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4 values
1212.4862v2_reasoning_000
1212.4862v2
How many numbered result statements appear from Theorem 0.7 through Corollary 0.10, inclusive?
4
Integer
reasoning
true
[ 2, 3 ]
[]
[ "images/1212.4862v2/page000.png", "images/1212.4862v2/page001.png", "images/1212.4862v2/page002.png", "images/1212.4862v2/page003.png", "images/1212.4862v2/page004.png", "images/1212.4862v2/page005.png", "images/1212.4862v2/page006.png", "images/1212.4862v2/page007.png", "images/1212.4862v2/page008....
85,987
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/1212.4862v2
CC-BY-4.0
33
31
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32 ]
[]
null
null
2
0.03125
near
1212.4862v2_reasoning_001
1212.4862v2
In Lemma 3.26, how many distinct ranges of the parameter l are used to define the Hilbert function HF_{d₁,d₂}(l)?
4
Integer
reasoning
true
[ 28 ]
[]
[ "images/1212.4862v2/page000.png", "images/1212.4862v2/page001.png", "images/1212.4862v2/page002.png", "images/1212.4862v2/page003.png", "images/1212.4862v2/page004.png", "images/1212.4862v2/page005.png", "images/1212.4862v2/page006.png", "images/1212.4862v2/page007.png", "images/1212.4862v2/page008....
85,995
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/1212.4862v2
CC-BY-4.0
33
31
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32 ]
[]
null
null
1
0
near
1601.06633v2_reasoning_000
1601.06633v2
What is the combined number of proposition-labeled results in subsections 4.2, “Trivial duality,” and 4.3, “Twisted duality”?
2
Integer
reasoning
true
[ 8, 9 ]
[]
[ "images/1601.06633v2/page000.png", "images/1601.06633v2/page001.png", "images/1601.06633v2/page002.png", "images/1601.06633v2/page003.png", "images/1601.06633v2/page004.png", "images/1601.06633v2/page005.png", "images/1601.06633v2/page006.png", "images/1601.06633v2/page007.png", "images/1601.06633v2...
44,367
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/1601.06633v2
CC-BY-4.0
17
16
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ]
[]
null
null
2
0.0625
near
1601.06633v2_reasoning_001
1601.06633v2
In Section 5.1’s four-piece breakdown of the proof of Theorem 1.1, by how many does the number of destination results labeled “Theorem” exceed the number labeled “Proposition”?
2
Integer
reasoning
true
[ 9 ]
[]
[ "images/1601.06633v2/page000.png", "images/1601.06633v2/page001.png", "images/1601.06633v2/page002.png", "images/1601.06633v2/page003.png", "images/1601.06633v2/page004.png", "images/1601.06633v2/page005.png", "images/1601.06633v2/page006.png", "images/1601.06633v2/page007.png", "images/1601.06633v2...
44,374
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/1601.06633v2
CC-BY-4.0
17
16
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ]
[]
null
null
1
0
near
1703.00544v5_reasoning_000
1703.00544v5
In the contribution overview of Section 1.2, how many numbered named results are stated from Theorem 1.1 through Theorem 1.7, counting both the theorem and corollary statements shown there?
7
Integer
reasoning
true
[ 2, 3 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,132
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
2
0.032258
near
1703.00544v5_reasoning_001
1703.00544v5
In Table 1, how many green FPT cells are shown across both parameter blocks?
5
Integer
reasoning
true
[ 4 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,105
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
1
0
near
1703.00544v5_reasoning_002
1703.00544v5
In Section 2.1, before the pre-evaluations paragraph, how many cardinality-constraint categories are introduced by the consecutive headings “Global cardinality constraints” and “Local cardinality constraints”?
2
Integer
reasoning
true
[ 5, 6 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,128
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
2
0.032258
near
1703.00544v5_reasoning_003
1703.00544v5
According to Definition 2.4, how many node types are listed for a nice tree decomposition?
4
Integer
reasoning
true
[ 7 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,107
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
1
0
near
1703.00544v5_reasoning_004
1703.00544v5
In the refinement discussion, multiply the number of cases in Definition 3.5’s shape definition by the maximum number of parts into which Lemma 3.8 can split a nonuniform type. What is the product?
8
Integer
reasoning
true
[ 13, 14 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,131
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
2
0.032258
near
1703.00544v5_reasoning_005
1703.00544v5
In the definition of a parameterized reduction in Section 2.3, how many bullet-point conditions are listed after “such that”?
2
Integer
reasoning
true
[ 8 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,114
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
1
0
near
1703.00544v5_reasoning_006
1703.00544v5
In the proof of Theorem 3.1, add the number of input items named in the LCC Subset problem box to the number of vertex groups listed in the construction of the graph H. What is the sum?
6
Integer
reasoning
true
[ 9, 10 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,132
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
2
0.032258
near
1703.00544v5_reasoning_007
1703.00544v5
In the displayed definition of the formula φ at the end of the proof of Theorem 1.3, how many conditions are conjoined for each v in C?
2
Integer
reasoning
true
[ 12 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,121
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
1
0
near
1703.00544v5_reasoning_008
1703.00544v5
Combining Proposition 3.7 and Lemma 3.10, how many bullet-point conclusions are listed in total?
4
Integer
reasoning
true
[ 14, 15 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,112
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
2
0.032258
near
1703.00544v5_reasoning_009
1703.00544v5
In Theorem 3.11’s integer linear program description, how many displayed constraint labels are shown from (0) through the shape constraints?
5
Integer
reasoning
true
[ 16 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,117
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
1
0
near
1703.00544v5_reasoning_010
1703.00544v5
How many more component bullets are listed in Definition 4.1 for a CSP instance than output-property bullets are listed in Theorem 4.6?
1
Integer
reasoning
true
[ 21, 22 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,118
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
2
0.032258
near
1703.00544v5_reasoning_011
1703.00544v5
How many labeled subfigures does Figure 3 contain?
2
Integer
reasoning
true
[ 28 ]
[]
[ "images/1703.00544v5/page000.png", "images/1703.00544v5/page001.png", "images/1703.00544v5/page002.png", "images/1703.00544v5/page003.png", "images/1703.00544v5/page004.png", "images/1703.00544v5/page005.png", "images/1703.00544v5/page006.png", "images/1703.00544v5/page007.png", "images/1703.00544v5...
81,098
gpt-5.5-2026-04-24
Computer Science
https://arxiv.org/abs/1703.00544v5
CC-BY-4.0
32
29
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 ]
[]
null
null
1
0
near
1811.01271v4_reasoning_000
1811.01271v4
For a strongly starlike function of order β = 1/2, by how much does the upper bound for |a₃| obtained from Theorem 3.3 exceed the sharp upper bound in Theorem 3.1?
0.25
Float
reasoning
true
[ 6, 8 ]
[]
[ "images/1811.01271v4/page000.png", "images/1811.01271v4/page001.png", "images/1811.01271v4/page002.png", "images/1811.01271v4/page003.png", "images/1811.01271v4/page004.png", "images/1811.01271v4/page005.png", "images/1811.01271v4/page006.png", "images/1811.01271v4/page007.png", "images/1811.01271v4...
41,779
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/1811.01271v4
CC-BY-4.0
16
14
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
2
0.133333
near
1811.01271v4_reasoning_001
1811.01271v4
In Remark 3.1, by how much does the upper bound for |a₄| in Case 1 exceed the upper bound in Case 2?
2.5
Float
reasoning
true
[ 10 ]
[]
[ "images/1811.01271v4/page000.png", "images/1811.01271v4/page001.png", "images/1811.01271v4/page002.png", "images/1811.01271v4/page003.png", "images/1811.01271v4/page004.png", "images/1811.01271v4/page005.png", "images/1811.01271v4/page006.png", "images/1811.01271v4/page007.png", "images/1811.01271v4...
41,762
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/1811.01271v4
CC-BY-4.0
16
14
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
1
0
near
1906.02754v2_reasoning_000
1906.02754v2
In the final-state object definitions, what is the numerical difference between the global Higgs rapidity cutoff |Y_H| < 2.5 and the truth-jet radius R = 0.4?
2.1
Float
reasoning
true
[ 4, 5 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,563
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.076923
near
1906.02754v2_reasoning_001
1906.02754v2
On the title page author-affiliation list, how many numbered affiliations are located in either France or the USA?
5
Integer
reasoning
true
[ 0 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,542
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
1906.02754v2_reasoning_002
1906.02754v2
Using the prose bin definitions for gg → H and electroweak qqH production, what is the difference in GeV between the largest m_jj boundary listed for the electroweak qqH m_jj > 350 GeV bin and the gg → H low/high-m_jj separation?
1150
Integer
reasoning
true
[ 6, 8 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,586
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.153846
near
1906.02754v2_reasoning_003
1906.02754v2
In the Contents, how many entries are listed under “4 Bin Definitions” when counting both its direct subsections and the two indented subsubsections under “Other Production Modes”?
