| {"candidate_id":"successive_percent_change-0018","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["130/100","70/100","115/100"]},"correct_answer":"2093/4","correct_answer_fraction":[2093,4],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"575","plausible_wrong_fraction":[575,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0018","parameters":{"base":500,"changes":[30,30,15],"signs":[1,-1,1]},"question":"A quantity starts at 500. It increases by 30%, then decreases by 30%, and finally increases by 15%. What is the final value? Give an exact value.","question_sha256":"065f94228bf2a3a37077effa07d42f09f2f5a8eb4f1882df91bae42f906464e4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":145,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0014","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":41,"total_score":3178},"correct_answer":"3178/41","correct_answer_fraction":[3178,41],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"236/3","plausible_wrong_fraction":[236,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0014","parameters":{"counts":[10,15,16],"means":[88,70,78]},"question":"Three classes contain 10, 15, and 16 students. Their mean test scores are 88, 70, and 78, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"f2f31d45761f8637c326bf1bd8d86eb435d1068c71e5740f0955a53360a33828","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0016","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[5,13,37,109,325,973,2917]},"correct_answer":"2917","correct_answer_fraction":[2917,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"973","plausible_wrong_fraction":[973,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0016","parameters":{"a0":5,"multiplier":3,"n":6,"offset":-2},"question":"A sequence is defined by a_0 = 5 and a_(k+1) = 3a_k - 2 for k >= 0. What is a_6?","question_sha256":"9b391c78bc22d3535dcdfcdd8a87a23edc4e3e1cc94859d424f46b14a84bdf22","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0023","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[7,15,39,111,327,975,2919,8751,26247]},"correct_answer":"26247","correct_answer_fraction":[26247,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"8751","plausible_wrong_fraction":[8751,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0023","parameters":{"a0":7,"multiplier":3,"n":8,"offset":-6},"question":"A sequence is defined by a_0 = 7 and a_(k+1) = 3a_k - 6 for k >= 0. What is a_8?","question_sha256":"62f2bbdddaa346da91a9cf3d351e53f3889a5e8665f7dae81c1b971590bd164e","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0023","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1485,"true_positive":95},"correct_answer":"19/316","correct_answer_fraction":[19,316],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"19/20","plausible_wrong_fraction":[19,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0023","parameters":{"population":10000,"prevalence":1,"sensitivity":95,"specificity":85},"question":"In a population, 1% of people have a condition. A test has 95% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"304093603c99059ad4e87b47ac799c9003fa905aa0252cc39b323b73bc761e16","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0008","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":48,"total_score":3240},"correct_answer":"135/2","correct_answer_fraction":[135,2],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"202/3","plausible_wrong_fraction":[202,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0008","parameters":{"counts":[8,13,27],"means":[76,55,71]},"question":"Three classes contain 8, 13, and 27 students. Their mean test scores are 76, 55, and 71, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"f108852af791ac16004ec1081c1da7751d64cad1b55b3a671c0082cc2414f9fa","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0004","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":297,"true_positive":90},"correct_answer":"10/43","correct_answer_fraction":[10,43],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"9/10","plausible_wrong_fraction":[9,10],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0004","parameters":{"population":10000,"prevalence":1,"sensitivity":90,"specificity":97},"question":"In a population, 1% of people have a condition. A test has 90% sensitivity and 97% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"c3703c85ec1c294a50031ae504de09a8297df0890b89fd141b58fbe952936f20","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0015","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["125/100","85/100","120/100"]},"correct_answer":"2295","correct_answer_fraction":[2295,1],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"2340","plausible_wrong_fraction":[2340,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0015","parameters":{"base":1800,"changes":[25,15,20],"signs":[1,-1,1]},"question":"A quantity starts at 1800. It increases by 25%, then decreases by 15%, and finally increases by 20%. What is the final value? Give an exact value.","question_sha256":"ba3274f031aa0a5b6f70ce9e2c471c6cb7137cecd8d24b3da4fb0037ea15c6cb","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0012","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":4,"total_symbols":5},"correct_answer":"30","correct_answer_fraction":[30,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"120","plausible_wrong_fraction":[120,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0012","parameters":{"counts":[2,2,1],"letters":["A","C","D"],"multiset":"AACCD"},"question":"How many distinct strings can be formed by rearranging all letters of AACCD?","question_sha256":"010770565a030b089cf5963c1c83cf37da195243ed8e26587dbe5b0c2603d45b","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":76,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0001","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":768,"true_positive":360},"correct_answer":"15/47","correct_answer_fraction":[15,47],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"9/10","plausible_wrong_fraction":[9,10],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0001","parameters":{"population":10000,"prevalence":4,"sensitivity":90,"specificity":92},"question":"In a population, 4% of people have a condition. A test has 90% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"ec89f34126952e0721e20010eb08013f3fbe7988234d67846f484b7c07c374e7","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0000","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[3,13,33,73,153,313,633,1273]},"correct_answer":"1273","correct_answer_fraction":[1273,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"633","plausible_wrong_fraction":[633,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0000","parameters":{"a0":3,"multiplier":2,"n":7,"offset":7},"question":"A sequence is defined by a_0 = 3 and a_(k+1) = 2a_k + 7 for k >= 0. What is a_7?","question_sha256":"43385f69ee27ee3a9321d7d8246d37f52a442d7225afeec9a0c04e5365e67418","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0019","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["112/100","75/100","108/100"]},"correct_answer":"24948/25","correct_answer_fraction":[24948,25],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1045","plausible_wrong_fraction":[1045,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0019","parameters":{"base":1100,"changes":[12,25,8],"signs":[1,-1,1]},"question":"A quantity starts at 1100. It increases by 12%, then decreases by 25%, and finally increases by 8%. What is the final value? Give an exact value.","question_sha256":"bd9db84e81f0b75c24a6711745ffa24db4715a74d516849b1f0fe1d9da69b4db","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":145,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0021","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":288,"total_symbols":9},"correct_answer":"1260","correct_answer_fraction":[1260,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"362880","plausible_wrong_fraction":[362880,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0021","parameters":{"counts":[4,3,2],"letters":["F","A","H"],"multiset":"FFFFAAAHH"},"question":"How many distinct strings can be formed by rearranging all letters of FFFFAAAHH?","question_sha256":"a8cb8939beebbdeb79f853f006821f584938cb1dec2de3ccba514d3a6619d4f0","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0020","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"110/100","width_multiplier":"70/100"},"correct_answer":"7315/2","correct_answer_fraction":[7315,2],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"3800","plausible_wrong_fraction":[3800,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0020","parameters":{"decrease":30,"increase":10,"length":95,"width":50},"question":"A rectangle initially has length 95 and width 50. Its length is increased by 10% while its width is decreased by 30%. What is the new area? Give an exact value.","question_sha256":"3e8a5026a2716a9abbb1877e1cc7bdd6f9269ffaba8e8eefaab2859fe8d07882","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0005","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"91/120","remaining_worker":"A"},"correct_answer":"64/5","correct_answer_fraction":[64,5],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"85/8","plausible_wrong_fraction":[85,8],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0005","parameters":{"a_hours":24,"b_hours":15,"together_hours":7},"question":"Worker A can finish a job alone in 24 hours and worker B can finish it alone in 15 hours. They work together for 7 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"d042483a37d728174cb89f072c08ba731d3f236397d5ca812940aa720b22e56a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0017","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["112/100","70/100","88/100"]},"correct_answer":"77616/125","correct_answer_fraction":[77616,125],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"630","plausible_wrong_fraction":[630,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0017","parameters":{"base":900,"changes":[12,30,12],"signs":[1,-1,-1]},"question":"A quantity starts at 900. It increases by 12%, then decreases by 30%, and finally decreases by 12%. What is the final value? Give an exact value.","question_sha256":"2ac7756d6be1fe11b1d49205c806196c16ec54b52f9b6912145f6d2ef9d1108a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":145,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0003","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1540,"favorable_subsets":468},"correct_answer":"117/385","correct_answer_fraction":[117,385],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"3159/10648","plausible_wrong_fraction":[3159,10648],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0003","parameters":{"blue":13,"draws":3,"red":9,"target_red":2},"question":"An urn contains 9 red balls and 13 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"d0ec7ef0806876c526de18d93699d67e27344ffab8eef7792288bf36a7cc88a2","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0003","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["130/100","92/100","85/100"]},"correct_answer":"10166/25","correct_answer_fraction":[10166,25],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"428","plausible_wrong_fraction":[428,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0003","parameters":{"base":400,"changes":[30,8,15],"signs":[1,-1,-1]},"question":"A quantity starts at 400. It increases by 30%, then decreases by 8%, and finally decreases by 15%. What is the final value? Give an exact value.","question_sha256":"7e88e76cd2908ea71d877ab1bf94110ad46a8532703957361bf1972dfb404b5e","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":144,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0006","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"120/100","width_multiplier":"85/100"},"correct_answer":"1683","correct_answer_fraction":[1683,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"3465/2","plausible_wrong_fraction":[3465,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0006","parameters":{"decrease":15,"increase":20,"length":30,"width":55},"question":"A rectangle initially has length 30 and width 55. Its length is increased by 20% while its width is decreased by 15%. What is the new area? Give an exact value.","question_sha256":"b5061c0a60790d9fb88cc9dd17657abe45e57ef92bfceef09457318106ba6a22","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0007","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["118/39","118/84"],"total_distance":236},"correct_answer":"2184/41","correct_answer_fraction":[2184,41],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"123/2","plausible_wrong_fraction":[123,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0007","parameters":{"distance":118,"speeds":[39,84]},"question":"A vehicle travels 118 km from A to B at 39 km/h and returns the same 118 km at 84 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"4ad76497ac8937e3910cd2e08c109c752abed97f254821dca2fcbc4133172dd2","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0022","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["120/100","92/100","130/100"]},"correct_answer":"50232/25","correct_answer_fraction":[50232,25],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1988","plausible_wrong_fraction":[1988,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0022","parameters":{"base":1400,"changes":[20,8,30],"signs":[1,-1,1]},"question":"A quantity starts at 1400. It increases by 20%, then decreases by 8%, and finally increases by 30%. What is the final value? Give an exact value.","question_sha256":"6705b6dc8f859296cd0a2a27a96a503d166edc8670732923ab9a282170c0f101","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":145,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0018","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":7,"failure_probability":"7/8"},"correct_answer":"1273609/2097152","correct_answer_fraction":[1273609,2097152],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"7/8","plausible_wrong_fraction":[7,8],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0018","parameters":{"success_denominator":8,"success_numerator":1,"trials":7},"question":"Each of 7 independent trials succeeds with probability 1/8. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"7812e5836d6a224e4d6a7646356ba1738b465e52dd16f5774ae12ad957746cc2","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":147,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0010","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":816,"favorable_subsets":396},"correct_answer":"33/68","correct_answer_fraction":[33,68],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"4/9","plausible_wrong_fraction":[4,9],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0010","parameters":{"blue":6,"draws":3,"red":12,"target_red":2},"question":"An urn contains 12 red balls and 6 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"488b510c6b2fdf0b225fdd90c499687f4e3f71c8ae820bb32805e9dfc5ff678f","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0007","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["120/100","70/100","125/100"]},"correct_answer":"1365","correct_answer_fraction":[1365,1],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1495","plausible_wrong_fraction":[1495,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0007","parameters":{"base":1300,"changes":[20,30,25],"signs":[1,-1,1]},"question":"A quantity starts at 1300. It increases by 20%, then decreases by 30%, and finally increases by 25%. What is the final value? Give an exact value.","question_sha256":"e524752563aa07f4dce7a1ef93fa15964df22007376c71a70679f66c77727d25","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0023","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["166/48","166/81"],"total_distance":332},"correct_answer":"2592/43","correct_answer_fraction":[2592,43],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"129/2","plausible_wrong_fraction":[129,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0023","parameters":{"distance":166,"speeds":[48,81]},"question":"A vehicle travels 166 km from A to B at 48 km/h and returns the same 166 km at 81 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"d6a8ba4ac1b23ec75245413ddfdb996827b56e122760fc3e68e4aec35d185d0f","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0022","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":288,"total_symbols":9},"correct_answer":"1260","correct_answer_fraction":[1260,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"362880","plausible_wrong_fraction":[362880,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0022","parameters":{"counts":[4,3,2],"letters":["G","B","E"],"multiset":"GGGGBBBEE"},"question":"How many distinct strings can be formed by rearranging all letters of GGGGBBBEE?","question_sha256":"0063da3c94dad163b93e86ca8fc004aba3f371b5a94ade8e72f2454ddae3f773","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0018","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"110/100","width_multiplier":"95/100"},"correct_answer":"51623/8","correct_answer_fraction":[51623,8],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"25935/4","plausible_wrong_fraction":[25935,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0018","parameters":{"decrease":5,"increase":10,"length":95,"width":65},"question":"A rectangle initially has length 95 and width 65. Its length is increased by 10% while its width is decreased by 5%. What is the new area? Give an exact value.","question_sha256":"f62fee1ff04815a5ca6892e0cd5a6dd79fc615d1df2d73d3d38692f8de557f61","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":159,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0010","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["130/100","75/100","75/100"]},"correct_answer":"8775/8","correct_answer_fraction":[8775,8],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1200","plausible_wrong_fraction":[1200,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0010","parameters":{"base":1500,"changes":[30,25,25],"signs":[1,-1,-1]},"question":"A quantity starts at 1500. It increases by 30%, then decreases by 25%, and finally decreases by 25%. What is the final value? Give an exact value.","question_sha256":"09112621933ada181fc68a4214ff974fc5d0d9b1518bf917f754fb0ed26b062d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0022","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":40,"total_score":2289},"correct_answer":"2289/40","correct_answer_fraction":[2289,40],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"58","plausible_wrong_fraction":[58,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0022","parameters":{"counts":[8,21,11],"means":[65,57,52]},"question":"Three classes contain 8, 21, and 11 students. Their mean test scores are 65, 57, and 52, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"6b46d0162390a597b899f28dde21566aa6202bcee5a0cd374c8a864a098f80d6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0021","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["88/69","88/51"],"total_distance":176},"correct_answer":"1173/20","correct_answer_fraction":[1173,20],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"60","plausible_wrong_fraction":[60,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0021","parameters":{"distance":88,"speeds":[69,51]},"question":"A vehicle travels 88 km from A to B at 69 km/h and returns the same 88 km at 51 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"41aad9c07b80d99be9286b31e00c3960f993d1521428fb6f36d893dda018b2f6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":167,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0012","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":560,"favorable_subsets":252},"correct_answer":"9/20","correct_answer_fraction":[9,20],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"1701/4096","plausible_wrong_fraction":[1701,4096],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0012","parameters":{"blue":7,"draws":3,"red":9,"target_red":2},"question":"An urn contains 9 red balls and 7 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"1cd0a664b706d9e9814968dcbc5b2c89d9cd64fada7c57dbd065b5ac33702063","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":187,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0020","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["155/81","155/57"],"total_distance":310},"correct_answer":"1539/23","correct_answer_fraction":[1539,23],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"69","plausible_wrong_fraction":[69,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0020","parameters":{"distance":155,"speeds":[81,57]},"question":"A vehicle travels 155 km from A to B at 81 km/h and returns the same 155 km at 57 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"5218a69f35604402ffc4e949f97065d728d5dc2470a65147a27efc3db9429fe8","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0009","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":8,"total_symbols":6},"correct_answer":"90","correct_answer_fraction":[90,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"720","plausible_wrong_fraction":[720,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0009","parameters":{"counts":[2,2,2],"letters":["B","D","C"],"multiset":"BBDDCC"},"question":"How many distinct strings can be formed by rearranging all letters of BBDDCC?","question_sha256":"39fb51315a2fc83629a4e5069f12ea66d07e4df6c3be1d4d99ee68e209e877d0","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":77,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0005","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":6,"failure_probability":"9/10"},"correct_answer":"468559/1000000","correct_answer_fraction":[468559,1000000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"3/5","plausible_wrong_fraction":[3,5],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0005","parameters":{"success_denominator":20,"success_numerator":2,"trials":6},"question":"Each of 6 independent trials succeeds with probability 1/10. