft/Phi-4-mini-reasoning",
"deepseek-ai/DeepSeek-R1-Distill-Qwen-7B"
],
"generator_families": [
"skywork",
"qwen",
"microsoft-phi",
"deepseek"
... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "bounding",
"step_sequence": [
"setup",
"simplify",
"differentiate",
"setup",
"differentiate",
"conclude",
"setup",
"differentiate",
"conclude",
"differentiate",
"setup",
"bound",
"conclude",
"solve_eq",
"conclude",
"differentiate",... | 4,096 |
algebra_func_derivative_sign_train_0352 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "For the function f(x) = 5(-1|(2((1x)/(1x + 2))^2 - 2) + 3| + 1) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
"content": "Alright, so I have th... | 2 | {
"num_distinct_models": 5,
"num_distinct_families": 4,
"generator_models": [
"deepseek-ai/DeepSeek-R1-Distill-Llama-8B",
"Skywork/Skywork-OR1-Math-7B",
"microsoft/Phi-4-mini-reasoning",
"deepseek-ai/DeepSeek-R1-Distill-Qwen-7B",
"mistralai/Mathstral-7B-v0.1"
],
"generator_families": [
... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "symbolic_simplification",
"step_sequence": [
"setup",
"simplify",
"setup",
"bound",
"conclude",
"simplify",
"conclude",
"simplify",
"differentiate",
"conclude",
"factor",
"setup",
"conclude",
"case",
"conclude",
"setup",
"concl... | 4,249 |
algebra_func_derivative_sign_train_0423 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-1|(-5(-3x^2 + 5x + 5) - 1) + 2| - 3))/(2(-1|(-5(-3x^2 + 5x + 5) - 1) + 2| - 3) - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
... | 2 | {
"num_distinct_models": 4,
"num_distinct_families": 4,
"generator_models": [
"microsoft/Phi-4-mini-reasoning",
"Qwen/Qwen3-8B",
"open-thoughts/OpenThinker3-7B",
"mistralai/Mathstral-7B-v0.1"
],
"generator_families": [
"microsoft-phi",
"qwen",
"openthoughts",
"mistral"
]
} | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "equation_solving",
"step_sequence": [
"setup",
"differentiate",
"setup",
"simplify",
"setup",
"simplify",
"case",
"setup",
"bound",
"setup",
"count",
"simplify",
"conclude",
"bound",
"differentiate",
"setup",
"differentiate",
... | 3,570 |
algebra_func_derivative_sign_train_0453 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(1|((3(2x) - 1)/(2(2x) - 3)) + 2| - 2)^2 + 3(1|((3(2x) - 1)/(2(2x) - 3)) + 2| - 2) + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
... | 2 | {
"num_distinct_models": 2,
"num_distinct_families": 2,
"generator_models": [
"microsoft/Phi-4-mini-reasoning",
"mistralai/Mathstral-7B-v0.1"
],
"generator_families": [
"microsoft-phi",
"mistral"
]
} | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "symbolic_simplification",
"step_sequence": [
"bound",
"setup",
"simplify",
"setup",
"conclude",
"differentiate",
"conclude",
"count",
"bound",
"conclude"
],
"contains_strategy_switch": true
} | 1,806 |
algebra_func_derivative_sign_train_0552 | HET_1 | HET | 1 | explorative | algebra_func_derivative_sign | [
{
"role": "user",
"content": "For the function f(x) = 1(-1((-1x - 3)/(3x + 2)) - 2)^2 + 4(-1((-1x - 3)/(3x + 2)) - 2) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
},
{
"role": "assistant",
"content"... | 2 | {
"num_distinct_models": 4,
"num_distinct_families": 4,
"generator_models": [
"deepseek-ai/DeepSeek-R1-Distill-Llama-8B",
"open-thoughts/OpenThinker3-7B",
"Skywork/Skywork-OR1-Math-7B",
"mistralai/Mathstral-7B-v0.1"
],
"generator_families": [
"deepseek",
"openthoughts",
"skywork",
... | {
"final_answer_match": true,
"answer_check_method": "exact_string",
"domain_check": "passed",
"reasoning_sanity": "passed",
"judge_reasoning_valid": null,
"judge_confidence": null
} | {
"strategy_label": "substitution",
"step_sequence": [
"differentiate",
"setup",
"differentiate",
"simplify",
"conclude",
"expand",
"simplify",
"conclude",
"setup",
"simplify",
"differentiate",
"setup",
"differentiate",
"conclude",
"factor",
"substitut... | 3,378 |
End of preview. Expand in Data Studio
OMEGA-HET-SFT-RL
Reasoning-trajectory corpora for studying whether heterogeneous (HET) multi-model SFT data improves post-RL out-of-distribution generalization on OMEGA math vs homogeneous (HOM) single-model data, under matched controls.
Conditions
- HOM: trajectories generated by a single model (Qwen3-4B).
- HET: trajectories composed via true token-level continuation across a roster of 7 reasoning models (each model resumes the previous model's own assistant turn token-for-token).
The two conditions cover the same prompt set / ground truth (the only shared, controlled variable); the reasoning data itself is never mixed.
Files
verified/verified_candidates.jsonl— full post-verification corpus. Each row carriesgenerator_type(HOM/HET),accepted, strategy annotations, and provenance.sft/*.jsonl— matched SFT training sets (HOM/HET at diversity levels {1, K4, ALL}), built with matched prompt IDs, trajectory counts, and token budget.
Base model trained: Qwen/Qwen3-4B-Base (full-parameter FT) → GRPO (NeMo-RL).
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