7
Integer
reasoning
true
[ 1 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,555
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
1906.02754v2_reasoning_004
1906.02754v2
In the stage 1.2 diagrams, what is the combined number of boxes immediately below the top process box for electroweak qqH and leptonic VH production?
6
Integer
reasoning
true
[ 7, 9 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,554
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.153846
near
1906.02754v2_reasoning_005
1906.02754v2
In the Overview’s list of concrete STXS-bin goals, how many goals are given?
4
Integer
reasoning
true
[ 3 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,537
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
1906.02754v2_reasoning_006
1906.02754v2
In the final-state object definitions, what is the numerical difference between the forward-electron rapidity reach mentioned for H → ZZ* → 4ℓ and the truth-jet radius R?
4.6
Float
reasoning
true
[ 4, 5 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,559
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.076923
near
1906.02754v2_reasoning_007
1906.02754v2
In Figure 1 for gg → H, how many top-level p_T^H ranges split the stage 1.2 diagram before the jet-category branches?
2
Integer
reasoning
true
[ 5 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,551
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
1906.02754v2_reasoning_008
1906.02754v2
What is the difference in GeV between the highest finite p_T^H boundary shown for ttH production and the highest p_T^V boundary stated for the q q′ → WH and q q̄ → ZH subprocesses in associated leptonic VH production?
50
Integer
reasoning
true
[ 9, 10 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,574
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.076923
near
1906.02754v2_reasoning_009
1906.02754v2
In the electroweak qqH production description, into how many jet bins is the cross section first split?
3
Integer
reasoning
true
[ 7 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,542
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
1906.02754v2_reasoning_010
1906.02754v2
If each dominant Higgs production process named in the abstract were paired with each major Higgs decay channel listed in the Introduction, how many production–decay pairings would that make?
20
Integer
reasoning
true
[ 0, 1 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,556
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.076923
near
1906.02754v2_reasoning_011
1906.02754v2
In Figure 4 for ttH production, how many finite p_T^H boundary labels greater than 0 are shown?
5
Integer
reasoning
true
[ 10 ]
[]
[ "images/1906.02754v2/page000.png", "images/1906.02754v2/page001.png", "images/1906.02754v2/page002.png", "images/1906.02754v2/page003.png", "images/1906.02754v2/page004.png", "images/1906.02754v2/page005.png", "images/1906.02754v2/page006.png", "images/1906.02754v2/page007.png", "images/1906.02754v2...
36,544
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/1906.02754v2
CC-BY-4.0
14
11
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
2001.11078v2_multi_distributed_000
2001.11078v2
How do the introductory prime-case proposition and Proposition 4.19 characterize the effect of quotienting power operations by transfer ideals, respectively for a genuine G-spectrum and for C-valued class functions?
["For an H∞-ring in genuine G-spectra and m = p prime, the ideals J(G/H) assemble into a Mackey ideal J ⊆ E^0(BΣp), minimal among those for which the reduced power operation Pp/J: E^0 → E^0(BΣp)/J is a map of G-Green functors.", "For C-valued class functions, Cl(G × Σm)/ITr is isomorphic to Cl(G), and the composite Cl(...
List
multi_distributed
true
[ 2, 35 ]
[]
[ "images/2001.11078v2/page000.png", "images/2001.11078v2/page001.png", "images/2001.11078v2/page002.png", "images/2001.11078v2/page003.png", "images/2001.11078v2/page004.png", "images/2001.11078v2/page005.png", "images/2001.11078v2/page006.png", "images/2001.11078v2/page007.png", "images/2001.11078v2...
104,067
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/2001.11078v2
CC-BY-4.0
41
39
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 ]
[]
null
null
2
0.825
far
2001.11078v2_reasoning_001
2001.11078v2
Across Example 4.5 and Example 4.10, what is the combined number of additive generators explicitly listed for the Burnside rings A(C₂ × Σ₂) and A(C₃ × Σ₃), respectively?
15
Integer
reasoning
true
[ 27, 30 ]
[]
[ "images/2001.11078v2/page000.png", "images/2001.11078v2/page001.png", "images/2001.11078v2/page002.png", "images/2001.11078v2/page003.png", "images/2001.11078v2/page004.png", "images/2001.11078v2/page005.png", "images/2001.11078v2/page006.png", "images/2001.11078v2/page007.png", "images/2001.11078v2...
103,926
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/2001.11078v2
CC-BY-4.0
41
39
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 ]
[]
null
null
2
0.075
near
2003.13227v3_multi_distributed_006
2003.13227v3
Compare Theorem 1.1 with the single-closed-subset version Theorem 3.4: what restriction and distance requirements do they impose on the constructed metric?
["Theorem 1.1: the constructed metric m satisfies m|A_i^2 = e_i for every i in I, and D_X(m,d) = sup_i D_{A_i}(e_i,d|A_i^2).", "Theorem 3.4: the constructed metric m satisfies m|A^2 = e, and D_X(m,d) = D_A(e,d|A^2)."]
List
multi_distributed
true
[ 1, 7 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,474
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
2
0.285714
medium
2003.13227v3_multi_distributed_011
2003.13227v3
What formulas does the paper give for D_X on Met(X) and for the metric E on C(X^2)?
["D_X(d,e) = sup_{(x,y) in X^2} |d(x,y) - e(x,y)|.", "E(f,g) = min{1, sup_{(x,y) in X^2} |f(x,y) - g(x,y)|}."]
List
multi_distributed
true
[ 0, 18 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,435
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
2
0.857143
far
2003.13227v3_multi_local_010
2003.13227v3
Across the later sections, what conclusions are stated in Theorem 4.7, Theorem 4.15, and Lemma 5.1 about spaces or sets of metrics?
["Theorem 4.7: for every non-discrete completely metrizable space X, the set of all d in Comp(X) for which (X,d) satisfies the anti-G-transmissible property is dense G_delta in Comp(X).", "Theorem 4.15: for every non-discrete metrizable space X, the set of all metrics d in Met(X) for which (X,d) has rich pseudo-cones i...
List
multi_local
true
[ 11, 15, 18 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,524
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
3
0.333333
medium
2003.13227v3_reasoning_000
2003.13227v3
In Example 1.1, how many properties on metric spaces are listed as transmissible properties?
6
Integer
reasoning
true
[ 2 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,371
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
1
0
near
2003.13227v3_reasoning_001
2003.13227v3
In the paper's subsection titled “Main results,” how many theorem statements labeled Theorem 1.1, Theorem 1.2, or Theorem 1.3 are introduced?
3
Integer
reasoning
true
[ 1, 3 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,390
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
2
0.095238
near
2003.13227v3_reasoning_002
2003.13227v3
In the preliminary material covering the Stone theorem, the Kuratowski embedding theorem, and Baire spaces, how many numbered theorem-or-lemma statements appear?
4
Integer
reasoning
true
[ 5 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,382
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
1
0
near
2003.13227v3_reasoning_003
2003.13227v3
In subsection 4.2, from Lemma 4.8 through Theorem 4.12, how many numbered Lemma, Proposition, or Theorem statements appear, excluding remarks?
5
Integer
reasoning
true
[ 12, 13 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,389
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
2
0.047619
near
2003.13227v3_reasoning_004
2003.13227v3
On the page where the ultratriangle and Ptolemy inequalities are defined, what is the difference between the number of points used in the Ptolemy inequality and the number of points used in the ultratriangle inequality?
1
Integer
reasoning
true
[ 16 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,398
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
1
0
near
2003.13227v3_reasoning_005
2003.13227v3
How many total conditions are explicitly listed for the constructed metric in Theorem 3.4 and for the auxiliary metric h in the proof of that theorem?
5
Integer
reasoning
true
[ 7, 8 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,382
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
2
0.047619
near
2003.13227v3_reasoning_007
2003.13227v3
In Lemma 4.5, how many cases are given in the displayed piecewise definition of the metric d_L?
4
Integer
reasoning
true
[ 10 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,375
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
1
0
near
2003.13227v3_single_009
2003.13227v3
What does Lemma 5.1 state about Met(X) for every second-countable locally compact metrizable space X?
Met(X) is completely metrizable; in particular, it is Baire.
String
single
true
[ 18 ]
[]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,391
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
1
0
near
2003.13227v3_unanswerable_008
2003.13227v3
What is the combined monetary funding amount awarded through the JSPS KAKENHI Grant Numbers 18J21300 and JP24KJ0182 acknowledged in the paper?
Not answerable.
Unanswerable
unanswerable
false
[]
[ 4 ]