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"c65bea381177f9a7daff1a81b2b06bf1c28ab25e0729ea7c00d447c816a10d98","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0009","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"120/161","remaining_worker":"A"},"correct_answer":"133/23","correct_answer_fraction":[133,23],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"69/7","plausible_wrong_fraction":[69,7],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0009","parameters":{"a_hours":7,"b_hours":23,"together_hours":4},"question":"Worker A can finish a job alone in 7 hours and worker B can finish it alone in 23 hours. They work together for 4 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"acefb6a272ada7e576bc57351733eb53265c9d13d08caec9c53f6c46322ec79c","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0022","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":776,"true_positive":240},"correct_answer":"30/127","correct_answer_fraction":[30,127],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"4/5","plausible_wrong_fraction":[4,5],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0022","parameters":{"population":10000,"prevalence":3,"sensitivity":80,"specificity":92},"question":"In a population, 3% of people have a condition. A test has 80% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"19e12175e69c0f3350511c8cc384fb55c4c89d9e0453e50903a45ea7dc6fae2f","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0018","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"22/39","remaining_worker":"A"},"correct_answer":"26/3","correct_answer_fraction":[26,3],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"90/13","plausible_wrong_fraction":[90,13],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0018","parameters":{"a_hours":13,"b_hours":9,"together_hours":3},"question":"Worker A can finish a job alone in 13 hours and worker B can finish it alone in 9 hours. They work together for 3 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"115f47839de40959b5aa9b6a65eb1ce90ba403d2e57ebab372f777ade0f92356","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0011","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[6,11,21,41,81,161]},"correct_answer":"161","correct_answer_fraction":[161,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"81","plausible_wrong_fraction":[81,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0011","parameters":{"a0":6,"multiplier":2,"n":5,"offset":-1},"question":"A sequence is defined by a_0 = 6 and a_(k+1) = 2a_k - 1 for k >= 0. What is a_5?","question_sha256":"f850edb7cb48c05a9f5bfd1e0f7a9d72eb5934dbf43295827ce94dce0449ca74","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0005","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":768,"true_positive":340},"correct_answer":"85/277","correct_answer_fraction":[85,277],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"17/20","plausible_wrong_fraction":[17,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0005","parameters":{"population":10000,"prevalence":4,"sensitivity":85,"specificity":92},"question":"In a population, 4% of people have a condition. A test has 85% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"cbc1e5f8797bf839ac4c3891cbe417053e19956e42e64cdecdcb2b5d0579a077","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0009","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[-4,-16,-52,-160,-484,-1456]},"correct_answer":"-1456","correct_answer_fraction":[-1456,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"-484","plausible_wrong_fraction":[-484,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0009","parameters":{"a0":-4,"multiplier":3,"n":5,"offset":-4},"question":"A sequence is defined by a_0 = -4 and a_(k+1) = 3a_k - 4 for k >= 0. What is a_5?","question_sha256":"083d72286bf634319f2e178fd072781d14ea78de5e8ff17c3964e8445fafa45b","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":81,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0000","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"125/100","width_multiplier":"70/100"},"correct_answer":"4725/2","correct_answer_fraction":[4725,2],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"2565","plausible_wrong_fraction":[2565,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0000","parameters":{"decrease":30,"increase":25,"length":90,"width":30},"question":"A rectangle initially has length 90 and width 30. Its length is increased by 25% while its width is decreased by 30%. What is the new area? Give an exact value.","question_sha256":"44d54abe8d0e0e2b4ea7413520e175bab1ab551603fae33d4a2ef45bdb117068","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0019","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":7,"failure_probability":"13/15"},"correct_answer":"108110858/170859375","correct_answer_fraction":[108110858,170859375],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"14/15","plausible_wrong_fraction":[14,15],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0019","parameters":{"success_denominator":15,"success_numerator":2,"trials":7},"question":"Each of 7 independent trials succeeds with probability 2/15. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"82f6cdc22baf3352afb239fef545fb44e4267dabd74093ef6a40c78ecdbec9cd","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0014","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"140/100","width_multiplier":"90/100"},"correct_answer":"3969","correct_answer_fraction":[3969,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"4095","plausible_wrong_fraction":[4095,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0014","parameters":{"decrease":10,"increase":40,"length":45,"width":70},"question":"A rectangle initially has length 45 and width 70. Its length is increased by 40% while its width is decreased by 10%. What is the new area? Give an exact value.","question_sha256":"7d9691f4dd342f71b8c0e6d0e626c64843ba4c332d78c96beafd673b5c17fc61","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0018","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":48,"total_symbols":7},"correct_answer":"105","correct_answer_fraction":[105,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"5040","plausible_wrong_fraction":[5040,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0018","parameters":{"counts":[4,2,1],"letters":["C","E","G"],"multiset":"CCCCEEG"},"question":"How many distinct strings can be formed by rearranging all letters of CCCCEEG?","question_sha256":"912f77fff9d9f15fbb43730e75eeed3a68aaf8a77cf597ce794bbe14fc6fa5b5","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":78,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0009","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":3,"failure_probability":"9/10"},"correct_answer":"271/1000","correct_answer_fraction":[271,1000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"3/10","plausible_wrong_fraction":[3,10],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0009","parameters":{"success_denominator":10,"success_numerator":1,"trials":3},"question":"Each of 3 independent trials succeeds with probability 1/10. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"575e72e63b78fe4a190898a9498078eff864cacbdc99b61e84544dffeecfa813","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0012","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["130/100","70/100","80/100"]},"correct_answer":"6552/5","correct_answer_fraction":[6552,5],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1440","plausible_wrong_fraction":[1440,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0012","parameters":{"base":1800,"changes":[30,30,20],"signs":[1,-1,-1]},"question":"A quantity starts at 1800. It increases by 30%, then decreases by 30%, and finally decreases by 20%. What is the final value? Give an exact value.","question_sha256":"d39b89bd4a944bffb5ee049a2d5b2b002522524cd4eb1bcfe2d2fbdd0ebba0ca","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0016","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":220,"favorable_subsets":105},"correct_answer":"21/44","correct_answer_fraction":[21,44],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"245/576","plausible_wrong_fraction":[245,576],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0016","parameters":{"blue":5,"draws":3,"red":7,"target_red":2},"question":"An urn contains 7 red balls and 5 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"f6b9795f260aa0580d32931d3d6c63cba9cde29c841ed86c0bed8e3d314e34a5","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":187,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0006","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["160/36","160/81"],"total_distance":320},"correct_answer":"648/13","correct_answer_fraction":[648,13],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"117/2","plausible_wrong_fraction":[117,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0006","parameters":{"distance":160,"speeds":[36,81]},"question":"A vehicle travels 160 km from A to B at 36 km/h and returns the same 160 km at 81 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"6ce2f794b974949e972d34d140babe43905d8b17103980ff0936728deaa06ce0","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0006","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["108/100","85/100","120/100"]},"correct_answer":"35802/25","correct_answer_fraction":[35802,25],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1469","plausible_wrong_fraction":[1469,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0006","parameters":{"base":1300,"changes":[8,15,20],"signs":[1,-1,1]},"question":"A quantity starts at 1300. It increases by 8%, then decreases by 15%, and finally increases by 20%. What is the final value? Give an exact value.","question_sha256":"40b5a561ff10b0e5bde0612a5bf0582082885762c386c48a20b136b605bb983b","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":145,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0003","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":5,"failure_probability":"7/8"},"correct_answer":"15961/32768","correct_answer_fraction":[15961,32768],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"5/8","plausible_wrong_fraction":[5,8],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0003","parameters":{"success_denominator":8,"success_numerator":1,"trials":5},"question":"Each of 5 independent trials succeeds with probability 1/8. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"90e31a6a42be1a3cd5f5cddfe155c92989e4d8ad3b6108b07da1997281d97306","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":147,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0015","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"28/65","remaining_worker":"A"},"correct_answer":"52/5","correct_answer_fraction":[52,5],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"150/13","plausible_wrong_fraction":[150,13],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0015","parameters":{"a_hours":13,"b_hours":15,"together_hours":3},"question":"Worker A can finish a job alone in 13 hours and worker B can finish it alone in 15 hours. They work together for 3 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"799a6258a1d1e02e1b5de10dca55fd92d76ef8288c8b6c3c1c936b8e5b44dd56","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0005","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["130/100","88/100","88/100"]},"correct_answer":"100672/125","correct_answer_fraction":[100672,125],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"848","plausible_wrong_fraction":[848,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0005","parameters":{"base":800,"changes":[30,12,12],"signs":[1,-1,-1]},"question":"A quantity starts at 800. It increases by 30%, then decreases by 12%, and finally decreases by 12%. What is the final value? Give an exact value.","question_sha256":"cdad15a675f46011ee1e119b1f57b2a2685a6a36e4e73cd5a4ebe0d5701510c0","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":145,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0006","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"20/33","remaining_worker":"A"},"correct_answer":"22/3","correct_answer_fraction":[22,3],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"72/11","plausible_wrong_fraction":[72,11],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0006","parameters":{"a_hours":11,"b_hours":9,"together_hours":3},"question":"Worker A can finish a job alone in 11 hours and worker B can finish it alone in 9 hours. They work together for 3 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"9c3aa16e4a0deb2ec25c5e7921bb7e0ec77806fe10b7668961e9f8247a24a816","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0019","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1485,"true_positive":85},"correct_answer":"17/314","correct_answer_fraction":[17,314],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"17/20","plausible_wrong_fraction":[17,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0019","parameters":{"population":10000,"prevalence":1,"sensitivity":85,"specificity":85},"question":"In a population, 1% of people have a condition. A test has 85% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"cee9e941b3e241abdc298d2b51c5201b916048605485421b14a222031e9c2353","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0013","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":12,"total_symbols":6},"correct_answer":"60","correct_answer_fraction":[60,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"720","plausible_wrong_fraction":[720,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0013","parameters":{"counts":[2,3,1],"letters":["B","G","H"],"multiset":"BBGGGH"},"question":"How many distinct strings can be formed by rearranging all letters of BBGGGH?","question_sha256":"2a18847175f3bec39e87f0c4262a68363063310b36f5a05162b1dc7c24e7339a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":77,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0023","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":48,"total_score":3953},"correct_answer":"3953/48","correct_answer_fraction":[3953,48],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"233/3","plausible_wrong_fraction":[233,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0023","parameters":{"counts":[19,20,9],"means":[91,86,56]},"question":"Three classes contain 19, 20, and 9 students. Their mean test scores are 91, 86, and 56, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"afac4dd087f4507a3f6b53061f63d6d78ccad8debfbe85f01acf61d7b938065f","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0021","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":2024,"favorable_subsets":715},"correct_answer":"65/184","correct_answer_fraction":[65,184],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"1573/4608","plausible_wrong_fraction":[1573,4608],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0021","parameters":{"blue":13,"draws":3,"red":11,"target_red":2},"question":"An urn contains 11 red balls and 13 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"884e79840638f9d373ecbc7f8d825b7f4c59d70e7453b5dce8aa79bb4cdb7a44","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0021","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":5,"failure_probability":"9/10"},"correct_answer":"40951/100000","correct_answer_fraction":[40951,100000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"1/2","plausible_wrong_fraction":[1,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0021","parameters":{"success_denominator":10,"success_numerator":1,"trials":5},"question":"Each of 5 independent trials succeeds with probability 1/10. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"eec603608fff1efc308f284d6aa3c215cd2cb395823cb983bb9234315bf356f4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0019","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":39,"total_score":2825},"correct_answer":"2825/39","correct_answer_fraction":[2825,39],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"212/3","plausible_wrong_fraction":[212,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0019","parameters":{"counts":[14,10,15],"means":[60,59,93]},"question":"Three classes contain 14, 10, and 15 students. Their mean test scores are 60, 59, and 93, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"218f76cd0368547f385e5ba4bd2f87ede4c38fff4b66df4a33a57f671ed12f7a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0017","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":5,"failure_probability":"5/6"},"correct_answer":"4651/7776","correct_answer_fraction":[4651,7776],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"5/6","plausible_wrong_fraction":[5,6],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0017","parameters":{"success_denominator":12,"success_numerator":2,"trials":5},"question":"Each of 5 independent trials succeeds with probability 1/6. