id stringclasses 10
values | question stringclasses 10
values | answer stringclasses 10
values | topic stringclasses 7
values | parent_seed_ids stringclasses 9
values | target_molecule stringclasses 9
values | candidate_molecule stringclasses 1
value | cohort_vector stringclasses 1
value | cohort_target stringclasses 1
value | merge_complexity stringclasses 3
values | audit_json stringclasses 10
values | clean_accept int64 1 1 | refinement_rounds int64 1 1 | accepted_at float64 1.78B 1.78B |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
122a5e4d4233ccfb | Four couriers are represented by points (t, d), where t is total time in hours and d is total distance in miles: A(3/4, 27/8), B(5/6, 7/4), C(2/3, 5/3), D(7/8, 2). Which courier had the greatest average speed? | A | algebra | ["648c41407ca96533", "a0176f34dbf9162a"] | {"parent_fingerprints": ["- Verify input values are allowed by the function (ensure none make a denominator zero).\n- For each required input value, substitute it into the expression to obtain a specific rational value; evaluate the resulting numerator and denominator to form a fraction.\n- Simplify each resulting frac... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.5176714062690735, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.4823285937309265, "verifier_agreements": 1, "verifier_answers": ["A"], "parent_fingerprints": ["- Verify input values are allowed by the function (ensure none make a denom... | 1 | 1 | 1,777,237,285.002237 |
61e2772310be8173 | Determine the polar coordinates (r, theta), with r > 0 and 0 <= theta < 2pi, of the point (-7, 24). | (25, pi - arctan(24/7)) | precalculus | ["701e1b0bd5df468f"] | {"parent_fingerprints": ["- Compute the radial coordinate as the distance from the origin to the point (the magnitude of the position vector).\n\n- Find a reference angle using the slope or inverse tangent of the ratio of the vertical to horizontal coordinate (i.e., use an inverse-trig function to get an acute referenc... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | LIGHT | {"synthesis_mode": "LIGHT", "spot_check_correctness": 1.0, "anti_distance": 0.30253714323043823, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.6974628567695618, "verifier_agreements": 1, "verifier_answers": ["(25, pi - arctan(24/7))"], "parent_fingerprints": ["- Compute the radial coordinate as the distance from ... | 1 | 1 | 1,777,237,412.653079 |
b86ed542892616f6 | A craftsperson makes regular polygon frames from identical straight segments, so a regular pentagon and a regular decagon he makes have the same side length. Each pentagon frame has perimeter 40 cm. Material costs $0.05 per cm of frame. He sells pentagon frames for $6 each and decagon frames in bundles of 3 for $25. On... | 107 | prealgebra | ["49807124e921340f", "0e2a833a7180fd41"] | {"parent_fingerprints": ["- Identify that the partitioning makes one side of the smaller congruent shape equal to one side of the larger polygon (so both perimeters are built from the same side length).\n- Represent each perimeter conceptually as (number of sides of that shape) \u00d7 (the common side length).\n- Obser... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.5787486732006073, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.5047330260276794, "verifier_agreements": 1, "verifier_answers": ["107"], "parent_fingerprints": ["- Identify that the partitioning makes one side of the smaller congruent ... | 1 | 1 | 1,777,237,617.421524 |
035f7da50cd56b67 | Let t be a positive real number. Determine the least value of t such that all roots of the cubic 2x^3 + 2t x^2 + (2 - t)x - (t + 4) are real. | sqrt(7) | intermediate_algebra | ["3b07e0e46345f8f8", "f0b63056c531c272"] | {"parent_fingerprints": ["", "- Observe that the polynomial admits a simple, parameter-independent root by direct substitution of an elementary value; conclude it factors as a linear factor times a quadratic factor.\n\n- Divide (or factor) out that linear factor to obtain a quadratic whose coefficients depend on the pa... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.3916904926300049, "novelty_max_minhash": 0.0703125, "novelty_max_cosine": 0.6083095073699951, "verifier_agreements": 1, "verifier_answers": ["sqrt(7)"], "parent_fingerprints": ["", "- Observe that the polynomial admits a simple, parameter-in... | 1 | 1 | 1,777,238,213.05439 |
622a36fc91d2bdfc | Let N = 11·22·33·...·110 (the product of the first ten positive multiples of 11). How many positive divisors of N are multiples of 11? | 2700 | number_theory | ["7e32d801337f5145", "47c5862d507cb2ab"] | {"parent_fingerprints": ["- Express the given integer as a product of distinct primes each raised to a positive integer exponent (its prime factorization).\n- Observe that any positive divisor can only use those primes, with each prime's exponent ranging from zero up to the exponent it has in the original number.\n- Fo... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | MEDIUM | {"synthesis_mode": "MEDIUM", "spot_check_correctness": 1.0, "anti_distance": 0.45180636644363403, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.6324580907821655, "verifier_agreements": 1, "verifier_answers": ["2700"], "parent_fingerprints": ["- Express the given integer as a product of distinct primes each raised... | 1 | 1 | 1,777,238,490.991886 |
