query_id large_stringlengths 16 16 | category large_stringclasses 6
values | generator large_stringclasses 8
values | model_tier large_stringclasses 4
values | register large_stringclasses 5
values | specificity large_stringclasses 2
values | paper_id large_stringlengths 9 16 | q large_stringlengths 4 1.78k | positives listlengths 1 10 | positive_scores listlengths 1 10 | hard_negatives listlengths 1 100 | no_in_batch_negatives bool 2
classes | dev_hard bool 1
class |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
422db4d6f7a6a997 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0409202 | Are quandles considered a specific type of set-theoretical solution to the quantum Yang-Baxter equation? | [
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81cc75f743f59dae | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0409202 | What is the relationship between the algebraic structure known as quandles and solutions to the quantum Yang-Baxter equation? | [
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96be9e3f34c5867e | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0410604 | What is the potential for applying polynomial invariants used to distinguish phylogenetic trees to the quantum setting? | [
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5fc6b3bf01f07287 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0410604 | I am looking for algebraic geometry methods that extend tree-distinguishing techniques from classical phylogenetics to quantum systems. | [
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da5a8c324c2cf205 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0410186 | I am looking for results concerning the compactness of the layer potential operator on boundaries with cylindrical ends where singularities are present. | [
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9a8357b3d5e8296b | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0410303 | Who established that the Hilbert function associated with the Ext module of a power of an m-primary ideal becomes a polynomial of degree equal to the ring's dimension? | [
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... | true | false |
965a7167f3fc1792 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0410604 | What algebraic objects are associated with the parameter space of the general Markov model in recent literature? | [
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21ecd3641bb745bc | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0412263 | What are the current theoretical developments and proven results regarding minimum spanning trees in recent decades? | [
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6d78d3af16d08efb | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0412263 | How has the study of minimum spanning trees evolved over the last few decades, and what significant theorems have been established? | [
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... | true | false |
5630d44463f4db36 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0412429 | How does applying kinetic theory to rarefied gases explain the universal behavior of wealth distribution and opinion formation in market economies? | [
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c6a58de8bfb6e31a | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0412475 | What are the stability conditions for a Pexiderized quadratic equation when the orthogonality relation is symmetric in a Banach space? | [
"math/0512007",
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963882939c21c98a | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0412475 | I am looking for results on the orthogonal stability of functional equations where the underlying structure involves both a symmetric orthogonality and a Banach space setting. | [
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072a3f10d272b229 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0412475 | Who provided the general solution and proved generalized Hyers-Ulam stability for functions mapping a real vector space to a real Banach space? | [
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b246a32e02437939 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0412475 | What are the specific contributions of Chang and Jung regarding the Pexiderized quadratic equation in the context of functional equations? | [
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0a1103b29734a987 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0502417 | What are the conditions under which Denham and Suciu proved a result regarding the homotopy Lie algebra of an arrangement? | [
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1766a86500d0930e | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0502417 | Which authors demonstrated that for hypersolvable hyperplane arrangements satisfying a specific technical constraint, the associated homotopy Lie algebra LA is well-defined? | [
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9e57ae9f782114f6 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0503035 | What applications have been identified for the Kantorovich metric in analyzing synthetic versus real continuous or mixed variables? | [
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c8e74b09456d77a9 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0503088 | What is the title of the seminal work by Raghunathan that establishes the existence of a specific nonzero ideal for every nonzero ideal in the context of the congruence subgroup problem? | [
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42845b35b48078c0 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0503118 | What is the spectral dimension of the uniform infinite planar tree, and how does comparing a random walk on a tree to this object improve known lower bounds? | [
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fc2550aef79d2bd6 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0503118 | In the context of random walks on trees, what specific spectral value is associated with the uniform infinite planar tree that serves as a benchmark for lower bounds? | [
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686664507d2f91d9 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0504049 | Which publication by Feng Luo and Jean-Marc Schlenker demonstrates the extension of the Casson-Rivin angle structure program to closed triangulated 3-manifolds? | [
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... | true | false |
0ab17b48248b9426 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0504049 | Identify the 2007 paper that treats the Möbius tetrahedron as the geometric prototype for an angled 3-simplex within the context of volume and angle structures. | [
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e858e24f94b2e984 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0504513 | What are the advantages of using a constrained heteroscedastic trimming algorithm for cluster analysis? | [