[ "images/2003.13227v3/page000.png", "images/2003.13227v3/page001.png", "images/2003.13227v3/page002.png", "images/2003.13227v3/page003.png", "images/2003.13227v3/page004.png", "images/2003.13227v3/page005.png", "images/2003.13227v3/page006.png", "images/2003.13227v3/page007.png", "images/2003.13227v3...
57,396
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2003.13227v3
CC-BY-4.0
22
20
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ]
[]
null
null
0
null
no_evidence
2004.10144v4_reasoning_000
2004.10144v4
Using Fig. 2 and Fig. 6, how many more named energy-spectrum phases are shown in Fig. 2 than plotted panels are shown in Fig. 6?
2
Integer
reasoning
true
[ 4, 7 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,080
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
2
0.214286
medium
2004.10144v4_reasoning_001
2004.10144v4
In the list of Fermi-surface situations in Section III, how many listed situations are not the 'Disconnected Fermi surfaces' case?
2
Integer
reasoning
true
[ 4 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,071
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
1
0
near
2004.10144v4_reasoning_002
2004.10144v4
Across Section II, how many lettered subsections are visible from the subsection headings 'Low-energy band dispersion' and 'Topological properties'?
2
Integer
reasoning
true
[ 1, 3 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,071
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
2
0.142857
near
2004.10144v4_reasoning_003
2004.10144v4
In Appendix B, how many separate matching conditions are displayed in Eq. (B5)?
4
Integer
reasoning
true
[ 9 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,061
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
1
0
near
2004.10144v4_reasoning_004
2004.10144v4
Adding Appendix A's matching-system equations in Eq. (A1) to Appendix B's matching conditions in Eq. (B5), how many equations or conditions are there in total?
8
Integer
reasoning
true
[ 8, 9 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,080
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
2
0.071429
near
2004.10144v4_reasoning_005
2004.10144v4
In Appendix C, how many fewer real longitudinal solutions are admitted at β = π/2 than the four possible solutions described for the general β ≠ 0, π/2 case?
2
Integer
reasoning
true
[ 10 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,080
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
1
0
near
2004.10144v4_reasoning_006
2004.10144v4
How many component entries are there in total when the three-entry normalized eigenstate in Eq. (C7) is combined with the three-entry eigenstate in Eq. (D5)?
6
Integer
reasoning
true
[ 10, 11 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,080
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
2
0.071429
near
2004.10144v4_reasoning_007
2004.10144v4
In Section II.A, Eq. (1) presents the Hamiltonian H as a 3-by-3 matrix. How many scalar positions does that matrix contain?
9
Integer
reasoning
true
[ 1 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,076
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
1
0
near
2004.10144v4_reasoning_008
2004.10144v4
Comparing the paper’s SKT-regime conductance formulas, what is the ratio of the coefficient multiplying the common factor G0 Ly kmax/π in Appendix A’s parallel-to-deformation result Gx^SKT to the coefficient in Section IV’s Eq. (29) result GSKT?
2
Integer
reasoning
true
[ 7, 9 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,106
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
2
0.142857
near
2004.10144v4_reasoning_009
2004.10144v4
In Fig. D-1, how many lower polar-plot panels are labeled by different β values?
3
Integer
reasoning
true
[ 12 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,064
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
1
0
near
2004.10144v4_reasoning_010
2004.10144v4
How many displayed lines are there in total when Eq. (23)'s two momentum-component transformations are combined with Eq. (25)'s two spatial-region wave-function expressions?
4
Integer
reasoning
true
[ 6, 7 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,080
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
2
0.071429
near
2004.10144v4_reasoning_011
2004.10144v4
In Appendix E, Eq. (E6) gives expressions for how many amplitudes?
2
Integer
reasoning
true
[ 12 ]
[]
[ "images/2004.10144v4/page000.png", "images/2004.10144v4/page001.png", "images/2004.10144v4/page002.png", "images/2004.10144v4/page003.png", "images/2004.10144v4/page004.png", "images/2004.10144v4/page005.png", "images/2004.10144v4/page006.png", "images/2004.10144v4/page007.png", "images/2004.10144v4...
38,062
gpt-5.5-2026-04-24
Physics
https://arxiv.org/abs/2004.10144v4
CC-BY-4.0
15
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]
[]
null
null
1
0
near
2006.05284v3_multi_local_000
2006.05284v3
How does the paper’s positive-renormalisation development connect abstract character properties, model construction, and translation invariance? State (1) the two algebra-morphism conclusions of Theorem 3.12, (2) Definition 4.1’s formulas for the model map \(\Pi_z\) and the character \(f_z\), and (3) Corollary 4.3’s id...
(1) Theorem 3.12 states that the counterterm map \(\varphi^-_{x,\bar x}\) is an algebra morphism from \(H^{\mathfrak D}_+\) into \(\mathcal H^-_x\), while the renormalised map \(\varphi^+_{x,\bar x}\) is an algebra morphism from \(H^{\mathfrak D}\) into \(\mathcal H\) and sends trees in \(\mathfrak T^{\mathfrak D}_+\) ...
String
multi_local
true
[ 12, 20, 21 ]
[]
[ "images/2006.05284v3/page000.png", "images/2006.05284v3/page001.png", "images/2006.05284v3/page002.png", "images/2006.05284v3/page003.png", "images/2006.05284v3/page004.png", "images/2006.05284v3/page005.png", "images/2006.05284v3/page006.png", "images/2006.05284v3/page007.png", "images/2006.05284v3...
73,307
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/2006.05284v3
CC-BY-4.0
28
26
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 ]
[]
null
null
3
0.333333
medium
2006.05284v3_single_001
2006.05284v3
According to Theorem 3.17 under Assumption 2, on which trees is the counter term map invariant in its second subscript?
Trees that have a zero node decoration at the root.
String
single
true
[ 17 ]
[]
[ "images/2006.05284v3/page000.png", "images/2006.05284v3/page001.png", "images/2006.05284v3/page002.png", "images/2006.05284v3/page003.png", "images/2006.05284v3/page004.png", "images/2006.05284v3/page005.png", "images/2006.05284v3/page006.png", "images/2006.05284v3/page007.png", "images/2006.05284v3...
73,013
gpt-5.6-sol
Mathematics
https://arxiv.org/abs/2006.05284v3
CC-BY-4.0
28
26
arxiv_research_paper
en
majority of full-context generator domain labels
gpt56_two_qa
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 ]
[]
null
null
1
0
near
2011.08259v2_multi_distributed_001
2011.08259v2
In Section 4's group-theoretic proof, what does Lemma 4.1 say about the morphism from G_0^0 to Sp(2n), what unique splitting property is stated in Lemma 4.7, and what central-extension lift is asserted by the Basic Lemma?
["Lemma 4.1 states that there is a surjective homomorphism G_0^0 -> Sp(2n) whose kernel is a unipotent algebraic group.", "Lemma 4.7 states that the restriction of the extension 1 -> W-hat -> G-tilde_0^e -> G_0 -> 1 to G_0^0 admits a unique splitting, equivalently a unique homomorphism G_0^0 -> G-tilde_0^e whose compos...
List
multi_distributed
true
[ 20, 25, 31 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,652
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
3
0.268293
medium
2011.08259v2_multi_distributed_006
2011.08259v2
Compare the definitions of Frobenius-constant and G_m-equivariant Frobenius-constant quantizations: what is the isomorphism s in the former definition, and what condition is imposed on O_h/(h) in the latter definition?
["For a Frobenius-constant quantization, s is an O_X'-[[h]]-algebra isomorphism s: O_X'[[h]] -> Z_h.", "For a G_m-equivariant Frobenius-constant quantization, the restriction O_h/(h) -> O_X is required to be an isomorphism of G_m-equivariant O_X'-algebras."]
List
multi_distributed
true
[ 1, 33 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,538
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
2
0.780488
far
2011.08259v2_multi_local_004
2011.08259v2
In the introduction, what vanishing condition makes the Bezrukavnikov-Kaledin map rho a bijection, and what separate vanishing condition in Theorem 1 makes O_h^circ a split Azumaya algebra?
["rho is a bijection when H^1_Zar(X', O_X'/O_X'^p) = 0 and H^2_Zar(X', O_X'/O_X'^p) = 0.", "Theorem 1 states that if H^2(X, O_X) = 0, then O_h^circ is a split Azumaya algebra."]
List
multi_local
true
[ 3, 5 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,530
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
2
0.04878
near
2011.08259v2_multi_local_009
2011.08259v2
In the review of the Bezrukavnikov-Kaledin construction, what is the algebra A_0 in the Darboux lemma, and what torsor description is used for restricted Poisson structures in the formal-geometry subsection?
["A_0 = k[x_1,y_1,...,x_n,y_n]/(x_1^p,y_1^p,...,x_n^p,y_n^p).", "The formal-geometry subsection says that restricted Poisson structures [eta] on X are in bijection with G_0-torsors over X' equipped with an isomorphism of Aut(A_0)-torsors."]
List
multi_local
true
[ 10, 11 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,541
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
2
0.02439
near
2011.08259v2_reasoning_002
2011.08259v2
Across Section 5, how many more numbered displayed equations appear on the page introducing Theorem 5 than on the page defining G_m-equivariant quantizations?
0
Integer
reasoning
true
[ 33, 34 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,439
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
2
0.02439