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"1dd5796f9fe4f6bed3df972e9c2f239df7aee524d788b974d0337230bab437af","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":147,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0013","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["180/36","180/90"],"total_distance":360},"correct_answer":"360/7","correct_answer_fraction":[360,7],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"63","plausible_wrong_fraction":[63,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0013","parameters":{"distance":180,"speeds":[36,90]},"question":"A vehicle travels 180 km from A to B at 36 km/h and returns the same 180 km at 90 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"4db47e29de9184b371c97b8f7e638d5deb402708ba881f1cc867d64b2ff67231","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0012","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"320/391","remaining_worker":"A"},"correct_answer":"207/17","correct_answer_fraction":[207,17],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"255/23","plausible_wrong_fraction":[255,23],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0012","parameters":{"a_hours":23,"b_hours":17,"together_hours":8},"question":"Worker A can finish a job alone in 23 hours and worker B can finish it alone in 17 hours. They work together for 8 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"967860d01a32fdd1478e90fd2e76c8f2cc79c52c6294ac291ce9160e586dbc32","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0021","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"19/88","remaining_worker":"A"},"correct_answer":"80/11","correct_answer_fraction":[80,11],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"77/8","plausible_wrong_fraction":[77,8],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0021","parameters":{"a_hours":8,"b_hours":11,"together_hours":1},"question":"Worker A can finish a job alone in 8 hours and worker B can finish it alone in 11 hours. They work together for 1 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"4c2c79ceff485176bb2588a8a939c5b29f79d0b783548fb4cd6653be880e0e41","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0021","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[8,28,88,268,808,2428,7288,21868,65608]},"correct_answer":"65608","correct_answer_fraction":[65608,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"21868","plausible_wrong_fraction":[21868,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0021","parameters":{"a0":8,"multiplier":3,"n":8,"offset":4},"question":"A sequence is defined by a_0 = 8 and a_(k+1) = 3a_k + 4 for k >= 0. What is a_8?","question_sha256":"eb8dc4536d7f0d0513c93e1d7f5c2f990571c78dd1ac408b1da39527a3bb7ea0","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0017","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["52/33","52/87"],"total_distance":104},"correct_answer":"957/20","correct_answer_fraction":[957,20],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"60","plausible_wrong_fraction":[60,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0017","parameters":{"distance":52,"speeds":[33,87]},"question":"A vehicle travels 52 km from A to B at 33 km/h and returns the same 52 km at 87 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"22c8d368726c55883b243c098139538e07c7a8c6f9622f8688660b645faff8f5","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":167,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0017","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[3,8,23,68,203,608]},"correct_answer":"608","correct_answer_fraction":[608,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"203","plausible_wrong_fraction":[203,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0017","parameters":{"a0":3,"multiplier":3,"n":5,"offset":-1},"question":"A sequence is defined by a_0 = 3 and a_(k+1) = 3a_k - 1 for k >= 0. What is a_5?","question_sha256":"ea15e88e516c6d867cfaafe98b785abfa5add31ebb9d14b42de4f14d2d397db4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0003","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":460,"true_positive":680},"correct_answer":"34/57","correct_answer_fraction":[34,57],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"17/20","plausible_wrong_fraction":[17,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0003","parameters":{"population":10000,"prevalence":8,"sensitivity":85,"specificity":95},"question":"In a population, 8% of people have a condition. A test has 85% sensitivity and 95% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"60f1e414389244c4819297f36d3b22aa67cf38e502485472f4241edc965fce2f","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0010","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":6,"failure_probability":"7/8"},"correct_answer":"144495/262144","correct_answer_fraction":[144495,262144],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"3/4","plausible_wrong_fraction":[3,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0010","parameters":{"success_denominator":8,"success_numerator":1,"trials":6},"question":"Each of 6 independent trials succeeds with probability 1/8. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"b0b778145ce3ecb5433c8f6d018f7887ee0aac0bcfe9b8ee609687d8ab1f277d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":147,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0022","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":5,"failure_probability":"17/20"},"correct_answer":"1780143/3200000","correct_answer_fraction":[1780143,3200000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"3/4","plausible_wrong_fraction":[3,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0022","parameters":{"success_denominator":20,"success_numerator":3,"trials":5},"question":"Each of 5 independent trials succeeds with probability 3/20. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"ab6337a3e9990e16d6e699b6811b2d9ae22fa8c2040f1cd25dc14dd3cc35fbd8","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0011","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"5/24","remaining_worker":"A"},"correct_answer":"20","correct_answer_fraction":[20,1],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"23/4","plausible_wrong_fraction":[23,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0011","parameters":{"a_hours":24,"b_hours":6,"together_hours":1},"question":"Worker A can finish a job alone in 24 hours and worker B can finish it alone in 6 hours. They work together for 1 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"65a7f220f87b35d32870157fd15be44da7295857a6fed0b4206152d12772a9ce","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0005","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[4,9,19,39,79,159,319]},"correct_answer":"319","correct_answer_fraction":[319,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"159","plausible_wrong_fraction":[159,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0005","parameters":{"a0":4,"multiplier":2,"n":6,"offset":1},"question":"A sequence is defined by a_0 = 4 and a_(k+1) = 2a_k + 1 for k >= 0. What is a_6?","question_sha256":"8b713f1aff1b3f555cf5c4b9fbf963d3fe888508a4744bfe52cc0f3f00c3d37d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0023","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"110/100","width_multiplier":"85/100"},"correct_answer":"10285/8","correct_answer_fraction":[10285,8],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"5225/4","plausible_wrong_fraction":[5225,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0023","parameters":{"decrease":15,"increase":10,"length":55,"width":25},"question":"A rectangle initially has length 55 and width 25. Its length is increased by 10% while its width is decreased by 15%. What is the new area? Give an exact value.","question_sha256":"fe9ab625f27798909e4fbb407577d38548dabe2d9e686920a0f25721d22002c2","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0005","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":560,"favorable_subsets":189},"correct_answer":"27/80","correct_answer_fraction":[27,80],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"1323/4096","plausible_wrong_fraction":[1323,4096],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0005","parameters":{"blue":9,"draws":3,"red":7,"target_red":2},"question":"An urn contains 7 red balls and 9 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"c53175d87cc1be7a1780792232300b3c6de5649481cfd45f240cd222bb4d595d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":187,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0023","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"140/153","remaining_worker":"A"},"correct_answer":"162/17","correct_answer_fraction":[162,17],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"85/9","plausible_wrong_fraction":[85,9],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0023","parameters":{"a_hours":18,"b_hours":17,"together_hours":8},"question":"Worker A can finish a job alone in 18 hours and worker B can finish it alone in 17 hours. They work together for 8 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"efc0fc617ba541bc19410d25bb14c6b3355db5a67b9ebf1a2ce23e8798998988","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0010","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":288,"total_symbols":9},"correct_answer":"1260","correct_answer_fraction":[1260,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"362880","plausible_wrong_fraction":[362880,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0010","parameters":{"counts":[4,3,2],"letters":["D","C","E"],"multiset":"DDDDCCCEE"},"question":"How many distinct strings can be formed by rearranging all letters of DDDDCCCEE?","question_sha256":"d98f25805c141cb1f998c184b71a113bd22dbf3dbb61078176d66a05d9a3dd94","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0008","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":12,"total_symbols":6},"correct_answer":"60","correct_answer_fraction":[60,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"720","plausible_wrong_fraction":[720,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0008","parameters":{"counts":[2,3,1],"letters":["A","G","B"],"multiset":"AAGGGB"},"question":"How many distinct strings can be formed by rearranging all letters of AAGGGB?","question_sha256":"dc180860f2efc51f9eec66dd965f8bc1944277797c7d02fa01818172a47cb37f","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":77,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0003","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":71,"total_score":5106},"correct_answer":"5106/71","correct_answer_fraction":[5106,71],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"217/3","plausible_wrong_fraction":[217,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0003","parameters":{"counts":[22,25,24],"means":[83,64,70]},"question":"Three classes contain 22, 25, and 24 students. Their mean test scores are 83, 64, and 70, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"a2aead8625d96cadc20d8c7b02f705d717245fa00e965fe54dc4217485c2d78e","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0000","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1140,"favorable_subsets":336},"correct_answer":"28/95","correct_answer_fraction":[28,95],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"36/125","plausible_wrong_fraction":[36,125],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0000","parameters":{"blue":12,"draws":3,"red":8,"target_red":2},"question":"An urn contains 8 red balls and 12 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"ed4dac653ac329a8cad0b954b41c2a8d3cf36ddb50f06c80e50de23182f05b6f","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0011","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"140/100","width_multiplier":"90/100"},"correct_answer":"756","correct_answer_fraction":[756,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"780","plausible_wrong_fraction":[780,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0011","parameters":{"decrease":10,"increase":40,"length":40,"width":15},"question":"A rectangle initially has length 40 and width 15. Its length is increased by 40% while its width is decreased by 10%. What is the new area? Give an exact value.","question_sha256":"293edf82fd5e6513d5922dc8338660011643f32e22c81e2f3deba71eddf3df44","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0013","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[8,18,38,78,158,318,638,1278,2558]},"correct_answer":"2558","correct_answer_fraction":[2558,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"1278","plausible_wrong_fraction":[1278,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0013","parameters":{"a0":8,"multiplier":2,"n":8,"offset":2},"question":"A sequence is defined by a_0 = 8 and a_(k+1) = 2a_k + 2 for k >= 0. What is a_8?","question_sha256":"c1c10ff86008ab7af3c85695d5791f6cb797892714552faafafc21e0efb22c82","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0013","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1320,"true_positive":900},"correct_answer":"15/37","correct_answer_fraction":[15,37],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"3/4","plausible_wrong_fraction":[3,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0013","parameters":{"population":10000,"prevalence":12,"sensitivity":75,"specificity":85},"question":"In a population, 12% of people have a condition. A test has 75% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"8ad697e86599a3160b8de66694af519174cc5e0f89d2762a5fca8a7fe509c1b7","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":258,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0023","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":7,"failure_probability":"19/20"},"correct_answer":"386128261/1280000000","correct_answer_fraction":[386128261,1280000000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"7/20","plausible_wrong_fraction":[7,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0023","parameters":{"success_denominator":20,"success_numerator":1,"trials":7},"question":"Each of 7 independent trials succeeds with probability 1/20. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"8db202a0b58e0b6d278772018952d4fdead240e5c13030a78efe98873049ae90","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0008","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["130/100","85/100","125/100"]},"correct_answer":"5525/4","correct_answer_fraction":[5525,4],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1400","plausible_wrong_fraction":[1400,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0008","parameters":{"base":1000,"changes":[30,15,25],"signs":[1,-1,1]},"question":"A quantity starts at 1000. It increases by 30%, then decreases by 15%, and finally increases by 25%. What is the final value? Give an exact value.","question_sha256":"b025fd89318bbd2182a6be62a8c67c6d78bdcc25368d290b763d95f4b460cf26","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0012","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["52/36","52/81"],"total_distance":104},"correct_answer":"648/13","correct_answer_fraction":[648,13],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"117/2","plausible_wrong_fraction":[117,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0012","parameters":{"distance":52,"speeds":[36,81]},"question":"A vehicle travels 52 km from A to B at 36 km/h and returns the same 52 km at 81 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"735da58b8ff9c8f5a533289eb809f10b6b0822f8e4f509dbb1d8f9f5b600fbd5","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":167,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0015","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[8,27,84,255,768,2307,6924]},"correct_answer":"6924","correct_answer_fraction":[6924,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"2307","plausible_wrong_fraction":[2307,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0015","parameters":{"a0":8,"multiplier":3,"n":6,"offset":3},"question":"A sequence is defined by a_0 = 8 and a_(k+1) = 3a_k + 3 for k >= 0. What is a_6?","question_sha256":"507bac877b437cb96a4ded256a685b21fe0e91000598e2c7c3ed44a971e63fb8","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0014","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":680,"favorable_subsets":330},"correct_answer":"33/68","correct_answer_fraction":[33,68],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"2178/4913","plausible_wrong_fraction":[2178,4913],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0014","parameters":{"blue":6,"draws":3,"red":11,"target_red":2},"question":"An urn contains 11 red balls and 6 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"e908ebdd3e52da22634e62f991ae2fc3a0458f36c219b3ed28d5a19fd6211932","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0016","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":55,"total_score":4136},"correct_answer":"376/5","correct_answer_fraction":[376,5],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"227/3","plausible_wrong_fraction":[227,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0016","parameters":{"counts":[27,8,20],"means":[76,78,73]},"question":"Three classes contain 27, 8, and 20 students. Their mean test scores are 76, 78, and 73, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"3875bd08def74d0e11b005645b496eb708a1881c2dd3fff30a05fe1efd9427b6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0017","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"5/21","remaining_worker":"A"},"correct_answer":"35/3","correct_answer_fraction":[35,3],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"39/7","plausible_wrong_fraction":[39,7],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0017","parameters":{"a_hours":14,"b_hours":6,"together_hours":1},"question":"Worker A can finish a job alone in 14 hours and worker B can finish it alone in 6 hours. They work together for 1 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"63950260067a216606485f4a2cff4255ce3cd984b065ac0ba205e4c11d419795","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0004","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"125/100","width_multiplier":"90/100"},"correct_answer":"20475/4","correct_answer_fraction":[20475,4],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"10465/2","plausible_wrong_fraction":[10465,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0004","parameters":{"decrease":10,"increase":25,"length":65,"width":70},"question":"A rectangle initially has length 65 and width 70. Its length is increased by 25% while its width is decreased by 10%. What is the new area? Give an exact value.","question_sha256":"079a5bf1d5c2d7811c75ce416196a72413682b1bf29684cdc98d4ab474f67761","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0003","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":72,"total_symbols":8},"correct_answer":"560","correct_answer_fraction":[560,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"40320","plausible_wrong_fraction":[40320,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0003","parameters":{"counts":[3,3,2],"letters":["H","D","F"],"multiset":"HHHDDDFF"},"question":"How many distinct strings can be formed by rearranging all letters of