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739b536334c967e2 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0504513 | Which study utilizes maximum likelihood estimation to identify outliers and then groups the remaining data points into distinct clusters? | [
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09784c1b200d8005 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0504513 | I am looking for a robust algorithm that handles outlier detection by applying maximum likelihood principles before performing simultaneous partitioning of the non-outlier data. | [
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1422212ac0427381 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0505120 | Which researcher has analyzed Schrödinger operators where the associated potential class is defined in a relatively large but rather implicit manner? | [
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681a35fee6e4c374 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0505120 | What work addresses the spectral theory for Schrödinger operators involving strongly singular potentials with an implicitly defined class of potentials? | [
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e42fb48aca6afa73 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0505120 | Who are the researchers who independently rediscovered and expanded upon spectral theory for Schrödinger operators with strongly singular potentials? | [
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e8edce1f989aacbd | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0505120 | Can you identify the specific pair of authors credited with reviving interest in the spectral analysis of Schrödinger operators featuring strong singularities? | [
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fdfcd65d613bfd1b | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0505219 | What condition defines a bottom tangle as boundary in terms of bounding mutually disjoint Seifert surfaces in three-dimensional space? | [
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... | true | false |
6dde453593ad4312 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0505334 | How does the technique of algebraic shifting transform an arbitrary simplicial complex into a shifted version, and what role does this play in establishing rigidity results for doubly Cohen-Macaulay complexes? | [
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92163462c60012df | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0506287 | Which prior work on structure constants in the spherical Hecke algebra is cited as the predecessor to the Gaussent-Littelmann formula? | [
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637b4a72465e4c95 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0506287 | What is the specific reference attributed by Schwer for an earlier result related to Hall-Littlewood polynomials and spherical Hecke algebra structure constants? | [
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cef1ef3578c4d3ca | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0505457 | Who demonstrated that solutions to the cubic NLS and DNLS are locally well-posed in L^p for 1 < p < infinity with global existence extending to 5/3 < p < 2? | [
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38ce7e98accf3ee3 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0506591 | Which study demonstrates that the Neuhauser-Pacala model converges to super-Brownian motion with a non-trivial drift upon appropriate scaling? | [
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"math/0612797",... | true | false |
76e977ecb2a92db2 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0507536 | How can one mathematically characterize a sequence of bounded variation to ensure it has a unique representation within its associated group structure? | [
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777745289548eee2 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0507536 | Which paper establishes the uniqueness of the signature for paths with bounded variation within the context of rough paths theory? | [
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0d1234676c5d894e | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0509262 | Could you explain the specific lower bound on the parameter alpha that Tao proved is required for the Lp boundedness of the multilinear restriction operator in dimension d? | [
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eba7a01d88759bb4 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0510529 | Is it possible for determinantal varieties derived from mixed ladder configurations to possess the Cohen-Macaulay property in their defining quotient structures? | [
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c0e2852ba467820f | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0512573 | I am looking for a reference that resolves the local Donaldson-Thomas theory for curves on toric manifolds via explicit computation. | [
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7c75df7b3f398d79 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0512573 | I am looking for the paper discussing local Donaldson-Thomas theory where it is shown that certain conjectures extend to specific geometric boundaries and underpin degeneration arguments. | [
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0d221a190fe4c1c3 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0512576 | What is the mechanism for defining composition in the context of coloured operads and homotopy algebras? | [
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3e2856d6f68945a9 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0512576 | What is the correspondence between the elements of the colored operad Delta and the fundamental components defining a category's structure? | [
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a9f209242764e624 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601054 | Who is the mathematician credited with pioneering noncommutative geometry in the 1980s, and what are some recent developments in this field? | [
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011e31b7da98c6b5 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601463 | How does Dyson's partition rank concept extend to overpartitions, specifically regarding the definition of the D-rank in terms of the largest part and number of parts? | [
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fd394002ac6d881f | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601463 | What is the explicit formula for the D-rank of an overpartition, defined as the difference between the largest part and the count of parts? | [
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fbefc10fcb265832 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601463 | How can a specific ordered sequence of alpha and beta steps be reinterpreted as a lattice path starting from a prescribed initial position to study Rogers-Ramanujan identities? | [