near
2011.08259v2_reasoning_007
2011.08259v2
Using the table of contents, how many printed pages separate the start of Section 5, “G_m-equivariant quantizations,” from the start of Section 6, “Appendix”?
2
Integer
reasoning
true
[ 1 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,445
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
1
0
near
2011.08259v2_single_003
2011.08259v2
In Proposition 6.2 about subgroups of LGL(n), what factorization through a conjugate of L^+GL(n) is guaranteed for a homomorphism phi: G -> LGL(n)?
There exists an element g in GL(n,k((h))) such that phi factors through g(L^+GL(n))g^{-1} -> LGL(n).
String
single
true
[ 37 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,481
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
1
0
near
2011.08259v2_single_005
2011.08259v2
According to the abstract, after inverting the Planck constant h, what is the Bezrukavnikov-Kaledin quantization of a symplectic variety in characteristic p equivalent to when H^2(X,O_X)=0?
It is Morita equivalent to a certain central reduction of the algebra of differential operators on X.
String
single
true
[ 0 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,472
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
1
0
near
2011.08259v2_single_008
2011.08259v2
In Section 2.6, what map rho is defined from isomorphism classes of Frobenius-constant quantizations compatible with [eta]?
rho: Q(X,[eta]) -> H^1_et(X', O_X'^*/O_X'^p).
String
single
true
[ 12 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,458
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
1
0
near
2011.08259v2_single_010
2011.08259v2
What invariant connection does Lemma 4.13 assert exists on alpha-tilde?
Lemma 4.13 asserts that there exists a unique Sp_{2n} ⋉ alpha-invariant W-hat-connection nabla on alpha-tilde.
String
single
true
[ 28 ]
[]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,459
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
1
0
near
2011.08259v2_unanswerable_000
2011.08259v2
The acknowledgements state that the work was partially supported by Russian Science Foundation grant No. 21-11-00153. Using the paper’s title block for the author count, what was the average monetary support per listed author from that grant?
Not answerable.
Unanswerable
unanswerable
false
[]
[ 0, 10 ]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,463
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
0
null
no_evidence
2011.08259v2_unanswerable_011
2011.08259v2
In the Acknowledgements, what specific technical difficulty did conversations with Dmitry Kaledin help the authors overcome?
Not answerable.
Unanswerable
unanswerable
false
[]
[ 10 ]
[ "images/2011.08259v2/page000.png", "images/2011.08259v2/page001.png", "images/2011.08259v2/page002.png", "images/2011.08259v2/page003.png", "images/2011.08259v2/page004.png", "images/2011.08259v2/page005.png", "images/2011.08259v2/page006.png", "images/2011.08259v2/page007.png", "images/2011.08259v2...
106,431
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2011.08259v2
CC-BY-4.0
42
40
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41 ]
[]
null
null
0
null
no_evidence
2102.01462v3_multi_distributed_000
2102.01462v3
In the paper’s Section 3 discussion of Pimsner-Popa bases, what does Vaughan Jones’s Question 3.1 ask about an extremal finite-index subfactor, and what does Corollary 3.15 later assert for irreducible depth-2 inclusions?
["Question 3.1 asks whether, if N is a II_1-factor and N ⊂ M is an extremal subfactor of finite index, M/N always has a two-sided Pimsner-Popa basis for M over N.", "Corollary 3.15 asserts that every finite index irreducible inclusion of II_1 factors of depth 2 admits a two-sided orthonormal basis."]
List
multi_distributed
true
[ 3, 8 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,716
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
2
0.333333
medium
2102.01462v3_multi_distributed_001
2102.01462v3
How does Definition 2.1 set up the algebraic ingredients of a weak bialgebra, and in Theorem 4.6 what weak Kac algebra conclusion is obtained for a regular inclusion with commutative first relative commutant?
["Definition 2.1 says a weak bialgebra is a quintuple (A, m, η, Δ, ε) such that (A, m, η) is an algebra and (A, Δ, ε) is a coalgebra, with compatibility conditions between the algebra and coalgebra structures.", "Theorem 4.6 concludes that there exists a biconnected weak Kac algebra K and a minimal action of K on N suc...
List
multi_distributed
true
[ 1, 13 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,736
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
2
0.8
far
2102.01462v3_multi_distributed_002
2102.01462v3
What three basis-related open or natural questions/problems are stated around Question 3.8, Conjecture 3.20, and the beginning of Section 4?
["Question 3.8 asks whether, if N ⊂ M is a depth-2 subfactor of type II_1 of finite index, M/N always has a two-sided basis.", "Conjecture 3.20 states that if N ⊂ M is a finite index regular inclusion of factors of type II_1, then M/N has a unitary orthonormal basis.", "At the beginning of Section 4, the authors state ...
List
multi_distributed
true
[ 5, 8, 12 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,722
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
3
0.466667
medium
2102.01462v3_multi_distributed_004
2102.01462v3
How do the paper’s group crossed-product examples differ between the outer-action example in Section 3.1 and the inner-action example in Example 4.7?
["In Example 3.2, if G acts outerly on a II_1-factor N, then N ⋊ G always possesses a two-sided unitary orthonormal basis over N ⋊ H.", "In Example 4.7, if a finite group G acts innerly on a II_1 factor N so that M = N ⋊ G is a II_1 factor, then the inclusion N ⊂ M is regular and N' ∩ M is nontrivial."]
List
multi_distributed
true
[ 3, 13 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,710
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
2
0.666667
far
2102.01462v3_multi_distributed_009
2102.01462v3
What three depth- or basis-related conclusions are given by Proposition 3.12, Theorem 3.21, and Theorem 4.3?
["Proposition 3.12 says that for a finite index depth-2 subfactor N ⊂ M of type II_1 with a tunnel construction, the inclusions N_{-2k} ⊂ N_{-2k+1} have depth 2 and M_{2k-1} ⊂ M_{2k} is also of depth 2 for all k ≥ 1.", "Theorem 3.21 says that if N ⊂ M is a finite index regular inclusion of factors of type II_1 and N' ∩...
List
multi_distributed
true
[ 6, 9, 12 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,799
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
3
0.4
medium
2102.01462v3_multi_local_006
2102.01462v3
What do Proposition 3.6, Theorem 3.21, and Theorem 4.6 respectively conclude about regular inclusions under prime-index or first-relative-commutant hypotheses?
["Proposition 3.6 concludes that if N ⊂ M is a finite index regular inclusion of II_1-factors with [M:N] = p prime, then N ⊂ M is irreducible and is isomorphic to N ⊂ N ⋊ G, where the cyclic group G = Z/pZ acts outerly on N.", "Theorem 3.21 concludes that if N ⊂ M is a finite index regular inclusion of factors of type ...
List
multi_local
true
[ 4, 9, 13 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,816
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
3
0.6
far
2102.01462v3_multi_local_011
2102.01462v3
What does Remark 2.5 say about when a finite groupoid’s groupoid algebra is biconnected, and what characterization does Theorem 2.9 give for finite-index irreducible depth-2 inclusions?
["Remark 2.5 says that for a finite groupoid G, the groupoid algebra C[G] is biconnected if and only if G is a group.", "Theorem 2.9 says that a finite index irreducible inclusion N ⊂ M of II_1-factors is of depth 2 if and only if there exist a biconnected weak Hopf C*-algebra H and a minimal action of H on M_1 such th...
List
multi_local
true
[ 2, 3 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,737
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
2
0.066667
near
2102.01462v3_reasoning_008
2102.01462v3
How many explicitly labeled Question statements appear in subsection 3.1.1 and in the opening part of subsection 3.2 ending with Conjecture 3.20, combined?
2
Integer
reasoning
true
[ 5, 8 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,614
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
2
0.2
near
2102.01462v3_single_003
2102.01462v3
In Corollary 4.4, what conclusion follows when N ⊂ M is a finite index regular inclusion of type II_1 factors and N' ∩ M is commutative?
It has depth 2.
String
single
true
[ 13 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,619
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
1
0
near
2102.01462v3_single_005
2102.01462v3
According to Definition 2.2, when is a weak Hopf C*-algebra called a weak Kac algebra?
A weak Hopf C*-algebra (A, m, η, Δ, ε, S) is called a weak Kac algebra if S^2 = Id_A and S is *-preserving.
String
single
true
[ 1 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,642
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
1
0
near
2102.01462v3_single_007
2102.01462v3
In Proposition 3.7, what is said about the Watatani index for a finite index regular inclusion of II_1-factors?
The Watatani index of the restriction of tr_M to N' ∩ M is a scalar.
String
single
true
[ 4 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,623
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
1
0
near
2102.01462v3_single_010
2102.01462v3
In the proof of Proposition 3.23, what set formed from the Sylvester-Weyl matrices U and V is stated to be a unitary error basis for M_n(C)?
The set {U^i V^j : 1 ≤ i, j ≤ n} is stated to form a unitary error basis for M_n(C).
String
single
true