HHHDDDFF?","question_sha256":"60821d0b09bd6a73ce1f0febd0d5ecad9fe3f6b65f8769f85ff26a60dcbd7efc","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":79,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0020","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":51,"total_score":3924},"correct_answer":"1308/17","correct_answer_fraction":[1308,17],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"76","plausible_wrong_fraction":[76,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0020","parameters":{"counts":[14,20,17],"means":[65,81,82]},"question":"Three classes contain 14, 20, and 17 students. Their mean test scores are 65, 81, and 82, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"247378d5d60401d06355e2b9c063a73cc3f64282fc896bc68110055075aba4b0","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0010","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":65,"total_score":4917},"correct_answer":"4917/65","correct_answer_fraction":[4917,65],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"76","plausible_wrong_fraction":[76,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0010","parameters":{"counts":[21,28,16],"means":[93,67,68]},"question":"Three classes contain 21, 28, and 16 students. Their mean test scores are 93, 67, and 68, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"78c6bf16f26d16bbc104c4f9940b4f86676b322959b6ce0442a61bd8afa0fff8","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0006","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":2024,"favorable_subsets":858},"correct_answer":"39/92","correct_answer_fraction":[39,92],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"1859/4608","plausible_wrong_fraction":[1859,4608],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0006","parameters":{"blue":11,"draws":3,"red":13,"target_red":2},"question":"An urn contains 13 red balls and 11 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"b9b0134001287bd2d77a0f98b6fb6823b77ceabaebb9151fbe35333001192988","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0004","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":35,"total_score":2730},"correct_answer":"78","correct_answer_fraction":[78,1],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"238/3","plausible_wrong_fraction":[238,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0004","parameters":{"counts":[6,16,13],"means":[82,70,86]},"question":"Three classes contain 6, 16, and 13 students. Their mean test scores are 82, 70, and 86, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"40fbe9250d850e4e3a56443c59db12d6fab9369b179c8d4b4ef8e257cc88710b","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0014","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":12,"total_symbols":6},"correct_answer":"60","correct_answer_fraction":[60,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"720","plausible_wrong_fraction":[720,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0014","parameters":{"counts":[2,3,1],"letters":["G","C","E"],"multiset":"GGCCCE"},"question":"How many distinct strings can be formed by rearranging all letters of GGCCCE?","question_sha256":"8509a665e7fea774c9088088a74cd18034ea46acd5c3794f1e88efe50c14402a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":77,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0016","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"130/100","width_multiplier":"75/100"},"correct_answer":"9945/4","correct_answer_fraction":[9945,4],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"5355/2","plausible_wrong_fraction":[5355,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0016","parameters":{"decrease":25,"increase":30,"length":85,"width":30},"question":"A rectangle initially has length 85 and width 30. Its length is increased by 30% while its width is decreased by 25%. What is the new area? Give an exact value.","question_sha256":"cad10391ec26adbed10003e6fe240dd15c16d99da21da2d09ed4093c2927696d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0010","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"52/133","remaining_worker":"A"},"correct_answer":"95/7","correct_answer_fraction":[95,7],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"119/19","plausible_wrong_fraction":[119,19],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0010","parameters":{"a_hours":19,"b_hours":7,"together_hours":2},"question":"Worker A can finish a job alone in 19 hours and worker B can finish it alone in 7 hours. They work together for 2 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"123009501a7ec31f8660a0cd2ea1e790057fd7d5b93126eb750bb2be8aaac81c","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0008","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"140/100","width_multiplier":"80/100"},"correct_answer":"588","correct_answer_fraction":[588,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"630","plausible_wrong_fraction":[630,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0008","parameters":{"decrease":20,"increase":40,"length":35,"width":15},"question":"A rectangle initially has length 35 and width 15. Its length is increased by 40% while its width is decreased by 20%. What is the new area? Give an exact value.","question_sha256":"996265ae17fa9ecd0e843a9a49fc8abb0e8b2e6eb4dc4dbbada65121ffec8ec3","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0002","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["178/24","178/33"],"total_distance":356},"correct_answer":"528/19","correct_answer_fraction":[528,19],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"57/2","plausible_wrong_fraction":[57,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0002","parameters":{"distance":178,"speeds":[24,33]},"question":"A vehicle travels 178 km from A to B at 24 km/h and returns the same 178 km at 33 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"adc00ff14628f4eeead98cb9d0593ad15bd97c837241224b6c104462bf060d0a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0006","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":3,"failure_probability":"11/12"},"correct_answer":"397/1728","correct_answer_fraction":[397,1728],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"1/4","plausible_wrong_fraction":[1,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0006","parameters":{"success_denominator":12,"success_numerator":1,"trials":3},"question":"Each of 3 independent trials succeeds with probability 1/12. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"b84ab7f3f024e95f1036467d6e6d9732733c0c0a1bba4e141c322c924204fef8","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0011","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1771,"favorable_subsets":819},"correct_answer":"117/253","correct_answer_fraction":[117,253],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"5292/12167","plausible_wrong_fraction":[5292,12167],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0011","parameters":{"blue":9,"draws":3,"red":14,"target_red":2},"question":"An urn contains 14 red balls and 9 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"8f68f82898b3bb0b6e84e404500e1040da455d97cae0653ff7fab7a8281796b1","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0020","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":4,"failure_probability":"17/20"},"correct_answer":"76479/160000","correct_answer_fraction":[76479,160000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"3/5","plausible_wrong_fraction":[3,5],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0020","parameters":{"success_denominator":20,"success_numerator":3,"trials":4},"question":"Each of 4 independent trials succeeds with probability 3/20. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"946a522cafa96553ef1d25284cdb844b430b023788690b67c6adcf504e04cb45","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0011","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":6,"failure_probability":"11/12"},"correct_answer":"1214423/2985984","correct_answer_fraction":[1214423,2985984],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"1/2","plausible_wrong_fraction":[1,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0011","parameters":{"success_denominator":12,"success_numerator":1,"trials":6},"question":"Each of 6 independent trials succeeds with probability 1/12. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"9da5dcfd909e62f0be1b32f9b33ac26f5c89e1b69b5fa461858e7348900862ff","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0013","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":2600,"favorable_subsets":1014},"correct_answer":"39/100","correct_answer_fraction":[39,100],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"3/8","plausible_wrong_fraction":[3,8],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0013","parameters":{"blue":13,"draws":3,"red":13,"target_red":2},"question":"An urn contains 13 red balls and 13 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"9d3b85f1e5d027a2c1dc9fe72efb340dbbe1169bacdba261e0af25472ab3dd59","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0019","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"29/138","remaining_worker":"A"},"correct_answer":"115/6","correct_answer_fraction":[115,6],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"132/23","plausible_wrong_fraction":[132,23],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0019","parameters":{"a_hours":23,"b_hours":6,"together_hours":1},"question":"Worker A can finish a job alone in 23 hours and worker B can finish it alone in 6 hours. They work together for 1 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"f1852eac843b3d30407a6193dfa78316b1b7f791118231182ce203b86131f5d1","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0011","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["146/69","146/24"],"total_distance":292},"correct_answer":"1104/31","correct_answer_fraction":[1104,31],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"93/2","plausible_wrong_fraction":[93,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0011","parameters":{"distance":146,"speeds":[69,24]},"question":"A vehicle travels 146 km from A to B at 69 km/h and returns the same 146 km at 24 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"5cf699f67f5d2ae70b7d66a87210d734d7f276faa2ab685e037a97431db0eb9c","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0007","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":736,"true_positive":736},"correct_answer":"1/2","correct_answer_fraction":[1,2],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"23/25","plausible_wrong_fraction":[23,25],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0007","parameters":{"population":10000,"prevalence":8,"sensitivity":92,"specificity":92},"question":"In a population, 8% of people have a condition. A test has 92% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"06ee8af3741fd69c1a55f9c015303a3c36c967321dff7726d7fba32908bcac57","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0013","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":37,"total_score":3219},"correct_answer":"87","correct_answer_fraction":[87,1],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"254/3","plausible_wrong_fraction":[254,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0013","parameters":{"counts":[12,9,16],"means":[94,67,93]},"question":"Three classes contain 12, 9, and 16 students. Their mean test scores are 94, 67, and 93, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"e015e91a756132283d65da3e6642460f2e15872082c6f97a107b8a327e7779b4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0019","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":72,"total_symbols":8},"correct_answer":"560","correct_answer_fraction":[560,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"40320","plausible_wrong_fraction":[40320,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0019","parameters":{"counts":[3,3,2],"letters":["G","D","H"],"multiset":"GGGDDDHH"},"question":"How many distinct strings can be formed by rearranging all letters of GGGDDDHH?","question_sha256":"db93030febeacd3d4f8447325de5c988b60c6498ee4641d181f75b792bbbf621","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":79,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0008","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"19/24","remaining_worker":"A"},"correct_answer":"12","correct_answer_fraction":[12,1],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"119/12","plausible_wrong_fraction":[119,12],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0008","parameters":{"a_hours":24,"b_hours":14,"together_hours":7},"question":"Worker A can finish a job alone in 24 hours and worker B can finish it alone in 14 hours. They work together for 7 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"51e635c8d2f450d159b8e1045974630e2fe3d0ed4eb3d7fca8a8cc79011e25f6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0007","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":969,"favorable_subsets":360},"correct_answer":"120/323","correct_answer_fraction":[120,323],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"2430/6859","plausible_wrong_fraction":[2430,6859],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0007","parameters":{"blue":10,"draws":3,"red":9,"target_red":2},"question":"An urn contains 9 red balls and 10 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"4431ec84b5d32086370b7c54ba611578f691b630682e47502e552e47375f6083","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0005","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"130/100","width_multiplier":"70/100"},"correct_answer":"5733/2","correct_answer_fraction":[5733,2],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"3150","plausible_wrong_fraction":[3150,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0005","parameters":{"decrease":30,"increase":30,"length":45,"width":70},"question":"A rectangle initially has length 45 and width 70. Its length is increased by 30% while its width is decreased by 30%. What is the new area? Give an exact value.","question_sha256":"2bd35df8f37616b904bdbc1b14f2f993440ad41b043e3f256a0fa8be8b4ca3fd","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0002","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["115/100","88/100","90/100"]},"correct_answer":"9108/5","correct_answer_fraction":[9108,5],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1860","plausible_wrong_fraction":[1860,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0002","parameters":{"base":2000,"changes":[15,12,10],"signs":[1,-1,-1]},"question":"A quantity starts at 2000. It increases by 15%, then decreases by 12%, and finally decreases by 10%. What is the final value? Give an exact value.","question_sha256":"8aebfc9250946783b5a44de93c3471a9d879f85f1970481ceacf9f8dcb03a9e6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0000","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["108/100","70/100","110/100"]},"correct_answer":"12474/25","correct_answer_fraction":[12474,25],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"528","plausible_wrong_fraction":[528,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0000","parameters":{"base":600,"changes":[8,30,10],"signs":[1,-1,1]},"question":"A quantity starts at 600. It increases by 8%, then decreases by 30%, and finally increases by 10%. What is the final value? Give an exact value.","question_sha256":"1bd6172c1373061966058994f2b0c2a1b9330da1eb02e04c6e713e6228516f8e","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":144,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0008","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":294,"true_positive":170},"correct_answer":"85/232","correct_answer_fraction":[85,232],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"17/20","plausible_wrong_fraction":[17,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0008","parameters":{"population":10000,"prevalence":2,"sensitivity":85,"specificity":97},"question":"In a population, 2% of people have a condition. A test has 85% sensitivity and 97% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"a59fab29a21b3047a959677d657151ac65a763af90fb4210b7ee4990e2d5a4c4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0005","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["150/66","150/33"],"total_distance":300},"correct_answer":"44","correct_answer_fraction":[44,1],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"99/2","plausible_wrong_fraction":[99,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0005","parameters":{"distance":150,"speeds":[66,33]},"question":"A vehicle travels 150 km from A to B at 66 km/h and returns the same 150 km at 33 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"b8d129b97e68e25bcef98f809de441b6a303f8a32d84023804bd1782849f4295","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0010","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["175/51","175/48"],"total_distance":350},"correct_answer":"544/11","correct_answer_fraction":[544,11],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"99/2","plausible_wrong_fraction":[99,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0010","parameters":{"distance":175,"speeds":[51,48]},"question":"A vehicle travels 175 km from A to B at 51 km/h and returns the same 175 km at 48 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"758ea51f968f11f587606050e5abb2b0824c4476bc6ed6de13c9fb18253d5480","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0014","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"9/10","remaining_worker":"A"},"correct_answer":"36/5","correct_answer_fraction":[36,5],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"15/2","plausible_wrong_fraction":[15,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0014","parameters":{"a_hours":12,"b_hours":15,"together_hours":6},"question":"Worker A can finish a job alone in 12 hours and worker B can finish it alone in 15 hours. They work together for 6 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"1db471740871bfb2b246a86781b7967f772ca9a74ed01ccb6286421b968670ab","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0008","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":560,"favorable_subsets":150},"correct_answer":"15/56","correct_answer_fraction":[15,56],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"135/512","plausible_wrong_fraction":[135,512],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0008","parameters":{"blue":10,"draws":3,"red":6,"target_red":2},"question":"An urn contains 6 red balls and 10 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"d58192b0649e30744296d51d78f723e29bf94c48dc056a8bf6c72ed4ecf66ecf","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0015","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":3,"failure_probability":"19/20"},"correct_answer":"1141/8000","correct_answer_fraction":[1141,8000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"3/20","plausible_wrong_fraction":[3,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0015","parameters":{"success_denominator":20,"success_numerator":1,"trials":3},"question":"Each of 3 independent trials succeeds with probability 1/20. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"97d49fcc256a8f873a21908ab28f12c2b8afb21a1e54fb2b8a47426c144caa26","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0008","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["81/36","81/75"],"total_distance":162},"correct_answer":"1800/37","correct_answer_fraction":[1800,37],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"111/2","plausible_wrong_fraction":[111,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0008","parameters":{"distance":81,"speeds":[36,75]},"question":"A vehicle travels 81 km from A to B at 36 km/h and returns the same 81 km at 75 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"5873e40786bd9331f705f1374ee298310babd07930a4e7f016e0e4a70590ebaf","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":167,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0014","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":7,"failure_probability":"14/15"},"correct_answer":"65445871/170859375","correct_answer_fraction":[65445871,170859375],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"7/15","plausible_wrong_fraction":[7,15],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0014","parameters":{"success_denominator":15,"success_numerator":1,"trials":7},"question":"Each of 7 independent trials succeeds with probability 1/15. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"d43d5fd99f163ea2e266f8d8437ee35fac9ece398ab4ecf34b7f38ba4bb3b6eb","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0014","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[8,11,17,29,53,101]},"correct_answer":"101","correct_answer_fraction":[101,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"53","plausible_wrong_fraction":[53,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0014","parameters":{"a0":8,"multiplier":2,"n":5,"offset":-5},"question":"A sequence is defined by a_0 = 8 and a_(k+1) = 2a_k - 5 for k >= 0. What is a_5?","question_sha256":"2e245fba1ba362acd23695483d6ba8ec3d30d3fd51e94f1dc10fefbf63ae0bf6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0004","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":5,"failure_probability":"11/12"},"correct_answer":"87781/248832","correct_answer_fraction":[87781,248832],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"5/12","plausible_wrong_fraction":[5,12],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0004","parameters":{"success_denominator":12,"success_numerator":1,"trials":5},"question":"Each of 5 independent trials succeeds with probability 1/12. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"e45d9f4830bc9d169949c8f95e527017753ec74e908c9de7aa619fbaaf929475","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0004","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["107/54","107/69"],"total_distance":214},"correct_answer":"2484/41","correct_answer_fraction":[2484,41],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"123/2","plausible_wrong_fraction":[123,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0004","parameters":{"distance":107,"speeds":[54,69]},"question":"A vehicle travels 107 km from A to B at 54 km/h and returns the same 107 km at 69 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"1002c45cd0dffb011f1fd092e736aa46365979fc9816241828c60c634106cf16","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0022","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"115/100","width_multiplier":"70/100"},"correct_answer":"3381/4","correct_answer_fraction":[3381,4],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"1785/2","plausible_wrong_fraction":[1785,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0022","parameters":{"decrease":30,"increase":15,"length":70,"width":15},"question":"A rectangle initially has length 70 and width 15. Its length is increased by 15% while its width is decreased by 30%. What is the new area? Give an exact value.","question_sha256":"73a7e73bf94404420b04e39aeac1babbddbf4b9908775883678563b1cec75230","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0013","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"37/168","remaining_worker":"A"},"correct_answer":"147/8","correct_answer_fraction":[147,8],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"304/21","plausible_wrong_fraction":[304,21],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0013","parameters":{"a_hours":21,"b_hours":16,"together_hours":2},"question":"Worker A can finish a job alone in 21 hours and worker B can finish it alone in 16 hours. They work together for 2 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"14b94d471a4bce5ecb52011325a0c63a1e7d5415e19c5194de75fe8ab7883947","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0001","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":3,"failure_probability":"13/15"},"correct_answer":"1178/3375","correct_answer_fraction":[1178,3375],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"2/5","plausible_wrong_fraction":[2,5],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0001","parameters":{"success_denominator":15,"success_numerator":2,"trials":3},"question":"Each of 3 independent trials succeeds with probability 2/15. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"6124fbc8d11c8b56cc009b561845b03d388d21a057dca285ee96d5d63092f1aa","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0015","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["122/24","122/84"],"total_distance":244},"correct_answer":"112/3","correct_answer_fraction":[112,3],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"54","plausible_wrong_fraction":[54,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0015","parameters":{"distance":122,"speeds":[24,84]},"question":"A vehicle travels 122 km from A to B at 24 km/h and returns the same 122 km at 84 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"25501add18943471f8bbfa8829154da769584dc0046e343c7d049148bb250cfb","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0002","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[1,6,21,66,201,606,1821,5466]},"correct_answer":"5466","correct_answer_fraction":[5466,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"1821","plausible_wrong_fraction":[1821,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0002","parameters":{"a0":1,"multiplier":3,"n":7,"offset":3},"question":"A sequence is defined by a_0 = 1 and a_(k+1) = 3a_k + 3 for k >= 0. What is a_7?","question_sha256":"2e853bb68e7eea5adabbedcb7f62f1d5393f2afecdf3d460e0494328b88ada0d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0013","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"140/100","width_multiplier":"70/100"},"correct_answer":"1470","correct_answer_fraction":[1470,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"1650","plausible_wrong_fraction":[1650,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0013","parameters":{"decrease":30,"increase":40,"length":20,"width":75},"question":"A rectangle initially has length 20 and width 75. Its length is increased by 40% while its width is decreased by 30%. What is the new area? Give an exact value.","question_sha256":"0d4a8d6c2d9d443aaf0316694c71a9e7489c7056afd3b4781f757353d0dcf9b8","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0007","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":3,"failure_probability":"17/20"},"correct_answer":"3087/8000","correct_answer_fraction":[3087,8000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"9/20","plausible_wrong_fraction":[9,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0007","parameters":{"success_denominator":20,"success_numerator":3,"trials":3},"question":"Each of 3 independent trials succeeds with probability 3/20. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"af502d4604530edc4911e332f4c70e8da48097a51196d51dec088e3bc19c4955","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0020","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1425,"true_positive":375},"correct_answer":"5/24","correct_answer_fraction":[5,24],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"3/4","plausible_wrong_fraction":[3,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0020","parameters":{"population":10000,"prevalence":5,"sensitivity":75,"specificity":85},"question":"In a population, 5% of people have a condition. A test has 75% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"9f6b633318df8748c6143e4ffc8a3b04ebf141fffe569c0a237b46ac3f1bbf06","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0015","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"130/100","width_multiplier":"70/100"},"correct_answer":"9555/4","correct_answer_fraction":[9555,4],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"2625","plausible_wrong_fraction":[2625,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0015","parameters":{"decrease":30,"increase":30,"length":35,"width":75},"question":"A rectangle initially has length 35 and width 75. Its length is increased by 30% while its width is decreased by 30%. What is the new area? Give an exact value.","question_sha256":"509583af692c5c8a220fef57a2c89bb47fd6fc691a0646aa1ba4d3b099b66c17","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0010","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1380,"true_positive":640},"correct_answer":"32/101","correct_answer_fraction":[32,101],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"4/5","plausible_wrong_fraction":[4,5],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0010","parameters":{"population":10000,"prevalence":8,"sensitivity":80,"specificity":85},"question":"In a population, 8% of people have a condition. A test has 80% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"b3e03a09dd21a07152a00d29dcfd512e87758042ee2340c2b8470399accda92b","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0008","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[6,17,39,83,171,347,699,1403,2811]},"correct_answer":"2811","correct_answer_fraction":[2811,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"1403","plausible_wrong_fraction":[1403,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0008","parameters":{"a0":6,"multiplier":2,"n":8,"offset":5},"question":"A sequence is defined by a_0 = 6 and a_(k+1) = 2a_k + 5 for k >= 0. What is a_8?","question_sha256":"b044bab2d4e7fb2acb8903596ba67757a4d22543fc1b5e6b0ef92a76787fd860","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0022","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":816,"favorable_subsets":324},"correct_answer":"27/68","correct_answer_fraction":[27,68],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"3/8","plausible_wrong_fraction":[3,8],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0022","parameters":{"blue":9,"draws":3,"red":9,"target_red":2},"question":"An urn contains 9 red balls and 9 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"02d22700676bc96bd2a4b3cfba368a6ba0e9849019ec0dc5350cd1626f4afce2","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":187,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0019","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1771,"favorable_subsets":585},"correct_answer":"585/1771","correct_answer_fraction":[585,1771],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"3900/12167","plausible_wrong_fraction":[3900,12167],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0019","parameters":{"blue":13,"draws":3,"red":10,"target_red":2},"question":"An urn contains 10 red balls and 13 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"75e3ec165fdcacd86c8c0326af6626b105811fb0a9b9878f38ada3482e400c2c","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0010","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"125/100","width_multiplier":"80/100"},"correct_answer":"3575","correct_answer_fraction":[3575,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"15015/4","plausible_wrong_fraction":[15015,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0010","parameters":{"decrease":20,"increase":25,"length":55,"width":65},"question":"A rectangle initially has length 55 and width 65. Its length is increased by 25% while its width is decreased by 20%. What is the new area? Give an exact value.","question_sha256":"db127bcf035cc3bea8b9a2363dc7ba1c77ca81186414fd43a76e2d6466ad1c59","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0010","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[6,20,62,188,566,1700,5102,15308]},"correct_answer":"15308","correct_answer_fraction":[15308,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"5102","plausible_wrong_fraction":[5102,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0010","parameters":{"a0":6,"multiplier":3,"n":7,"offset":2},"question":"A sequence is defined by a_0 = 6 and a_(k+1) = 3a_k + 2 for k >= 0. What is a_7?","question_sha256":"857bd76cc59f223b30d496c35e471963e970b51f3b81af88e002231e48a7df8d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0012","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":58,"total_score":4264},"correct_answer":"2132/29","correct_answer_fraction":[2132,29],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"76","plausible_wrong_fraction":[76,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0012","parameters":{"counts":[26,19,13],"means":[64,78,86]},"question":"Three classes contain 26, 19, and 13 students. Their mean test scores are 64, 78, and 86, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"55256fa5bc14a5b38841580e0c6fbbe6e28ae1cc5c23a5db006c65964003f069","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0004","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["108/100","92/100","112/100"]},"correct_answer":"904176/625","correct_answer_fraction":[904176,625],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1456","plausible_wrong_fraction":[1456,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0004","parameters":{"base":1300,"changes":[8,8,12],"signs":[1,-1,1]},"question":"A quantity starts at 1300. It increases by 8%, then decreases by 8%, and finally increases by 12%. What is the final value? Give an exact value.","question_sha256":"e0e3e53c21cb44f9d31dab7b941c42eb45fa3615197f9abf2ff12ebf86e52933","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":144,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0003","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"3/16","remaining_worker":"A"},"correct_answer":"14","correct_answer_fraction":[14,1],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"15/2","plausible_wrong_fraction":[15,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0003","parameters":{"a_hours":16,"b_hours":8,"together_hours":1},"question":"Worker A can finish a job alone in 16 hours and worker B can finish it alone in 8 hours. They work together for 1 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"94cc3e03ed906dece733eb59bc997e4895dc8661c06b8a92a21f8f39abded18e","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0001","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"15/28","remaining_worker":"A"},"correct_answer":"40/7","correct_answer_fraction":[40,7],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"21/4","plausible_wrong_fraction":[21,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0001","parameters":{"a_hours":8,"b_hours":7,"together_hours":2},"question":"Worker A can finish a job alone in 8 hours and worker B can finish it alone in 7 hours. They work together for 2 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"bc98b3524e8d7768f5370ef0488a5d71bc2b0afb64d402af4f474ee26905fd8c","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":259,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0009","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":60,"total_score":3822},"correct_answer":"637/10","correct_answer_fraction":[637,10],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"63","plausible_wrong_fraction":[63,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0009","parameters":{"counts":[15,21,24],"means":[53,79,57]},"question":"Three classes contain 15, 21, and 24 students. Their mean test scores are 53, 79, and 57, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"25a6f141b7a9ba94ba95c68ffe8305aa470806a631dc43c98ab902d83856bb6d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0015","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":288,"total_symbols":9},"correct_answer":"1260","correct_answer_fraction":[1260,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"362880","plausible_wrong_fraction":[362880,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0015","parameters":{"counts":[4,3,2],"letters":["E","H","B"],"multiset":"EEEEHHHBB"},"question":"How many distinct strings can be formed by rearranging all letters of EEEEHHHBB?","question_sha256":"e5cf4d7f43f981ea6b83d843d07edeea45dcfd3e2025102c2124f2d01099cd4d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0000","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["86/78","86/87"],"total_distance":172},"correct_answer":"4524/55","correct_answer_fraction":[4524,55],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"165/2","plausible_wrong_fraction":[165,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0000","parameters":{"distance":86,"speeds":[78,87]},"question":"A vehicle travels 86 km from A to B at 78 km/h and returns the same 86 km at 87 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"8a48443d801afd24bc3ea0977d9893453f124c02d97b8dd22464580ad311b65a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":167,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0002","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":3,"failure_probability":"7/8"},"correct_answer":"169/512","correct_answer_fraction":[169,512],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"3/8","plausible_wrong_fraction":[3,8],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0002","parameters":{"success_denominator":8,"success_numerator":1,"trials":3},"question":"Each of 3 independent trials succeeds with probability 1/8. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"aab662857e58a1da4d26de08228a148a35ea68c1d22db513e87b57fbfd592f6c","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":147,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0009","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["173/33","173/72"],"total_distance":346},"correct_answer":"1584/35","correct_answer_fraction":[1584,35],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"105/2","plausible_wrong_fraction":[105,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0009","parameters":{"distance":173,"speeds":[33,72]},"question":"A vehicle travels 173 km from A to B at 33 km/h and returns the same 173 km at 72 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"0ae07168bfb682e4efd4b7a4499d97be67044aec6cbff365274c91f540ad9898","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0018","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":455,"favorable_subsets":216},"correct_answer":"216/455","correct_answer_fraction":[216,455],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"54/125","plausible_wrong_fraction":[54,125],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0018","parameters":{"blue":6,"draws":3,"red":9,"target_red":2},"question":"An urn contains 9 red balls and 6 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"1628958e8175124ee36c3f08eb87a128119235833d9e2f856a4b7287da1d6082","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":187,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0007","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[0,5,20,65,200,605]},"correct_answer":"605","correct_answer_fraction":[605,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"200","plausible_wrong_fraction":[200,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0007","parameters":{"a0":0,"multiplier":3,"n":5,"offset":5},"question":"A sequence is defined by a_0 = 0 and a_(k+1) = 3a_k + 5 for k >= 0. What is a_5?","question_sha256":"c8c40102ffe8ed1a4e8609ebd567b74c6a299178fd8ea1b3113cdf5c1edb49b7","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0007","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":72,"total_symbols":8},"correct_answer":"560","correct_answer_fraction":[560,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"40320","plausible_wrong_fraction":[40320,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0007","parameters":{"counts":[3,3,2],"letters":["F","E","H"],"multiset":"FFFEEEHH"},"question":"How many distinct strings can be formed by rearranging all letters of FFFEEEHH?","question_sha256":"72d399e1e28d1f406e5b99dff709cc71b821e949844d390dd3dc79b44217761a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":79,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0011","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["130/100","70/100","90/100"]},"correct_answer":"2457/2","correct_answer_fraction":[2457,2],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1350","plausible_wrong_fraction":[1350,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0011","parameters":{"base":1500,"changes":[30,30,10],"signs":[1,-1,-1]},"question":"A quantity starts at 1500. It increases by 30%, then decreases by 30%, and finally decreases by 10%. What is the final value? Give an exact value.","question_sha256":"22d6bddd3fa814e8a9c0aee6c03e37739e00dd65e4ba0ff200693322c3af1836","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0016","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":48,"total_symbols":7},"correct_answer":"105","correct_answer_fraction":[105,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"5040","plausible_wrong_fraction":[5040,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0016","parameters":{"counts":[4,2,1],"letters":["G","D","C"],"multiset":"GGGGDDC"},"question":"How many distinct strings can be formed by rearranging all letters of GGGGDDC?","question_sha256":"31d9371ab6f6e96c3f24eb68839b0dc82d6942436f014017ead7de6c7b0a74c9","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":78,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0002","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1330,"favorable_subsets":630},"correct_answer":"9/19","correct_answer_fraction":[9,19],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"150/343","plausible_wrong_fraction":[150,343],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0002","parameters":{"blue":6,"draws":3,"red":15,"target_red":2},"question":"An urn contains 15 red balls and 6 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"cb3b2b6e96d02372a7c80288917e6c58e385fa236cfd4ca1297e8b2597924669","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0009","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["120/100","88/100","70/100"]},"correct_answer":"31416/25","correct_answer_fraction":[31416,25],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1326","plausible_wrong_fraction":[1326,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0009","parameters":{"base":1700,"changes":[20,12,30],"signs":[1,-1,-1]},"question":"A quantity starts at 1700. It increases by 20%, then decreases by 12%, and finally decreases by 30%. What is the final value? Give an exact value.","question_sha256":"d5e8b061b478afe4a2df075f0abfdb29fff36f739ea77f93a8649127d9dd56ac","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0017","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1920,"true_positive":360},"correct_answer":"3/19","correct_answer_fraction":[3,19],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"9/10","plausible_wrong_fraction":[9,10],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0017","parameters":{"population":10000,"prevalence":4,"sensitivity":90,"specificity":80},"question":"In a population, 4% of people have a condition. A test has 90% sensitivity and 80% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"3f4f43eae6c547be64c75e6473f58f93820bc4516edca0a7258370368bfea59e","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0016","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1425,"true_positive":475},"correct_answer":"1/4","correct_answer_fraction":[1,4],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"19/20","plausible_wrong_fraction":[19,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0016","parameters":{"population":10000,"prevalence":5,"sensitivity":95,"specificity":85},"question":"In a population, 5% of people have a condition. A test has 95% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"d48ab1b04dc7fcae0a1b0d04324db15aae5960b9d9ce509eceefbad4dfd1f0e6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0019","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"110/100","width_multiplier":"95/100"},"correct_answer":"2717/2","correct_answer_fraction":[2717,2],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"1365","plausible_wrong_fraction":[1365,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0019","parameters":{"decrease":5,"increase":10,"length":65,"width":20},"question":"A rectangle initially has length 65 and width 20. Its length is increased by 10% while its width is decreased by 5%. What is the new area? Give an exact value.","question_sha256":"5fa5b2a1209c9e5aa20a3e8f2d57cab057b6228a235e305c45eae5ad67ab5214","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":159,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0001","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":24,"total_symbols":7},"correct_answer":"210","correct_answer_fraction":[210,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"5040","plausible_wrong_fraction":[5040,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0001","parameters":{"counts":[3,2,2],"letters":["A","F","B"],"multiset":"AAAFFBB"},"question":"How many distinct strings can be formed by rearranging all letters of AAAFFBB?","question_sha256":"76021d9c5c98a8068d9c5d2aea219bfea93ac5058728a3a0fc7bba9d9734d152","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":78,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0009","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":286,"favorable_subsets":80},"correct_answer":"40/143","correct_answer_fraction":[40,143],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"600/2197","plausible_wrong_fraction":[600,2197],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0009","parameters":{"blue":8,"draws":3,"red":5,"target_red":2},"question":"An urn contains 5 red balls and 8 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"add04d058565adf640a9dcfff297703a340740655997c15a65ac6487629c10ef","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":187,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0007","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"129/230","remaining_worker":"A"},"correct_answer":"161/10","correct_answer_fraction":[161,10],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"340/23","plausible_wrong_fraction":[340,23],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0007","parameters":{"a_hours":23,"b_hours":20,"together_hours":6},"question":"Worker A can finish a job alone in 23 hours and worker B can finish it alone in 20 hours. They work together for 6 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"409baccb3c88e74e8c99eeb2c1b3d5e71d91f4910b906bc6bddf25d5d5456c4b","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0021","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1380,"true_positive":720},"correct_answer":"12/35","correct_answer_fraction":[12,35],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"9/10","plausible_wrong_fraction":[9,10],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0021","parameters":{"population":10000,"prevalence":8,"sensitivity":90,"specificity":85},"question":"In a population, 8% of people have a condition. A test has 90% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"244079c43563edbfc924c744f7e75c27e1c786ee2aa81ebc60dce74661abd9d4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0001","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":68,"total_score":4174},"correct_answer":"2087/34","correct_answer_fraction":[2087,34],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"188/3","plausible_wrong_fraction":[188,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0001","parameters":{"counts":[24,25,19],"means":[58,52,78]},"question":"Three classes contain 24, 25, and 19 students. Their mean test scores are 58, 52, and 78, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"a1ac2a05ededd1310e279d69a1c2e0c6c9289275102fb53afff7d0aad853f40a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0018","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1380,"true_positive":760},"correct_answer":"38/107","correct_answer_fraction":[38,107],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"19/20","plausible_wrong_fraction":[19,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0018","parameters":{"population":10000,"prevalence":8,"sensitivity":95,"specificity":85},"question":"In a population, 8% of people have a condition. A test has 95% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"8e265a1942d14a165627a7545814750d4d80311a4a680f5e57aaeca41655b7a2","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0014","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["112/100","70/100","75/100"]},"correct_answer":"5292/5","correct_answer_fraction":[5292,5],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1026","plausible_wrong_fraction":[1026,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0014","parameters":{"base":1800,"changes":[12,30,25],"signs":[1,-1,-1]},"question":"A quantity starts at 1800. It increases by 12%, then decreases by 30%, and finally decreases by 25%. What is the final value? Give an exact value.","question_sha256":"82e21dfbaa3519e93de85e903728fbcba70b1fd0ad6a3142d1010c3966414d75","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0001","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[8,21,60,177,528,1581,4740,14217,42648]},"correct_answer":"42648","correct_answer_fraction":[42648,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"14217","plausible_wrong_fraction":[14217,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0001","parameters":{"a0":8,"multiplier":3,"n":8,"offset":-3},"question":"A sequence is defined by a_0 = 8 and a_(k+1) = 3a_k - 3 for k >= 0. What is a_8?","question_sha256":"8362885a92689cbb2335161abb77f30ddd855c761f9272b01e02adae6ee04d03","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0004","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1140,"favorable_subsets":273},"correct_answer":"91/380","correct_answer_fraction":[91,380],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"1911/8000","plausible_wrong_fraction":[1911,8000],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0004","parameters":{"blue":13,"draws":3,"red":7,"target_red":2},"question":"An urn contains 7 red balls and 13 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"892565e68d799d42fd363187367de62d2c3cbf6052e2a5063ffc1e82e8515e31","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0017","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1771,"favorable_subsets":726},"correct_answer":"66/161","correct_answer_fraction":[66,161],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"4752/12167","plausible_wrong_fraction":[4752,12167],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0017","parameters":{"blue":11,"draws":3,"red":12,"target_red":2},"question":"An urn contains 12 red balls and 11 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"6e1c52549d1cad535266baae879d0ecbb8db68a3b036523e27214291a63e670e","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0018","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":49,"total_score":3671},"correct_answer":"3671/49","correct_answer_fraction":[3671,49],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"73","plausible_wrong_fraction":[73,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0018","parameters":{"counts":[12,17,20],"means":[59,79,81]},"question":"Three classes contain 12, 17, and 20 students. Their mean test scores are 59, 79, and 81, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"96aa932df09090df717a29f3ff2fe81359675d42d2632505b60f9d224ba3a337","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0018","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["79/24","79/90"],"total_distance":158},"correct_answer":"720/19","correct_answer_fraction":[720,19],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"57","plausible_wrong_fraction":[57,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0018","parameters":{"distance":79,"speeds":[24,90]},"question":"A vehicle travels 79 km from A to B at 24 km/h and returns the same 79 km at 90 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"9b8957180a8b1a7d95237512e837a4c979ed46c56cf917bee7092426bdfa5f3d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":167,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0011","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":485,"true_positive":225},"correct_answer":"45/142","correct_answer_fraction":[45,142],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"3/4","plausible_wrong_fraction":[3,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0011","parameters":{"population":10000,"prevalence":3,"sensitivity":75,"specificity":95},"question":"In a population, 3% of people have a condition. A test has 75% sensitivity and 95% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"9030c56904071fc2dc7080fb5047f5fe0d6e3a45cbf112447c5c389247db3c35","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0002","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"125/100","width_multiplier":"75/100"},"correct_answer":"1125","correct_answer_fraction":[1125,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"1200","plausible_wrong_fraction":[1200,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0002","parameters":{"decrease":25,"increase":25,"length":40,"width":30},"question":"A rectangle initially has length 40 and width 30. Its length is increased by 25% while its width is decreased by 25%. What is the new area? Give an exact value.","question_sha256":"d03af6b2ee1a4034c1f5047e511a4f17a80a0015a014ecea5471d2122fad6f8a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0019","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["149/78","149/63"],"total_distance":298},"correct_answer":"3276/47","correct_answer_fraction":[3276,47],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"141/2","plausible_wrong_fraction":[141,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0019","parameters":{"distance":149,"speeds":[78,63]},"question":"A vehicle travels 149 km from A to B at 78 km/h and returns the same 149 km at 63 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"df32898e6c7311345af900b88d643cc2f3dac5afba69c5889d888a1d60c0c7f8","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0016","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["115/100","80/100","112/100"]},"correct_answer":"41216/25","correct_answer_fraction":[41216,25],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1712","plausible_wrong_fraction":[1712,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0016","parameters":{"base":1600,"changes":[15,20,12],"signs":[1,-1,1]},"question":"A quantity starts at 1600. It increases by 15%, then decreases by 20%, and finally increases by 12%. What is the final value? Give an exact value.","question_sha256":"8fc2ace4581c9532fea6574138d441e4d94cc93efcec6b7578f9f59b8ccedf73","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0019","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[3,8,18,38,78,158,318]},"correct_answer":"318","correct_answer_fraction":[318,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"158","plausible_wrong_fraction":[158,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0019","parameters":{"a0":3,"multiplier":2,"n":6,"offset":2},"question":"A sequence is defined by a_0 = 3 and a_(k+1) = 2a_k + 2 for k >= 0. What is a_6?","question_sha256":"b097b47f6ccbcdc24e7781f8369be0e799d1f28a9b907134640e73be6d47c8f6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0003","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[-3,-10,-31,-94,-283,-850,-2551,-7654]},"correct_answer":"-7654","correct_answer_fraction":[-7654,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"-2551","plausible_wrong_fraction":[-2551,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0003","parameters":{"a0":-3,"multiplier":3,"n":7,"offset":-1},"question":"A sequence is defined by a_0 = -3 and a_(k+1) = 3a_k - 1 for k >= 0. What is a_7?","question_sha256":"2a68424a9daeb23df5dca2746c6b1553efb3db64cff51a47142341b6597f46be","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":81,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0007","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"125/100","width_multiplier":"75/100"},"correct_answer":"2625","correct_answer_fraction":[2625,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"2800","plausible_wrong_fraction":[2800,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0007","parameters":{"decrease":25,"increase":25,"length":70,"width":40},"question":"A rectangle initially has length 70 and width 40. Its length is increased by 25% while its width is decreased by 25%. What is the new area? Give an exact value.","question_sha256":"e1d81a4714576897bd67128113c5c2196326355c7b9934a00335a6c020ee6b1d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0006","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1320,"true_positive":1020},"correct_answer":"17/39","correct_answer_fraction":[17,39],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"17/20","plausible_wrong_fraction":[17,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0006","parameters":{"population":10000,"prevalence":12,"sensitivity":85,"specificity":85},"question":"In a population, 12% of people have a condition. A test has 85% sensitivity and 85% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"081b21566a9034272e6ffabb6c379345bf64c4225352be70dcd2a3a8b7cfc5c3","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":258,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0004","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"56/57","remaining_worker":"A"},"correct_answer":"117/19","correct_answer_fraction":[117,19],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"19/3","plausible_wrong_fraction":[19,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0004","parameters":{"a_hours":9,"b_hours":19,"together_hours":6},"question":"Worker A can finish a job alone in 9 hours and worker B can finish it alone in 19 hours. They work together for 6 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"f6516eab83c70f829661e776efb1c7a71e86b0db5830fad35ed07ea331967db6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0006","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[-2,0,4,12,28,60,124]},"correct_answer":"124","correct_answer_fraction":[124,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"60","plausible_wrong_fraction":[60,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0006","parameters":{"a0":-2,"multiplier":2,"n":6,"offset":4},"question":"A