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6ac07c658e334a04 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601463 | How are lattice paths encoded using a binary word and an initial vertical position to characterize overpartitions in the context of Rogers-Ramanujan identities? | [
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554fc437474248fc | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601463 | What is the relationship between the structure of fully characterized lattice paths defined by a binary sequence and their connection to Rogers-Ramanujan identities? | [
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3ed2ccafefc3feb3 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601635 | Which paper establishes that stationary viscous Hamilton-Jacobi equations admit a unique solution in L1 with an L1 gradient? | [
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c803509d86385d5b | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601635 | I am looking for results on the uniqueness of unbounded solutions for stationary viscous Hamilton-Jacobi equations where both the function and its gradient are integrable. | [
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904e367af72b404a | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601635 | Under what conditions on the gradient and function space can one establish uniqueness for stationary viscous Hamilton-Jacobi equations with unbounded solutions? | [
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16a9ad8f47c1eb01 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601635 | Which paper demonstrates that a solution to a stationary viscous Hamilton-Jacobi equation exists uniquely within the class of functions in L-infinity where the gradient is also in L-infinity? | [
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25e5df33f3f1b4f4 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601635 | What is known about the uniqueness of unbounded solutions for stationary viscous Hamilton-Jacobi equations? | [
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8dbdef7b59a7daa6 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0601759 | I am looking for research on minimal entropy and geometric decompositions specifically applied to four-dimensional manifolds with Seifert fibrations or geodesic circle foliations. | [
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91446bacd0466e6b | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0602606 | What are the main results regarding deformation rings and Hecke algebras established in a manuscript circulated by Fujiwara over totally real fields? | [
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509c1b8c0734271f | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0603079 | What is the established lower bound for A2(D) in U-type designs that serves as a benchmark for design evaluation? | [
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6551809f30d5632d | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0603079 | Which study provided a useful lower bound on the A2(D) criterion specifically for U-type designs to assist in evaluating their quality? | [
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33d2624df49c4b1b | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0603079 | How do existing measures of supersaturated designs relate to each other in the context of Xu and Wu's work? | [
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ee2d4a88c4737e00 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0603079 | What specific connection did Xu and Wu demonstrate between the standard criteria used for evaluating supersaturated designs? | [
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2c22d3a4d6220f7e | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0043 | How are specific lattice Boltzmann method limiters constructed by decomposing the distribution function into its quasiequilibrium component and a nonequilibrium part? | [
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08a05e3ce26c825d | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0043 | What is the standard mathematical representation of the nonequilibrium contribution in LBM limiters, expressed as a product of a norm and another term? | [
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1af8c9ef7f26cdb2 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0159 | What is the primary alternative explanation proposed for the formation of the commensurate 2x2x2 state in 1T-TiSe$_{2}$? | [
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c98682e25fe6da80 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0159 | Does the transition to a specific commensurate structure in 1T-TiSe$_{2}$ result from exciton condensation or some other mechanism? | [
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e68bb0a524763340 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0159 | Which material is identified in recent literature as a primary candidate for hosting an excitonic insulator phase, specifically linked to the observation of a charge-density wave instability near 200 K? | [
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f8771319ef8dac19 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0159 | I am looking for research discussing the proposal that a specific transition metal dichalcogenide, characterized by a low-temperature charge-density wave transition, could be the host for an excitonic insulator state. | [
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4fbeff4fb506bd22 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0268 | How does the ADCR method contribute to the holistic characterization required in quantum circuit layout generation? | [
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0ccfd4b8a9b67152 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0268 | How do researchers automate the generation of layout and control parameters for quantum circuits? | [
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f95bff7f2e9f8440 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0268 | What is the process for deriving a complete quantum circuit from a tile-based layout by computing qubit movement from storage? | [
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693d0fa53ba5b564 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0737 | What is the status of deriving the proposed structure for soft terms when generalized to Calabi-Yau models? | [
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9c1146ed6b1ee46a | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0737 | Are there existing derivations that explain how soft term structures apply in large volume compactifications within Calabi-Yau geometry? | [
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31134135049f97fe | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0737 | What are the two key observations used to conjecture the specific form of soft terms arising from large volume compactifications in string theory? | [
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cf9717b0c9cea5d2 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0802 | How does a random access protocol function within a distributed multiple-relay-single-destination architecture in hybrid automatic repeat request systems? | [