[ 10 ]
[]
[ "images/2102.01462v3/page000.png", "images/2102.01462v3/page001.png", "images/2102.01462v3/page002.png", "images/2102.01462v3/page003.png", "images/2102.01462v3/page004.png", "images/2102.01462v3/page005.png", "images/2102.01462v3/page006.png", "images/2102.01462v3/page007.png", "images/2102.01462v3...
40,645
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.01462v3
CC-BY-4.0
16
15
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]
[]
null
null
1
0
near
2102.13259v2_multi_distributed_007
2102.13259v2
In the construction leading to Theorem 2.7, state the trigonometric form required in Lemma 2.3, the hyperbolicity condition from Definition 2.5, and the polynomial identity chosen for A in Theorem 2.7.
["Lemma 2.3 uses F(t:phi)=t^{n+1}+p_n t^n+...+p_1 t+p_0 - u cos(phi) - v sin(phi).", "Definition 2.5 requires Q(1,0,0)>0 and Q(t,x0,y0)=0 to have m real solutions counting multiplicities for every (x0,y0) with x0^2+y0^2>0.", "Theorem 2.7 chooses A so that F_A(t,x,y)=(G_n(t,x,y)-|alpha_n x+gamma_n y|^2 H_n(t,x,y))^2 - 4...
List
multi_distributed
true
[ 5, 8, 9 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,722
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
3
0.307692
medium
2102.13259v2_multi_local_005
2102.13259v2
How do the introduction and Theorem 2.7 each describe the finite-matrix reduction of a periodic tridiagonal operator’s closed numerical range?
["The introduction says the closure of the numerical range of an n+1 periodic tridiagonal operator is the numerical range of a 2(n+1) × 2(n+1) matrix.", "Theorem 2.7 states that for T(a,b,c) there exists a 2(n+1) × 2(n+1) complex matrix A such that overline{W(T(a,b,c))} = W(A)."]
List
multi_local
true
[ 0, 8 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,631
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.615385
far
2102.13259v2_multi_local_011
2102.13259v2
For Examples 2.10 and 2.12, what coefficient equality makes a gamma term vanish, and what common geometric conclusion do the examples draw for overline{W(T(a,b,c))}?
["Example 2.10: if a0 = c1, then gamma1 = 0; overline{W(T(a,b,c))} is the convex hull of two ellipses, possibly degenerate, each a translation of a single ellipse centered at the origin.", "Example 2.12: if c0 = a1, then gamma0 = 0; overline{W(T(a,b,c))} is likewise the convex hull of two ellipses, possibly degenerate,...
List
multi_local
true
[ 10, 11 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,669
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.076923
near
2102.13259v2_reasoning_001
2102.13259v2
Compared with the symbol matrix T_phi defined for n>1, by what factor is the number of entries in the matrix A from Theorem 2.7 larger?
4
Integer
reasoning
true
[ 1, 8 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,545
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.538462
far
2102.13259v2_reasoning_004
2102.13259v2
Lemma 2.3 assumes that F(t:phi) has n+1 real roots for any angle phi. If n = 4, how many real roots are assumed?
5
Integer
reasoning
true
[ 5 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,547
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
2102.13259v2_reasoning_010
2102.13259v2
Add the number of rows in the matrix S displayed in Proposition 2.8 to the number of vertices listed for the square described in Example 2.11. What is the total?
8
Integer
reasoning
true
[ 9, 11 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,550
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
2
0.153846
near
2102.13259v2_single_000
2102.13259v2
In the abstract, what finite-dimensional object is the closure of the numerical range of an n+1-periodic tridiagonal operator shown to equal?
The numerical range of a 2(n+1) × 2(n+1) complex matrix.
String
single
true
[ 0 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,560
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
2102.13259v2_single_002
2102.13259v2
In the notation introduced before Proposition 2.2, how are alpha_j and gamma_j defined for 0 ≤ j < n?
alpha_j = (c_j + overline{a_{j+1}})/2 and gamma_j = (c_j - overline{a_{j+1}})/(2i).
String
single
true
[ 3 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,575
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
2102.13259v2_single_003
2102.13259v2
According to Definition 2.5, what condition makes the real homogeneous polynomial Q hyperbolic with respect to (1,0,0)?
Q is hyperbolic with respect to (1,0,0) if Q(1,0,0) > 0 and, for every (x0,y0) in R^2 with x0^2 + y0^2 > 0, the equation Q(t,x0,y0)=0 in t has m real solutions counting multiplicities.
String
single
true
[ 8 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,613
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
2102.13259v2_single_006
2102.13259v2
In Example 2.11, what geometric set is overline{W(T(a,b,c))} identified with?
The square with vertices -1 - i, -1 + i, 1 - i, and 1 + i.
String
single
true
[ 11 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,559
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
2102.13259v2_single_008
2102.13259v2
What is the title of the paper?
THE NUMERICAL RANGE OF A PERIODIC TRIDIAGONAL OPERATOR REDUCES TO THE NUMERICAL RANGE OF A FINITE MATRIX
String
single
true
[ 0 ]
[]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,547
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
1
0
near
2102.13259v2_unanswerable_009
2102.13259v2
What software or plotting package was used to create Figure 1 showing the boundary of the numerical range of S?
Not answerable.
Unanswerable
unanswerable
false
[]
[ 10 ]
[ "images/2102.13259v2/page000.png", "images/2102.13259v2/page001.png", "images/2102.13259v2/page002.png", "images/2102.13259v2/page003.png", "images/2102.13259v2/page004.png", "images/2102.13259v2/page005.png", "images/2102.13259v2/page006.png", "images/2102.13259v2/page007.png", "images/2102.13259v2...
35,535
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2102.13259v2
CC-BY-4.0
14
12
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ]
[]
null
null
0
null
no_evidence
2103.05478v6_reasoning_000
2103.05478v6
On the title page of “Small errors in random zeroth-order optimization are imaginary,” how many authors are listed under the title?
3
Integer
reasoning
true
[ 0 ]
[]
[ "images/2103.05478v6/page000.png", "images/2103.05478v6/page001.png", "images/2103.05478v6/page002.png", "images/2103.05478v6/page003.png", "images/2103.05478v6/page004.png", "images/2103.05478v6/page005.png", "images/2103.05478v6/page006.png", "images/2103.05478v6/page007.png", "images/2103.05478v6...
86,021
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2103.05478v6
CC-BY-4.0
33
28
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32 ]
[]
null
null
1
0
near
2103.05478v6_reasoning_002
2103.05478v6
Figure 7.1 contains panels labeled (a) through (d). How many panels does the figure contain?
4
Integer
reasoning
true
[ 23 ]
[]
[ "images/2103.05478v6/page000.png", "images/2103.05478v6/page001.png", "images/2103.05478v6/page002.png", "images/2103.05478v6/page003.png", "images/2103.05478v6/page004.png", "images/2103.05478v6/page005.png", "images/2103.05478v6/page006.png", "images/2103.05478v6/page007.png", "images/2103.05478v6...
86,018
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2103.05478v6
CC-BY-4.0
33
28
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32 ]
[]
null
null
1
0
near
2103.05478v6_reasoning_003
2103.05478v6
Compare the denominator constants in two step-size formulas: Theorem 4.1 uses μ = 1/(2nL1), while the numerical experiments use μk = 1/(4(n+4)L1). What is the difference between the constants 4 and 2?
2
Integer
reasoning
true
[ 16, 22 ]
[]
[ "images/2103.05478v6/page000.png", "images/2103.05478v6/page001.png", "images/2103.05478v6/page002.png", "images/2103.05478v6/page003.png", "images/2103.05478v6/page004.png", "images/2103.05478v6/page005.png", "images/2103.05478v6/page006.png", "images/2103.05478v6/page007.png", "images/2103.05478v6...
86,053
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2103.05478v6
CC-BY-4.0
33
28
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32 ]
[]
null
null
2
0.1875
near
2103.05478v6_reasoning_004
2103.05478v6
In Example 2.8, the comparison is shown at test points x = -1, x = 0, and x = 10. What is the numerical range between the largest and smallest of these x-values?
11
Integer
reasoning
true
[ 10 ]
[]
[ "images/2103.05478v6/page000.png", "images/2103.05478v6/page001.png", "images/2103.05478v6/page002.png", "images/2103.05478v6/page003.png", "images/2103.05478v6/page004.png", "images/2103.05478v6/page005.png", "images/2103.05478v6/page006.png", "images/2103.05478v6/page007.png", "images/2103.05478v6...
86,042
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2103.05478v6
CC-BY-4.0
33
28
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32 ]
[]
null
null
1
0
near
2103.05478v6_reasoning_005
2103.05478v6
Example 7.1 sets n = 5, while Example 7.3 considers dimensions n ∈ {1, 10, 100}. What is the difference between the largest dimension in Example 7.3 and the value of n in Example 7.1?
95
Integer
reasoning
true
[ 23, 24 ]
[]
[ "images/2103.05478v6/page000.png", "images/2103.05478v6/page001.png", "images/2103.05478v6/page002.png", "images/2103.05478v6/page003.png", "images/2103.05478v6/page004.png", "images/2103.05478v6/page005.png", "images/2103.05478v6/page006.png", "images/2103.05478v6/page007.png", "images/2103.05478v6...
86,055
gpt-5.5-2026-04-24
Mathematics
https://arxiv.org/abs/2103.05478v6
CC-BY-4.0
33
28
arxiv_research_paper
en
majority of full-context generator domain labels
gpt55_production
legacy_full_document
[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32 ]
[]
null
null
2
0.03125
near
End of preview. Expand in Data Studio