sequence is defined by a_0 = -2 and a_(k+1) = 2a_k + 4 for k >= 0. What is a_6?","question_sha256":"4ee30c6ea9a3546e2cb7b41f9b403299ae05ba58e7d088c0adcb7f5e3cd60b9c","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":81,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0011","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":24,"total_symbols":7},"correct_answer":"210","correct_answer_fraction":[210,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"5040","plausible_wrong_fraction":[5040,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0011","parameters":{"counts":[2,3,2],"letters":["B","C","E"],"multiset":"BBCCCEE"},"question":"How many distinct strings can be formed by rearranging all letters of BBCCCEE?","question_sha256":"0feeb4d52f7772105a46814dc1a0dfd00e43b8c6b023c651dee1b6b1702477e5","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":78,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0004","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[7,23,71,215,647,1943,5831,17495,52487]},"correct_answer":"52487","correct_answer_fraction":[52487,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"17495","plausible_wrong_fraction":[17495,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0004","parameters":{"a0":7,"multiplier":3,"n":8,"offset":2},"question":"A sequence is defined by a_0 = 7 and a_(k+1) = 3a_k + 2 for k >= 0. What is a_8?","question_sha256":"2a4059b4b81d48d0913fe4d32c95f3939ee8335f45fd7e2e1589ea3ebd829bd4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0012","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[-3,-12,-39,-120,-363,-1092,-3279,-9840]},"correct_answer":"-9840","correct_answer_fraction":[-9840,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"-3279","plausible_wrong_fraction":[-3279,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0012","parameters":{"a0":-3,"multiplier":3,"n":7,"offset":-3},"question":"A sequence is defined by a_0 = -3 and a_(k+1) = 3a_k - 3 for k >= 0. What is a_7?","question_sha256":"332c51dd0053de99f86dbae1dc636d692ca5ea654c8ca2e726a924db30ec4680","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":81,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0002","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":950,"true_positive":450},"correct_answer":"9/28","correct_answer_fraction":[9,28],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"9/10","plausible_wrong_fraction":[9,10],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0002","parameters":{"population":10000,"prevalence":5,"sensitivity":90,"specificity":90},"question":"In a population, 5% of people have a condition. A test has 90% sensitivity and 90% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"65668125929e702544d68ad1329efa1a5a2a31d542880374669c9dbe9b9fc313","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0004","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":72,"total_symbols":8},"correct_answer":"560","correct_answer_fraction":[560,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"40320","plausible_wrong_fraction":[40320,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0004","parameters":{"counts":[3,3,2],"letters":["H","G","F"],"multiset":"HHHGGGFF"},"question":"How many distinct strings can be formed by rearranging all letters of HHHGGGFF?","question_sha256":"1c9855b7e389972732c90e129ae54520e48fbd10a2586c2febc1db4644382f52","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":79,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0021","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"125/100","width_multiplier":"80/100"},"correct_answer":"5000","correct_answer_fraction":[5000,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"5250","plausible_wrong_fraction":[5250,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0021","parameters":{"decrease":20,"increase":25,"length":100,"width":50},"question":"A rectangle initially has length 100 and width 50. Its length is increased by 25% while its width is decreased by 20%. What is the new area? Give an exact value.","question_sha256":"7f2d798574aea7c3ca7a49f6deed74bc1efbd17d9227e6bfd38cda796d4a359d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":161,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0018","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[5,16,38,82,170,346,698,1402]},"correct_answer":"1402","correct_answer_fraction":[1402,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"698","plausible_wrong_fraction":[698,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0018","parameters":{"a0":5,"multiplier":2,"n":7,"offset":6},"question":"A sequence is defined by a_0 = 5 and a_(k+1) = 2a_k + 6 for k >= 0. What is a_7?","question_sha256":"c7bf9fe7ef048eb9b6aea11e3d5700874484097d0fc64aa85ea7a1ab8b833303","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0000","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"10/11","remaining_worker":"A"},"correct_answer":"117/11","correct_answer_fraction":[117,11],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"11","plausible_wrong_fraction":[11,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0000","parameters":{"a_hours":18,"b_hours":22,"together_hours":9},"question":"Worker A can finish a job alone in 18 hours and worker B can finish it alone in 22 hours. They work together for 9 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"78cad8c2de487942d78cf35b4ef18521aebf9377ceb10d64452ba2cc979853ef","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0017","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":55,"total_score":3529},"correct_answer":"3529/55","correct_answer_fraction":[3529,55],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"64","plausible_wrong_fraction":[64,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0017","parameters":{"counts":[14,20,21],"means":[62,69,61]},"question":"Three classes contain 14, 20, and 21 students. Their mean test scores are 62, 69, and 61, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"7d13ebdf2eab2d140f07ef5a95384f334c9f741cfd205089367ae9ff1696249d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0014","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["154/66","154/33"],"total_distance":308},"correct_answer":"44","correct_answer_fraction":[44,1],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"99/2","plausible_wrong_fraction":[99,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0014","parameters":{"distance":154,"speeds":[66,33]},"question":"A vehicle travels 154 km from A to B at 66 km/h and returns the same 154 km at 33 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"a9b846df6c055fc5ddee85446e31287f1fe4939cb896d2b4f26fb30883e5b8ed","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0005","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":41,"total_score":2740},"correct_answer":"2740/41","correct_answer_fraction":[2740,41],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"196/3","plausible_wrong_fraction":[196,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0005","parameters":{"counts":[22,6,13],"means":[75,69,52]},"question":"Three classes contain 22, 6, and 13 students. Their mean test scores are 75, 69, and 52, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"fb9e19498544c4620e4281f6f39b737b30d3e9038dd47c4f11aa2d4a8c8bcd28","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0021","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["130/100","90/100","108/100"]},"correct_answer":"44226/25","correct_answer_fraction":[44226,25],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1792","plausible_wrong_fraction":[1792,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0021","parameters":{"base":1400,"changes":[30,10,8],"signs":[1,-1,1]},"question":"A quantity starts at 1400. It increases by 30%, then decreases by 10%, and finally increases by 8%. What is the final value? Give an exact value.","question_sha256":"0d1ebfccb59fe1f09a2e42e58d8f9b463a90fba4e09541dd67162cbc53344c42","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":145,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0002","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":144,"total_symbols":8},"correct_answer":"280","correct_answer_fraction":[280,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"40320","plausible_wrong_fraction":[40320,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0002","parameters":{"counts":[4,3,1],"letters":["E","F","A"],"multiset":"EEEEFFFA"},"question":"How many distinct strings can be formed by rearranging all letters of EEEEFFFA?","question_sha256":"d04232c7660dc2e319565ac5d6309e942dfb19c6da2899fa870efcfa3e8d44c6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":79,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0000","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":40,"total_score":2341},"correct_answer":"2341/40","correct_answer_fraction":[2341,40],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"63","plausible_wrong_fraction":[63,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0000","parameters":{"counts":[16,7,17],"means":[52,82,55]},"question":"Three classes contain 16, 7, and 17 students. Their mean test scores are 52, 82, and 55, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"8a25ef3d5bc5fd9565d616f4b88473281358081ed8dc6dd5378193947bc45e76","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0009","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"120/100","width_multiplier":"90/100"},"correct_answer":"6318","correct_answer_fraction":[6318,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"6435","plausible_wrong_fraction":[6435,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0009","parameters":{"decrease":10,"increase":20,"length":90,"width":65},"question":"A rectangle initially has length 90 and width 65. Its length is increased by 20% while its width is decreased by 10%. What is the new area? Give an exact value.","question_sha256":"36ae33f413d9b852ca5821d2a3f4a692b45a6f1241dd54fbd339f5608b307618","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0012","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"130/100","width_multiplier":"90/100"},"correct_answer":"6318","correct_answer_fraction":[6318,1],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"6480","plausible_wrong_fraction":[6480,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0012","parameters":{"decrease":10,"increase":30,"length":90,"width":60},"question":"A rectangle initially has length 90 and width 60. Its length is increased by 30% while its width is decreased by 10%. What is the new area? Give an exact value.","question_sha256":"ce568c0509b8e1b43a5c14a8ab4db805f6902069fabb728bbf347761e4cb2daf","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0015","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1330,"favorable_subsets":637},"correct_answer":"91/190","correct_answer_fraction":[91,190],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"4/9","plausible_wrong_fraction":[4,9],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0015","parameters":{"blue":7,"draws":3,"red":14,"target_red":2},"question":"An urn contains 14 red balls and 7 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"83906ec45a058cf87a885f2d1871d199259a37030073b398bcd7fc26bab3f984","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0002","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"7/15","remaining_worker":"A"},"correct_answer":"10","correct_answer_fraction":[10,1],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"26/5","plausible_wrong_fraction":[26,5],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0002","parameters":{"a_hours":15,"b_hours":6,"together_hours":2},"question":"Worker A can finish a job alone in 15 hours and worker B can finish it alone in 6 hours. They work together for 2 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"b871470e5aaa24ec6f931ea0cbb8e980d1e6dcb759408ddf6547604a3594e099","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0020","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[8,19,52,151,448,1339,4012,12031,36088]},"correct_answer":"36088","correct_answer_fraction":[36088,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"12031","plausible_wrong_fraction":[12031,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0020","parameters":{"a0":8,"multiplier":3,"n":8,"offset":-5},"question":"A sequence is defined by a_0 = 8 and a_(k+1) = 3a_k - 5 for k >= 0. What is a_8?","question_sha256":"ce6e0882103bff3bb3b0e942bddda66bdbff823957777536dcfc3723525fbe12","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":80,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0020","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":24,"total_symbols":7},"correct_answer":"210","correct_answer_fraction":[210,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"5040","plausible_wrong_fraction":[5040,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0020","parameters":{"counts":[2,3,2],"letters":["F","A","B"],"multiset":"FFAAABB"},"question":"How many distinct strings can be formed by rearranging all letters of FFAAABB?","question_sha256":"cd06dbb5dc226cc58fbfed0fb44c2397c2914e2d6ef58510651ac056fdb4a5c2","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":78,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0013","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":6,"failure_probability":"19/20"},"correct_answer":"16954119/64000000","correct_answer_fraction":[16954119,64000000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"3/10","plausible_wrong_fraction":[3,10],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0013","parameters":{"success_denominator":20,"success_numerator":1,"trials":6},"question":"Each of 6 independent trials succeeds with probability 1/20. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"1af03be70fcf7d98de50a95d17cc5037530c929c8d7dad06ba74a406072b55f5","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0007","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":52,"total_score":4148},"correct_answer":"1037/13","correct_answer_fraction":[1037,13],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"227/3","plausible_wrong_fraction":[227,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0007","parameters":{"counts":[10,24,18],"means":[59,89,79]},"question":"Three classes contain 10, 24, and 18 students. Their mean test scores are 59, 89, and 79, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"1f7c12a5d836f36040c70fc4fc2baa1c5347d9cfe97ad2c2772dab068ad57fcc","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0001","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1140,"favorable_subsets":525},"correct_answer":"35/76","correct_answer_fraction":[35,76],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"27/64","plausible_wrong_fraction":[27,64],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0001","parameters":{"blue":5,"draws":3,"red":15,"target_red":2},"question":"An urn contains 15 red balls and 5 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"c7076a954001cc7047a28d20d499d6abbe028172ea40c02a4e1780bf6fca90c4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0001","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["120/100","92/100","115/100"]},"correct_answer":"6348/5","correct_answer_fraction":[6348,5],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1270","plausible_wrong_fraction":[1270,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0001","parameters":{"base":1000,"changes":[20,8,15],"signs":[1,-1,1]},"question":"A quantity starts at 1000. It increases by 20%, then decreases by 8%, and finally increases by 15%. What is the final value? Give an exact value.","question_sha256":"75a80b065e20a09aac537296035753fe534bb79da71fba8ff7b90fee99766394","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":145,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0015","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":37,"total_score":2680},"correct_answer":"2680/37","correct_answer_fraction":[2680,37],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"72","plausible_wrong_fraction":[72,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0015","parameters":{"counts":[11,13,13],"means":[64,70,82]},"question":"Three classes contain 11, 13, and 13 students. Their mean test scores are 64, 70, and 82, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"40fad7cdfe7606c062490a67cb4586bf675b2362a934ea2c2e7dcaca278cf260","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0023","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["120/100","85/100","85/100"]},"correct_answer":"11271/10","correct_answer_fraction":[11271,10],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"1170","plausible_wrong_fraction":[1170,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0023","parameters":{"base":1300,"changes":[20,15,15],"signs":[1,-1,-1]},"question":"A quantity starts at 1300. It increases by 20%, then decreases by 15%, and finally decreases by 15%. What is the final value? Give an exact value.","question_sha256":"14c676625cb78d7c05960987f32d832abdcd88e4d6ad674217f86625add90a72","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0000","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":36,"total_symbols":7},"correct_answer":"140","correct_answer_fraction":[140,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"5040","plausible_wrong_fraction":[5040,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0000","parameters":{"counts":[3,3,1],"letters":["F","G","E"],"multiset":"FFFGGGE"},"question":"How many distinct strings can be formed by rearranging all letters of FFFGGGE?","question_sha256":"5b38040f680d843d328a8e7dadc0397c09b56066da870872bb247493b22c6075","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":78,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0020","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":2600,"favorable_subsets":825},"correct_answer":"33/104","correct_answer_fraction":[33,104],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"5445/17576","plausible_wrong_fraction":[5445,17576],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0020","parameters":{"blue":15,"draws":3,"red":11,"target_red":2},"question":"An urn contains 11 red balls and 15 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"2f1c76d3679a3406de38aa545a668d2c4c312350deb0881b9bc021c55dbd334e","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0009","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":776,"true_positive":285},"correct_answer":"285/1061","correct_answer_fraction":[285,1061],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"19/20","plausible_wrong_fraction":[19,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0009","parameters":{"population":10000,"prevalence":3,"sensitivity":95,"specificity":92},"question":"In a population, 3% of people have a condition. A test has 95% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"e86e2a8459fd04ead22ef5dc31093cb0d0cf4b530a8f09d080bff52f581e899d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0002","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":41,"total_score":3080},"correct_answer":"3080/41","correct_answer_fraction":[3080,41],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"73","plausible_wrong_fraction":[73,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0002","parameters":{"counts":[9,18,14],"means":[54,71,94]},"question":"Three classes