a66e58a5a12587c9 | A right circular cylinder has a string wrapped tightly around its base; the string’s length is 16π cm. The cylinder’s volume is 256π cubic centimeters. What is the cylinder’s height? | 4 cm | geometry | ["7d0d01901243518b"] | {"parent_fingerprints": ["- Recognize the solid type and the corresponding volume relation: volume equals base area times height. \n- Identify the base shape and write its area in terms of the base dimension given (e.g., circular base area as a function of radius). \n- Read the diagram/labels to determine which measu... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | LIGHT | {"synthesis_mode": "LIGHT", "spot_check_correctness": 1.0, "anti_distance": 0.3827410936355591, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.6172589063644409, "verifier_agreements": 1, "verifier_answers": ["4"], "parent_fingerprints": ["- Recognize the solid type and the corresponding volume relation: volume equ... | 1 | 1 | 1,777,238,556.735662 |
579fe23907b3564f | Along each side of a regular 18-gon, an identical regular pentagon is attached externally so that it shares exactly that side. If the perimeter of one pentagon is 65 cm, what is the perimeter of the 18-gon? | 234 cm | prealgebra | ["49807124e921340f"] | {"parent_fingerprints": ["- Identify that the partitioning makes one side of the smaller congruent shape equal to one side of the larger polygon (so both perimeters are built from the same side length).\n- Represent each perimeter conceptually as (number of sides of that shape) \u00d7 (the common side length).\n- Obser... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | LIGHT | {"synthesis_mode": "LIGHT", "spot_check_correctness": 1.0, "anti_distance": 0.42226046323776245, "novelty_max_minhash": 0.0, "novelty_max_cosine": 0.6213156580924988, "verifier_agreements": 1, "verifier_answers": ["234 cm"], "parent_fingerprints": ["- Identify that the partitioning makes one side of the smaller congrue... | 1 | 1 | 1,777,238,770.537976 |
ee80c0965485a306 | Find the polar coordinates (r, θ), with r > 0 and θ ∈ [0, 2π), of the point (−4, 4√3). | (8, 2π/3) | precalculus | ["701e1b0bd5df468f"] | {"parent_fingerprints": ["- Compute the radial coordinate as the distance from the origin to the point (the magnitude of the position vector).\n\n- Find a reference angle using the slope or inverse tangent of the ratio of the vertical to horizontal coordinate (i.e., use an inverse-trig function to get an acute referenc... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | LIGHT | {"synthesis_mode": "LIGHT", "spot_check_correctness": 1.0, "anti_distance": 0.29681284725666046, "novelty_max_minhash": 0.0234375, "novelty_max_cosine": 0.8469347357749939, "verifier_agreements": 1, "verifier_answers": ["(8, 2\u03c0/3)"], "parent_fingerprints": ["- Compute the radial coordinate as the distance from the... | 1 | 1 | 1,777,238,879.450956 |
e73e754ecb947919 | Ten distinct people, including Alice, Bob, and Carol, are to sit around a round table. How many distinct seatings, considered the same up to rotation, are there in which Carol sits next to neither Alice nor Bob? | 211680 | counting__probability | ["3717b13fffb488aa"] | {"parent_fingerprints": ["- Break the circular symmetry by fixing one designated person in a reference seat; treat all other placements relative to this anchor to avoid overcounting rotations.\n\n- Classify possible placements of a second designated person by the number of intervening seats (i.e., by their distance aro... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | LIGHT | {"synthesis_mode": "LIGHT", "spot_check_correctness": 1.0, "anti_distance": 0.346962571144104, "novelty_max_minhash": 0.0078125, "novelty_max_cosine": 0.6621044874191284, "verifier_agreements": 1, "verifier_answers": ["211680"], "parent_fingerprints": ["- Break the circular symmetry by fixing one designated person in a... | 1 | 1 | 1,777,239,145.5964 |
dfaa1c3a6a7df06a | To reach a target amount A exactly two months from now, Dana deposits 40% of A today and 30% of A one month from today into an account that compounds monthly at a fixed rate r. What is the smallest monthly interest rate r (as a percentage) that ensures the account has at least A on the target date? | 25% | algebra | ["648c41407ca96533", "a0176f34dbf9162a", "489856633c9bc7c8", "cf0b8c3bf6ab521f"] | {"parent_fingerprints": ["- Verify input values are allowed by the function (ensure none make a denominator zero).\n- For each required input value, substitute it into the expression to obtain a specific rational value; evaluate the resulting numerator and denominator to form a fraction.\n- Simplify each resulting frac... | {} | [0.0, 0.0, 0.0, 0.0, 0.0] | [0.0, 0.0, 0.0, 0.0, 0.0] | FULL | {"synthesis_mode": "FULL", "spot_check_correctness": 1.0, "anti_distance": 0.4118701219558716, "novelty_max_minhash": 0.03125, "novelty_max_cosine": 0.5881298780441284, "verifier_agreements": 1, "verifier_answers": ["25%"], "parent_fingerprints": ["- Verify input values are allowed by the function (ensure none make a d... | 1 | 1 | 1,777,239,513.853659 |
README.md exists but content is empty.
- Downloads last month
- 31