MMProLong-Data-Public

MMProLong paper MMProLong GitHub Public dataset

This is a newly constructed public corpus associated with MMProLong, not the original training data used in the paper. Due to ByteDance's internal data governance and management requirements, we cannot open-source the paper's original training corpus. This release is constructed separately from publicly accessible documents. It supports research on long-context document understanding; it does not establish reproduction of the paper's reported results.

Current production uses GPT-5.6, recorded as gpt-5.6-sol. The release also retains historical GPT-5.5 examples, with actual model identifiers on every QA row. See generation provenance for current counts and the model-specific loading example below.

Public snapshot (2026-11-10): 39,739 QA examples, 8,538 source PDFs, 191,774 unique page images, and 2,368,519,161 estimated training tokens (approximately 2.369B).

If you use the dataset, annotations, or synthesis methodology, please cite the MMProLong paper. The BibTeX entry is provided in Citation.

Quick links

Relationship to the paper

The paper is Training Long-Context Vision-Language Models Effectively with Generalization Beyond 128K Context, NeurIPS 2026. Its code is available in the MMProLong GitHub repository.

Aspect Original paper This public release
Data availability Original corpus cannot be released under ByteDance's internal data governance requirements Separately constructed public-document corpus
Document sources A multi-source pool of 1,537,504 PDFs, including papers, books, and manuals Admitted public research papers; see measured source counts below
Generation model Seed 2.0 for the paper's VQA synthesis Current pipeline: GPT-5.6-sol; retained historical GPT-5.5 examples are labeled
VQA construction Generate from coherent 8-15-page segments, then restore full-document context Full-document generation/review, explicit local/distributed evidence constraints, and unanswerable examples
Default VQA page range 32-50 pages Observed range: 14-50 pages
Supervision Three VQA tasks; OCR transcription studied separately Five QA types; no OCR-transcription training split
Experiment claims Results and ablations reported in the paper No claim that this snapshot produced those results

The paper's default VQA study reports 177,774 examples and approximately 15.16B tokens across three task-specific pools. Its 5B-token training budget is per experimental run. Those quantities describe the paper's data and experiments, not this public snapshot. The manuscript uses binary prefixes (K = 2^10, B = 2^30); quoted paper statistics retain that convention. This public card uses decimal K = 1,000 and B = 1,000,000,000, with exact token counts available. The >=100Ki statistic uses 102,400 tokens to match the paper's 100K threshold.

Dataset details and statistics

All counts below describe admitted QA examples. Rejected candidates, held documents, and uncommitted production outputs are excluded. A unique PDF is counted once in document statistics; its context is counted again for each QA in training-sample statistics.

Corpus scale

Statistic Public snapshot value
Admitted unique PDFs 8,538
Document family Public research papers
Unique rendered page images 191,774
Document pages: mean / median 22.46 / 20
Document pages: range / 5th-95th percentile 14-50 / 14-38
Admitted QA examples 39,739
Estimated training tokens 2,368,519,161 (2.369B)
Per-QA tokens: mean / median 59.602K / 53.273K
Observed token range 33,547-125,503
At least 100,000 tokens 2,633 (6.63%)
At least 100Ki = 102,400 tokens (paper threshold) 2,212 (5.57%)
Page references across all QA contexts 932,381

Document sources

Source Unique documents
arxiv 4,386
elife 20
plos 4,132

Tokens are the stored Qwen2.5-VL serialized-sample estimate, including full page-image context and QA/prompt text. A PDF used by several questions contributes its context repeatedly to the training-token total. This is not a count of unique-text tokens or billed API tokens. Page images are physically stored once per document.

Public-corpus overview

Task-level statistics

Task QA Avg. pages Avg. K tokens B tokens Pages K-token range >=100Ki
single 14,409 23.32 59.21 0.853 14-50 33.80-125.13 5.50%
multi_local 7,083 23.60 60.03 0.425 14-50 33.85-125.50 5.53%
multi_distributed 7,174 23.40 59.47 0.427 14-50 33.84-125.29 5.58%
reasoning 7,181 23.39 59.39 0.427 14-50 33.55-125.11 5.32%
unanswerable 3,892 23.98 60.88 0.237 14-50 33.79-125.09 6.32%
Total 39,739 23.46 59.60 2.369 14-50 33.55-125.50 5.57%

K = 1,000, B = 1,000,000,000; 100Ki = 102,400 tokens. Average pages in this table are QA-weighted, whereas the corpus-scale document average counts each PDF once. The two multi-page rows may be combined for comparison with the paper's broader extraction category. Unanswerable QA is an additional public-data task. Exact values, quantiles, and the combined task grouping are in metadata/statistics.json.

