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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 | [
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"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 | [
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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
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"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 | [
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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 | [
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9
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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,
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"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 | [
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1703.00544v5_reasoning_011 | 1703.00544v5 | How many labeled subfigures does Figure 3 contain? | 2 | Integer | reasoning | true | [
28
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"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 | [
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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 | [
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"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 | [
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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
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"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 | [
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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 | [
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"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 | [
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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
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"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 | [
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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 | [
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"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 | [
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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
] | [] | [
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"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 | [
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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 | [
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9
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
] | [] | [
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"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 | [
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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 | [
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10
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"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 | [
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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
] | [] | [
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"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 | [
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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 | [
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"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 | [
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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
] | [] | [
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"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 | [
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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 | [
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35
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"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 | [
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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
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"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 | [
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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 | [
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"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 | [
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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 | [
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"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 | [
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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 | [
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"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 | [
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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
] | [] | [
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
] | [] | [
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
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"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 | [
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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
] | [] | [
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"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 | [
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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
] | [] | [
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"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 | [
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2004.10144v4_reasoning_003 | 2004.10144v4 | In Appendix B, how many separate matching conditions are displayed in Eq. (B5)? | 4 | Integer | reasoning | true | [
9
] | [] | [
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"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 | [
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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
] | [] | [
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"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 | [
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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
] | [] | [
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"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 | [
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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
] | [] | [
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"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 | [
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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
] | [] | [
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"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 | [
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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
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"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 | [
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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
] | [] | [
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"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 | [
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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
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"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 | [
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2004.10144v4_reasoning_011 | 2004.10144v4 | In Appendix E, Eq. (E6) gives expressions for how many amplitudes? | 2 | Integer | reasoning | true | [
12
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"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 | [
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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 | [
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"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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [] | [
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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 | [] | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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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 | [
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"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 | [
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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 | [
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"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 | [
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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 | [] | [
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"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 | [
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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 | [
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"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 | [
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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
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"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 | [
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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 | [
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22
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"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 | [
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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
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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
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"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 | [
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2103.05478v6_reasoning_006 | 2103.05478v6 | Figure 7.2 displays panels labeled (a), (b), (c), and (d). How many panels are displayed? | 4 | Integer | reasoning | true | [
24
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"images/2103.05478v6... | 86,022 | 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 | [
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