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54bb7ea435b076c0 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0802 | What are the characteristics of a scheme where multiple relay nodes and a single sink node operate using distributed hybrid ARQ with opportunistic selection? | [
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dfee937bc49f4dc7 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.1249 | Identify the literature describing maximal Cohen-Macaulay modules for isolated complete local commutative Gorenstein singularities as instances of exact stably 2-Calabi-Yau categories. | [
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946496d346d52df5 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | math/0603225 | How are square and triangular involutions classified for grid polygons derived from permutations using the kernel method, specifically regarding their maximum number of faces? | [
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37e226a3a2130155 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.1249 | What are the specific examples of stably 2-Calabi-Yau categories arising from isolated hypersurface singularities and preprojective algebras associated with Dynkin quivers? | [
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7c4c1ef4e6aac173 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.1249 | Which paper provides concrete instances of stably 2-CY categories, such as Cohen-Macaulay modules over isolated hypersurface singularities or representations of preprojective algebras for Dynkin types? | [
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2b457cc82d81a439 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0268 | I am looking for research that establishes upper bounds on the effectiveness of layout-preserving quantum circuit optimizations alongside practical automation methods for these transformations. | [
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03efeb8d14a48d86 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.0737 | How do one-loop open string corrections and alpha-prime effects influence the resulting FI models in string theory compactification scenarios? | [
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b73b7f6253f17117 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.1249 | What is the stable category of maximal Cohen–Macaulay modules for one-dimensional hypersurface singularities? | [
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bf81f83ac7f58733 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.3647 | What do existing research findings indicate about human motivation and capability to sustain personal digital archives across local and cloud storage environments? | [
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9d2ecab271f7c1b6 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.0145 | What historical limitation in stellar occultation analysis of Titan's atmosphere prevented the study of nitrogen cross sections prior to recent years? | [
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9360bbd6df36724f | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.0145 | Why were measurements limited to hydrocarbon components during the earlier phase of stellar occultation studies on Titan? | [
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cf292dc058e8b231 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.0145 | What is the primary methodological distinction between ISS observations and UVIS measurements regarding how they derive extinction coefficients in Titan's upper atmosphere? | [
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da228f980f4fe926 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.0436 | What are the proposed strategies for enhancing search efficiency in network navigation, specifically regarding multi-source random walks and route information integration? | [
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092eebc0c9befc4d | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.0436 | How can network search efficiency be improved by incorporating route information or employing random-walk strategies from multiple starting points? | [
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9acd040f2822e214 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.0436 | What specific modifications to navigation on networks involve using routes and multi-source random walks to enhance search performance? | [
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5650444bfdb949a8 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.3647 | What are the common behaviors of individuals regarding the long-term preservation of their digital assets when they depend on internet service providers? | [
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75460136163c3e3d | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.0886 | What is the electrical behavior of the original topological insulator state near the Dirac point, specifically regarding how conductance scales? | [
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178a04efbb9fb582 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.0886 | I am looking for experimental evidence of one-parameter scaling laws that apply to the electronic properties of graphene at its charge neutrality point. | [
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4443dd0607c5dfbe | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0704.3647 | What are the key parallels between curating internet-based personal data and managing local digital assets? | [
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f0290a04d484c18a | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.0886 | How does the theta term influence the flow of a system with small conductivity toward fixed points in graphene models? | [
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"cond-mat/0603... | true | false |
a0648d7104cffd56 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.1194 | How does a transverse magnetic field gradient influence the refractive index profile of an Electromagnetically Induced Transparency medium to steer a light beam? | [
"1901.00096",
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... | true | false |
e0801b7c264f495e | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.1194 | What mechanism causes optical beam deflection in EIT media when the magnetic susceptibility becomes spatially inhomogeneous due to field gradients? | [
"0709.4109",
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... | true | false |
7576368aaabce2b6 | cit_rewrite | cit_rewrite | local-qwen3.5-9b | question | specific | 0705.2286 | I need a model that improves accuracy over earlier approaches when estimating the frequency trajectory of a beneficial allele in regions with large recombination rates. | [
"1904.09922",
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... | true | false |
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