Token-length distributions by task

Primary-domain distribution

Primary domain Documents Document share QA QA share
Physics 1,325 15.52% 9,290 23.38%
Computer Science 1,269 14.86% 9,189 23.12%
Mathematics 1,239 14.51% 8,830 22.22%
Biology 983 11.51% 1,917 4.82%
Medicine 922 10.80% 2,038 5.13%
Social Science 807 9.45% 1,951 4.91%
Economics 787 9.22% 1,927 4.85%
Engineering 771 9.03% 3,413 8.59%
Earth Science 410 4.80% 1,075 2.71%
Language and Literature 16 0.19% 51 0.13%
Other 9 0.11% 58 0.15%

Document and QA shares differ because historical phases generated different numbers of questions per PDF. Domain labels describe the source PDF, not a separate topic inferred for each question.

Answer types and per-document sampling

Answer format QA Share
Integer 5,962 15.00%
Float 2,710 6.82%
List 13,722 34.53%
String 13,453 33.85%
Unanswerable 3,892 9.79%

There are 35,847 answerable and 3,892 unanswerable QA examples. The observed necessary-evidence page counts are: 0 pages: 3,892, 1 pages: 18,080, 2 pages: 12,043, 3 pages: 4,492, 4 pages: 1,220, 5 pages: 7, 6 pages: 3, 7 pages: 1, 8 pages: 1.

Observed QA count per source document
QA per document Documents
1 1,047
2 5,084
6 1
8 1
9 7
10 51
11 259
12 2,084
20 4

The 20-QA documents belong to the initial pilot; the two-QA limit applies to the current GPT-5.6 phase.

Generation methods

Recorded method QA
legacy_full_document 32,432
released_prompt_window_v1 4,569
document_tool_agent_v1 2,738

Domain-label provenance

Recorded method Documents
majority of full-context generator domain labels 4,330
arXiv primary category mapping 113
manual primary-topic classification for validated pilot batches 9
majority of independent full-document verifier topic labels 3,994
Crossref subject-query sampling; provisional until generator topic vote 92

Language annotation

Estimated document language Documents Document share Associated QA
English (en) 8,533 99.941% 39,699
Spanish (es) 2 0.023% 14
French (fr) 1 0.012% 2
Russian (ru) 1 0.012% 12
Chinese (zh) 1 0.012% 12

Language labels are automatic estimates of the source document's dominant sampled language, not human-verified labels. We apply langid==1.1.6 to embedded PDF text from up to six pages spanning the document body. Non-English or uncertain predictions are rechecked after Unicode normalization and filtering short equation-like lines. Low-scoring or text-poor cases use und (undetermined). No OCR is run for this annotation. The normalized classifier score is not a calibrated accuracy estimate. QA prompts and generated answers are in English.

Per-document sampling pages, status, method, and score are available in metadata/document_languages.jsonl. The raw initial prediction is retained for rechecked cases.

Classification and annotation schema

Every admitted document has a primary-domain label. This single-label topical taxonomy is separate from the QA task taxonomy. Labels come from recorded generator votes, independent full-document verifier votes, arXiv primary-category mapping, provisional journal subject queries, or pilot assignments; counts and recorded methods appear in the provenance table above. These labels have not undergone comprehensive human validation.

The documents viewer and metadata/document_labels.parquet provide one row per source PDF: title, URL, source hash, document type, domain and its assignment method, automatic language annotation, page counts, unique image-token estimate, QA count, training-token sum, question types, generation models, and source license.

The default viewer provides one row per QA:

Field(s) Meaning
id, document_id Stable QA identifier and source-PDF join key
question, answer, answer_format Question, rendered answer, and answer type; list answers are JSON strings in the viewer table
kind single, multi_local, multi_distributed, reasoning, or unanswerable
answerable Whether the complete source document supports an answer
source_domain, domain_tag_method Primary topical domain and recorded assignment procedure
model, generation_phase Actual recorded generator identifier and historical sampling phase
document_type, document_language Source family and automatic language estimate; language provenance is in the document table
document_page_count, content_page_count Complete PDF pages and content-bearing pages used by the production policy
image_paths Ordered relative paths to every page image in the complete source PDF
token_count Stored Qwen2.5-VL estimate for the complete serialized training sample
evidence_pages, evidence_page_count Necessary evidence pages, using zero-based original PDF indices
evidence_span_normalized, evidence_distance_bin Actual evidence span; separate from local/distributed task labels
related_context_pages Inspection anchors for unanswerable questions, not answer evidence
source_url, source_license Source attribution and article-level license

Question types

  • single: factual extraction requiring one evidence page.
  • multi_local: aggregate distinct necessary facts from multiple pages within an assigned contiguous 8-15-page window.
  • multi_distributed: combine necessary evidence from separated positions in the full PDF; medium/far span constraints are recorded.
  • reasoning: calculate, compare, count, or otherwise reason over grounded document evidence.
  • unanswerable: the complete document does not supply the answer or a required operand; the exact target is Not answerable. and evidence_pages is empty.

For nonempty evidence, normalized span is (last_evidence_page - first_evidence_page) / (document_page_count - 1). Near is at most 0.2, medium is greater than 0.2 and at most 0.5, and far is greater than 0.5. Empty evidence is null / no_evidence, rather than a near-span example. A local sampling window can produce a medium normalized span in a short PDF; the sampling task and actual evidence distance should not be conflated.

Evidence position and actual span

Generation provenance

Recorded generation model Documents QA QA share B training tokens
gpt-5.5-2026-04-24 2,407 28,524 71.78% 1.745
gpt-5.6-sol 6,131 11,215 28.22% 0.624
Phase Documents QA Maximum QA per document
Initial pilot (GPT-5.5) 4 80 20
GPT-5.5 production 2,403 28,444 12
Current GPT-5.6 production 6,131 11,215 2

The current snapshot is a mixed-model historical release, not an all-GPT-5.6 corpus. Use the model field when a model-specific subset is required.

The current production configuration uses GPT-5.6-sol, at most two QA examples per document, and one target QA at a time. New hybrid candidates pass structural checks and two independent full-document verification calls. The GPT-5.6 phase additionally applies a semantic-redundancy comparison across candidate questions from the same document. Historical examples retain their original recorded model and sampling policy.

The current hybrid recipe reuses the released window sampler, generation prompt, and two LongDocURL few-shot exemplars for single/local extraction and locally planned numeric reasoning. Distributed extraction, multi-page-planned numeric reasoning, and unanswerable tasks use a document-scoped GPT-5.6 API tool loop: overview, full-text search, page-text/image inspection, and bounded arithmetic. The CLI run was a workflow prototype; production records are generated through the GPT-5.6 API.

Tool agents have access to the complete document, but their recorded image views may be selective. Unanswerable agents must receive every extracted text page and inspect related page images before submission; two separate verification calls then receive all PDF page images. A failed literal search is never accepted as an absence proof. generation_method, generation_text_pages, teacher_pages, generation_model_turns, generation_tool_calls, and generation_trace record the actual process. verification_policy distinguishes the new two-check policy from historical records. Generation traces are archived with admitted examples. The final training context remains the complete ordered PDF for every task.

When running the included production code with journal_prefetch: true, start python code/data_synthesis_doc_vqa/journal_intake.py --root <corpus-root> --policy <policy.json> in a separate process alongside local_corpus.py run with the same root and policy. The supervised production controller starts and monitors intake automatically. The prepared-input buffer is bounded by both document count and disk space; the model worker remains the sole writer of the admitted-sample ledger.

Independent document prefetch downloads and renders complete journal PDFs while the model worker processes prepared documents. Generation, verification, retries, and semantic-redundancy review advance per document. Intake favors underrepresented domains by unique-PDF counts; this is a sampling policy, not a claim that the released corpus is already balanced. Local generation uses the released 8–15-page window; independent verification and the final training sample retain every PDF page.

