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Sa
{ "domain": "stackexchange.com", "id": null, "lm_label": "1. YES\n2. YES", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9658995742876885, "lm_q1q2_score": 0.8170954400681838, "lm_q2_score": 0.8459424373085146, "openwebmath_perplexity": 448.53102314873036, "openwebmath_score": 0.8942179083824158, "tags": null, "url": "https://math.stackexchange.com/questions/710452/prove-1222-cdotsn2-n1-choose22n1-choose3" }
ro
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qi
{ "domain": "quantumcomputing.stackexchange", "id": 2036, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "qiskit, programming, ibm-q-experience, hhl-algorithm", "url": null }
lo
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mo
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hu
{ "domain": "biology.stackexchange", "id": 9657, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "human-biology, human-physiology, menstrual-cycle, ovulation", "url": null }
$\
{ "domain": "proofwiki.org", "id": null, "lm_label": "1. YES\n2. YES", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9932024678460111, "lm_q1q2_score": 0.8143200802288806, "lm_q2_score": 0.8198933315126791, "openwebmath_perplexity": 350.15779197942726, "openwebmath_score": 0.9226561188697815, "tags": null, "url": "https://proofwiki.org/wiki/Closed_Form_for_Triangular_Numbers" }
py
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#
{ "domain": "stackexchange.com", "id": null, "lm_label": "1. YES\n2. YES", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9724147193720649, "lm_q1q2_score": 0.8060723048345432, "lm_q2_score": 0.8289388146603365, "openwebmath_perplexity": 376.8754494467181, "openwebmath_score": 0.7786919474601746, "tags": null, "url": "https://math.stackexchange.com/questions/2858371/how-to-follow-matrix-operations-in-proofs" }
ja
{ "domain": "codereview.stackexchange", "id": 12511, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "java, performance, trie", "url": null }
If
{ "domain": "physicsforums.com", "id": null, "lm_label": "1. YES\n2. YES\n\n", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9697854138058637, "lm_q1q2_score": 0.8102397398126763, "lm_q2_score": 0.8354835289107307, "openwebmath_perplexity": 768.2508445259857, "openwebmath_score": 0.6681009531021118, "tags": null, "url": "https://www.physicsforums.com/threads/find-array-mapping.452233/" }
py
{ "domain": "codereview.stackexchange", "id": 34405, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "python, python-3.x, parsing", "url": null }
en
{ "domain": "codereview.stackexchange", "id": 22845, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "enum, rust", "url": null }
5)
{ "domain": "charlyedance.it", "id": null, "lm_label": "1. YES\n2. YES", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9814534398277176, "lm_q1q2_score": 0.8437199397400613, "lm_q2_score": 0.8596637451167997, "openwebmath_perplexity": 971.650366932591, "openwebmath_score": 0.5433921813964844, "tags": null, "url": "http://ipmq.charlyedance.it/permutations-with-repetition-worksheet.html" }
ga
{ "domain": "physics.stackexchange", "id": 94871, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "gauss-law", "url": null }
If
{ "domain": "stackexchange.com", "id": null, "lm_label": "1. YES\n2. YES", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9744347853343059, "lm_q1q2_score": 0.876135140981467, "lm_q2_score": 0.8991213718636752, "openwebmath_perplexity": 190.1505767583916, "openwebmath_score": 0.9396748542785645, "tags": null, "url": "https://math.stackexchange.com/questions/257434/if-a-b-1-then-prove-ab-ab-1" }
ho
{ "domain": "physics.stackexchange", "id": 20353, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "homework-and-exercises", "url": null }
la
{ "domain": "biology.stackexchange", "id": 11221, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "lab-techniques", "url": null }
ge
{ "domain": "physics.stackexchange", "id": 88022, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "general-relativity, differential-geometry", "url": null }
ma
{ "domain": "astronomy.stackexchange", "id": 4929, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "mars, impact, weather", "url": null }
c+
{ "domain": "codereview.stackexchange", "id": 12807, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "c++, algorithm, c++14, combinatorics", "url": null }
al
{ "domain": "cs.stackexchange", "id": 6823, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "algorithms, optimization, permutations", "url": null }
or
{ "domain": "chemistry.stackexchange", "id": 12632, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "organic-chemistry, acid-base, hydrocarbons, halogenation", "url": null }
mf
{ "domain": "physicsforums.com", "id": null, "lm_label": "1. YES\n2. YES\n\n", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9740426405416756, "lm_q1q2_score": 0.8008472802059274, "lm_q2_score": 0.8221891392358015, "openwebmath_perplexity": 781.678504735111, "openwebmath_score": 0.9385164380073547, "tags": null, "url": "https://www.physicsforums.com/threads/proving-an-inequality-from-an-equation.876612/" }
c#
{ "domain": "codereview.stackexchange", "id": 21391, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "c#", "url": null }
##
{ "domain": "wangchaofeng.com", "id": null, "lm_label": "1. YES\n2. YES", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9926541744034383, "lm_q1q2_score": 0.8356417448337378, "lm_q2_score": 0.8418256492357358, "openwebmath_perplexity": 689.2078322191647, "openwebmath_score": 0.9768717885017395, "tags": null, "url": "http://wangchaofeng.com/parseNote.php?note=notes_math_elementaryAlgebra.note" }
vi
{ "domain": "biology.stackexchange", "id": 5041, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "virus", "url": null }
A
{ "domain": "stackexchange.com", "id": null, "lm_label": "1. YES\n2. YES", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9850429169195593, "lm_q1q2_score": 0.8053459424503397, "lm_q2_score": 0.817574471748733, "openwebmath_perplexity": 247.10309310520032, "openwebmath_score": 0.8898147940635681, "tags": null, "url": "http://math.stackexchange.com/questions/194621/how-to-define-a-bijection-between-natural-numbers-and-the-set-of-all-polynomials" }
ho
{ "domain": "physics.stackexchange", "id": 18818, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "homework-and-exercises, newtonian-mechanics, energy, energy-conservation", "url": null }
dn
{ "domain": "biology.stackexchange", "id": 6177, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "dna, nomenclature", "url": null }
a.
{ "domain": "gmatclub.com", "id": null, "lm_label": "1. Yes\n2. Yes", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9626731169394881, "lm_q1q2_score": 0.8220388550573391, "lm_q2_score": 0.8539127566694178, "openwebmath_perplexity": 901.0038358520754, "openwebmath_score": 0.8301273584365845, "tags": null, "url": "https://gmatclub.com/forum/for-every-integer-k-from-1-to-10-inclusive-the-kth-term-of-a-certain-88874.html" }
re
{ "domain": "chemistry.stackexchange", "id": 16687, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "redox, titration", "url": null }
ro
{ "domain": "robotics.stackexchange", "id": 37655, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "ros, buildfarm", "url": null }
∆x
{ "domain": "ciadarredamenti.it", "id": null, "lm_label": "1. YES\n2. YES", "lm_name": "Qwen/Qwen-72B", "lm_q1_score": 0.9898303401461468, "lm_q1q2_score": 0.8373394866206931, "lm_q2_score": 0.8459424334245618, "openwebmath_perplexity": 598.200690655468, "openwebmath_score": 0.9244123101234436, "tags": null, "url": "http://hobp.ciadarredamenti.it/polar-coordinates-pdf.html" }
al
{ "domain": "cs.stackexchange", "id": 10689, "lm_label": null, "lm_name": null, "lm_q1_score": null, "lm_q1q2_score": null, "lm_q2_score": null, "openwebmath_perplexity": null, "openwebmath_score": null, "tags": "algorithms", "url": null }