Configured token-mixture weights are 36% single-page extraction, 18% local multi-page extraction, 18% distributed multi-page extraction, 18% reasoning, and 10% unanswerable. These are configuration weights, not fixed row quotas. Among answerable examples, the intended extraction/reasoning proportions correspond to 4:4:2. Observed counts and token totals are reported above.

The public pipeline and policy are included under code/. The original research code and training recipes are maintained on GitHub. The original paper's Seed 2.0/OCR pipeline and this public GPT-based pipeline are different releases.

Continuous scheduling and lossless image transport

The current public runtime keeps 64 document workers supplied across storage-batch boundaries. Generation, both full-PDF reviews, tool calls, novelty checks, and retries share one 64-request concurrency limit and a rolling 1,000-QPM gate. Completed documents are admitted transactionally; a separate publisher freezes a consistent snapshot and uploads it while generation continues. Only verified, inactive local assets are evicted.

API image transport uses a smaller lossless WebP encoding when beneficial. Every conversion is decoded and checked for exact pixel equality and unchanged dimensions. Original corpus PNGs, full-document coverage, prompts, two independent reviews, and training-token accounting are preserved. Connection, request-body transfer, and response timings are recorded without headers, URLs, or payloads. The public runtime and policy are available on GitHub.

Download and use

Load the QA or document table

from datasets import load_dataset

repo = "ZhaoweiWang/MMProLong-Data-Public"
qa = load_dataset(repo, "default", split="train")
documents = load_dataset(repo, "documents", split="train")

# Select the examples actually generated with GPT-5.6.
gpt56 = qa.filter(lambda row: row["model"] == "gpt-5.6-sol")

# Example topical/task filter.
physics_reasoning = qa.filter(
    lambda row: row["source_domain"] == "Physics" and row["kind"] == "reasoning"
)

The documents configuration is metadata with one row per PDF, not a second QA training split. Use document_id to join the two tables. Pin the dataset revision to a commit hash when reporting reproducible experiments.

Restore page images with bounded temporary disk usage

Use Python 3.12+ for the restoration scripts. Install the Hub CLI and table dependencies:

python -m pip install -U huggingface_hub datasets pyarrow

hf download ZhaoweiWang/MMProLong-Data-Public \
  --repo-type dataset --local-dir MMProLong-Data-Public \
  --include 'README.md' 'data/*' 'training/*' 'metadata/*' 'tools/*' \
            'corpus.jsonl.gz' 'release_manifest.json'

python MMProLong-Data-Public/tools/hydrate_assets.py \
  --root MMProLong-Data-Public --revision main --groups images

The helper downloads and verifies one archive at a time, extracts it, and removes that temporary archive. It refuses to overwrite a different existing file. Use --groups images sources provenance when PDFs and provenance records are also needed. Replace main with a fixed commit for reproducible restoration. Existing production ledgers are preserved.

Images are stored once per document. The QA table's image_paths and the training table's images are relative path strings, not embedded image bytes. Resolve them against the restored corpus directory on demand:

from pathlib import Path

root = Path("MMProLong-Data-Public")
page_paths = [root / path for path in qa[0]["image_paths"]]
assert all(path.is_file() for path in page_paths)

The canonical training/data.parquet stores VeOmni/LLaVA-style conversations with shared-image references. Adapt the image-loading step if a trainer expects bytes rather than paths. GPU training ingestion of this public snapshot has not yet been validated.

Download the complete backup

hf download ZhaoweiWang/MMProLong-Data-Public \
  --repo-type dataset --local-dir MMProLong-Data-Public
python MMProLong-Data-Public/tools/restore.py --root MMProLong-Data-Public

Check the current file sizes in release_manifest.json before downloading; full extraction also needs space for the unpacked assets. Every base and dated incremental archive listed in the current manifest is required. --verify-only checks the downloaded package without extracting it. In a fresh directory, add --resume to restore the SQLite ledger and discovery checkpoint from backup/. This backup contains admitted QA; incomplete production candidates and all historical raw model responses are not part of the release.

Files and formats

Path Contents
data/train-*.parquet QA viewer table with filtering labels and derived evidence fields
training/data.parquet Canonical conversations and relative shared-image paths
corpus.jsonl.gz Full admitted records, original answer types, evidence, verification records, and provenance
metadata/documents.jsonl Original source-document metadata, authors, URLs, licenses, and PDF hashes
metadata/document_labels.parquet, .jsonl One row per PDF with domain, language, document type, page counts, and associated QA statistics
metadata/document_languages.jsonl Automatic language-detection evidence, status, and method
metadata/statistics.json Exact totals, per-task statistics, quantiles, domain/model distributions, and histogram bins
metadata/asset_members.jsonl.gz Individual archive-member paths, sizes, and SHA-256 hashes
assets/*.png Public-corpus statistical figures used in this card
archives/images-*.tar Ordered page images under images/<document_id>/pageNNN.png
archives/sources-*.tar Source PDFs used by admitted QA
archives/provenance-*.tar Source/license evidence and discovery metadata
backup/, code/ Production ledger/checkpoint and the public synthesis pipeline snapshot
package_manifest.json, release_manifest.json, checksums.sha256 Integrity records for the complete release
tools/ Checksum verification, restoration, and statistics utilities

Quality checks and limitations

  • Every admitted QA passed structural validation and stored full-document model review. The exact PDF hash and all reviewed page indices are retained. GPT-5.6 document-level novelty checks are recorded where required.
  • All referenced page images and source-PDF hashes are verified when each snapshot is prepared. Model reviews and automatic topic/language labels can still contain errors; they are not human gold annotations.
  • This snapshot contains public research papers; the measured source and topic distributions above describe its coverage. New intake prioritizes underrepresented domains and supports PLOS and eLife journal articles alongside arXiv candidates. Books, manuals, and other document families from the original paper's pool are not represented by this release.
  • Source PDFs were selected for article-level CC BY 4.0, with an explicit third-party-rights notice filter. Article-level licensing and text scanning are not exhaustive clearance of every figure. Original authors, URLs, licenses, and exceptions remain applicable. No new blanket license for synthetic QA is assigned by this intermediate release; the project's code license does not replace source-document rights.
  • The held document 2609.29669v1 and its 20 pilot examples are excluded.
  • Benchmark decontamination, comprehensive human review, and GPU training-ingestion checks remain incomplete for this public corpus. Do not transfer the original paper's completed checks or reported benchmark results to this separate dataset.

Reproduce the statistics

The profiling and annotation scripts are available on GitHub and mirrored in tools/.

python -m pip install numpy pyarrow matplotlib
python MMProLong-Data-Public/tools/profile_public_dataset.py \
  --snapshot-root MMProLong-Data-Public \
  --language-labels MMProLong-Data-Public/metadata/document_languages.jsonl \
  --output-dir public-corpus-profile

This reproduces aggregate statistics, labels, and figures from the small metadata/QA files. To recompute language annotations from source PDFs, install pymupdf requests langid==1.1.6 and run annotate_public_document_languages.py, followed by recheck_public_document_languages.py; both expose --help. The first pass streams verified tar archives in memory, and the recheck fetches only selected PDF byte ranges. Neither retains the PDF corpus on disk.

Statistics and annotations are computed from the admitted records in each published release. Exact token counts, source hashes, and file checksums are retained with the snapshot.

Contact

Open an issue in the MMProLong GitHub repository, or contact Zhaowei Wang at zwanggy@cse.ust.hk.

Citation

If you use this public dataset, its annotations, or the synthesis methodology, please cite MMProLong and identify this separately constructed public release and its revision in your experiment description.

@inproceedings{wang2026mmprolong,
  title={Training Long-Context Vision-Language Models Effectively with Generalization Beyond 128K Context},
  author={Wang, Zhaowei and Luo, Lishu and Duan, Haodong and Liu, Weiwei and Wu, Sijin and Luo, Ji and Yan, Shen and Peng, Shuai and Yuan, Sihang and Huang, Chaoyi and Lin, Yi and Song, Yangqiu},
  booktitle={Advances in Neural Information Processing Systems (NeurIPS 2026)},
  year={2026},
  url={https://arxiv.org/abs/2605.13831}
}
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