contain 9, 18, and 14 students. Their mean test scores are 54, 71, and 94, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"bf74549c42d160c213444f83f440df9576bd2abeef67d1b4c257fb38f7154022","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":188,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0017","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"120/100","width_multiplier":"85/100"},"correct_answer":"11271/2","correct_answer_fraction":[11271,2],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"23205/4","plausible_wrong_fraction":[23205,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0017","parameters":{"decrease":15,"increase":20,"length":85,"width":65},"question":"A rectangle initially has length 85 and width 65. Its length is increased by 20% while its width is decreased by 15%. What is the new area? Give an exact value.","question_sha256":"33bea32ba8cadaf60503323aa11c38b7842d0445309333739e09b01bbdfe977f","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0022","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"8/9","remaining_worker":"A"},"correct_answer":"20/3","correct_answer_fraction":[20,3],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"6","plausible_wrong_fraction":[6,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0022","parameters":{"a_hours":15,"b_hours":9,"together_hours":5},"question":"Worker A can finish a job alone in 15 hours and worker B can finish it alone in 9 hours. They work together for 5 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"68b9f0c3e93038ba9dc9650f166753c1a9dc6c9a6a8a27bfac29cf87f648bdc6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"recurrence_indexing-0022","family":"recurrence_indexing","misconception":{"description":"Treats a_0 as the first update and performs n-1 rather than n transitions.","id":"apply_recurrence_one_time_too_few","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"trajectory":[-3,-14,-47,-146,-443,-1334,-4007]},"correct_answer":"-4007","correct_answer_fraction":[-4007,1],"independent_verifier":"curcon.coherent_wrong_labels:recurrence_indexing","plausible_wrong_answer":"-1334","plausible_wrong_fraction":[-1334,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"recurrence_indexing-0022","parameters":{"a0":-3,"multiplier":3,"n":6,"offset":-5},"question":"A sequence is defined by a_0 = -3 and a_(k+1) = 3a_k - 5 for k >= 0. What is a_6?","question_sha256":"7a907d12a88b6508233d0eed64d8d70f81b56a1382377a8d1d8f005c7a22a2f5","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":81,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0005","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":48,"total_symbols":7},"correct_answer":"105","correct_answer_fraction":[105,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"5040","plausible_wrong_fraction":[5040,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0005","parameters":{"counts":[4,2,1],"letters":["G","H","B"],"multiset":"GGGGHHB"},"question":"How many distinct strings can be formed by rearranging all letters of GGGGHHB?","question_sha256":"4012ff973d11a2a0d8eb3ba85faa24176e6ddc427f10ae35ccca050f3d5ddbb4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":78,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0015","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":784,"true_positive":190},"correct_answer":"95/487","correct_answer_fraction":[95,487],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"19/20","plausible_wrong_fraction":[19,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0015","parameters":{"population":10000,"prevalence":2,"sensitivity":95,"specificity":92},"question":"In a population, 2% of people have a condition. A test has 95% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"f46fafc630331ac596349aa7839e17e5b1221e7004464d8edec60f15aa3adb5c","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0023","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":4,"total_symbols":5},"correct_answer":"30","correct_answer_fraction":[30,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"120","plausible_wrong_fraction":[120,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0023","parameters":{"counts":[2,2,1],"letters":["E","C","B"],"multiset":"EECCB"},"question":"How many distinct strings can be formed by rearranging all letters of EECCB?","question_sha256":"318edefbe7118d9319115cd7a271861a5c2e13eb332a8d6d39946b012cc79fe5","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":76,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0020","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["115/100","70/100","115/100"]},"correct_answer":"3703/10","correct_answer_fraction":[3703,10],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"400","plausible_wrong_fraction":[400,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0020","parameters":{"base":400,"changes":[15,30,15],"signs":[1,-1,1]},"question":"A quantity starts at 400. It increases by 15%, then decreases by 30%, and finally increases by 15%. What is the final value? Give an exact value.","question_sha256":"ff0d664670fc97b7fd00ccdbb38fc71f300a514d22836afa84d58abe3f69773d","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":145,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0017","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":12,"total_symbols":6},"correct_answer":"60","correct_answer_fraction":[60,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"720","plausible_wrong_fraction":[720,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0017","parameters":{"counts":[2,3,1],"letters":["C","E","H"],"multiset":"CCEEEH"},"question":"How many distinct strings can be formed by rearranging all letters of CCEEEH?","question_sha256":"3001cc6e9e091de3553a867a197960fa1dcf83cd42b0a89723c54ba9a26d0ef8","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":77,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0003","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"130/100","width_multiplier":"75/100"},"correct_answer":"5265/4","correct_answer_fraction":[5265,4],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"2835/2","plausible_wrong_fraction":[2835,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0003","parameters":{"decrease":25,"increase":30,"length":45,"width":30},"question":"A rectangle initially has length 45 and width 30. Its length is increased by 30% while its width is decreased by 25%. What is the new area? Give an exact value.","question_sha256":"8550deabed390710c7d30eeed199aeacee14de3aa049f7cb8621b38590550237","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"repeated_object_permutations-0006","family":"repeated_object_permutations","misconception":{"description":"Uses n! without dividing by factorials of repeated multiplicities.","id":"treat_repeated_objects_as_distinct","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multiplicity_factor":24,"total_symbols":7},"correct_answer":"210","correct_answer_fraction":[210,1],"independent_verifier":"curcon.coherent_wrong_labels:repeated_object_permutations","plausible_wrong_answer":"5040","plausible_wrong_fraction":[5040,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"repeated_object_permutations-0006","parameters":{"counts":[2,3,2],"letters":["F","E","B"],"multiset":"FFEEEBB"},"question":"How many distinct strings can be formed by rearranging all letters of FFEEEBB?","question_sha256":"5f33fae5208670f3cf474b3a3f2d1e822fa05a0bb9449ff29bb258a0d59788d0","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":78,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0003","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["49/75","49/51"],"total_distance":98},"correct_answer":"425/7","correct_answer_fraction":[425,7],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"63","plausible_wrong_fraction":[63,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0003","parameters":{"distance":49,"speeds":[75,51]},"question":"A vehicle travels 49 km from A to B at 75 km/h and returns the same 49 km at 51 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"f5e5cf37041ef4a1057eaa0f91a06c14896c63486725819f47247314b6d1fb6f","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":167,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0012","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":4,"failure_probability":"14/15"},"correct_answer":"12209/50625","correct_answer_fraction":[12209,50625],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"4/15","plausible_wrong_fraction":[4,15],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0012","parameters":{"success_denominator":15,"success_numerator":1,"trials":4},"question":"Each of 4 independent trials succeeds with probability 1/15. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"498ac58a35573d13530925a0b7460a35498b6623bdbecf2597fefb7ec3a05557","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0012","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":264,"true_positive":1020},"correct_answer":"85/107","correct_answer_fraction":[85,107],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"17/20","plausible_wrong_fraction":[17,20],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0012","parameters":{"population":10000,"prevalence":12,"sensitivity":85,"specificity":97},"question":"In a population, 12% of people have a condition. A test has 85% sensitivity and 97% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"d924803b2b6bcea5d7c98e2cf540373b4e051fcbbd6be588c3bd0b294b1fb10a","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":258,"tool_access_required":false}} | |
| {"candidate_id":"successive_percent_change-0013","family":"successive_percent_change","misconception":{"description":"Adds signed percentage changes instead of composing multiplicative factors.","id":"add_percentage_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"multipliers":["130/100","90/100","88/100"]},"correct_answer":"48906/25","correct_answer_fraction":[48906,25],"independent_verifier":"curcon.coherent_wrong_labels:successive_percent_change","plausible_wrong_answer":"2052","plausible_wrong_fraction":[2052,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"successive_percent_change-0013","parameters":{"base":1900,"changes":[30,10,12],"signs":[1,-1,-1]},"question":"A quantity starts at 1900. It increases by 30%, then decreases by 10%, and finally decreases by 12%. What is the final value? Give an exact value.","question_sha256":"b87279e7da237d8bf640bc70427b510f6eeca9e30c0988fd2ec56f572b58a74c","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":146,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0011","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":36,"total_score":2521},"correct_answer":"2521/36","correct_answer_fraction":[2521,36],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"209/3","plausible_wrong_fraction":[209,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0011","parameters":{"counts":[14,11,11],"means":[74,58,77]},"question":"Three classes contain 14, 11, and 11 students. Their mean test scores are 74, 58, and 77, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"cc7184993d903badac933176da362df69a56f7e3b5d76b7597e0ed58de6318f4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0016","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"13/20","remaining_worker":"A"},"correct_answer":"48/5","correct_answer_fraction":[48,5],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"15/2","plausible_wrong_fraction":[15,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0016","parameters":{"a_hours":16,"b_hours":10,"together_hours":4},"question":"Worker A can finish a job alone in 16 hours and worker B can finish it alone in 10 hours. They work together for 4 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"dffb1cbe8901235f5607fe49ebc182781f19df7f5179c9099181f7bd5ca7ff06","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":261,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0000","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":7,"failure_probability":"9/10"},"correct_answer":"5217031/10000000","correct_answer_fraction":[5217031,10000000],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"7/10","plausible_wrong_fraction":[7,10],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0000","parameters":{"success_denominator":20,"success_numerator":2,"trials":7},"question":"Each of 7 independent trials succeeds with probability 1/10. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"4e9e5b89d52e0a0c5e72764bcfbf3806acbb8dda35ed18ea924e5ef6dc689a99","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"area_scaling-0001","family":"area_scaling","misconception":{"description":"Treats the area percentage change as the signed sum of side changes.","id":"add_length_and_width_percent_changes","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"length_multiplier":"125/100","width_multiplier":"90/100"},"correct_answer":"6075/8","correct_answer_fraction":[6075,8],"independent_verifier":"curcon.coherent_wrong_labels:area_scaling","plausible_wrong_answer":"3105/4","plausible_wrong_fraction":[3105,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"area_scaling-0001","parameters":{"decrease":10,"increase":25,"length":45,"width":15},"question":"A rectangle initially has length 45 and width 15. Its length is increased by 25% while its width is decreased by 10%. What is the new area? Give an exact value.","question_sha256":"7b6799ea355ed8cbb733ddb165c199557ca1c13d61ffcd41e6c9f1b4adb66913","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":160,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0016","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":5,"failure_probability":"14/15"},"correct_answer":"221551/759375","correct_answer_fraction":[221551,759375],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"1/3","plausible_wrong_fraction":[1,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0016","parameters":{"success_denominator":15,"success_numerator":1,"trials":5},"question":"Each of 5 independent trials succeeds with probability 1/15. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"8a004a6bc6f02a668174c2df510d2a75ee172ea1d146dd4427e200adce448b67","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":148,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0001","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["126/75","126/48"],"total_distance":252},"correct_answer":"2400/41","correct_answer_fraction":[2400,41],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"123/2","plausible_wrong_fraction":[123,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0001","parameters":{"distance":126,"speeds":[75,48]},"question":"A vehicle travels 126 km from A to B at 75 km/h and returns the same 126 km at 48 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"b02b8936e5e96c54da558813a5a26dd751314b372ab199f9b415a6b3d6c578c4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":169,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0014","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":1760,"true_positive":1104},"correct_answer":"69/179","correct_answer_fraction":[69,179],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"23/25","plausible_wrong_fraction":[23,25],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0014","parameters":{"population":10000,"prevalence":12,"sensitivity":92,"specificity":80},"question":"In a population, 12% of people have a condition. A test has 92% sensitivity and 80% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"54a5499665d32a058203c18055ca5e5439c3e8b2110d7a59cfbc1cef12380ab4","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":258,"tool_access_required":false}} | |
| {"candidate_id":"at_least_one_probability-0008","family":"at_least_one_probability","misconception":{"description":"Adds individual success probabilities and ignores overlap between trials.","id":"add_overlapping_success_events","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"complement_power":3,"failure_probability":"5/6"},"correct_answer":"91/216","correct_answer_fraction":[91,216],"independent_verifier":"curcon.coherent_wrong_labels:at_least_one_probability","plausible_wrong_answer":"1/2","plausible_wrong_fraction":[1,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"at_least_one_probability-0008","parameters":{"success_denominator":12,"success_numerator":2,"trials":3},"question":"Each of 3 independent trials succeeds with probability 1/6. What is the probability of at least one success? Give the answer as a reduced fraction.","question_sha256":"84c1591bc7fb49270a57f69ecb2c8e810cdf155e7ab2f5ba9b04a69072df71a0","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":147,"tool_access_required":false}} | |
| {"candidate_id":"combined_work_rate-0020","family":"combined_work_rate","misconception":{"description":"Correctly computes remaining work but uses B's solo time after B has left.","id":"use_departed_workers_rate_for_remainder","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"completed_fraction":"7/33","remaining_worker":"A"},"correct_answer":"55/3","correct_answer_fraction":[55,3],"independent_verifier":"curcon.coherent_wrong_labels:combined_work_rate","plausible_wrong_answer":"63/11","plausible_wrong_fraction":[63,11],"task_validity":"valid_unique_exact_answer"},"pair_id":"combined_work_rate-0020","parameters":{"a_hours":22,"b_hours":6,"together_hours":1},"question":"Worker A can finish a job alone in 22 hours and worker B can finish it alone in 6 hours. They work together for 1 hours; then B leaves and A finishes the remaining work alone. How many hours elapse from the start until the job is finished? Give an exact value.","question_sha256":"591a2ebc5a49f53ebe24f59a7cde7b1c5a7112b3abb8b77070cc715955d66af6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":260,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0021","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":46,"total_score":3190},"correct_answer":"1595/23","correct_answer_fraction":[1595,23],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"70","plausible_wrong_fraction":[70,1],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0021","parameters":{"counts":[20,11,15],"means":[60,65,85]},"question":"Three classes contain 20, 11, and 15 students. Their mean test scores are 60, 65, and 85, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"f5e09f6a63e77c16336862f2539a22f523770088396d86d59f4dafe66b4d63d6","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"without_replacement_probability-0023","family":"without_replacement_probability","misconception":{"description":"Uses a binomial calculation with a fixed red probability for every draw.","id":"treat_without_replacement_as_independent","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"all_subsets":1771,"favorable_subsets":780},"correct_answer":"780/1771","correct_answer_fraction":[780,1771],"independent_verifier":"curcon.coherent_wrong_labels:without_replacement_probability","plausible_wrong_answer":"5070/12167","plausible_wrong_fraction":[5070,12167],"task_validity":"valid_unique_exact_answer"},"pair_id":"without_replacement_probability-0023","parameters":{"blue":10,"draws":3,"red":13,"target_red":2},"question":"An urn contains 13 red balls and 10 blue balls. Three balls are drawn uniformly without replacement. What is the probability that exactly two are red? Give the answer as a reduced fraction.","question_sha256":"c95ab45c4bdb2f6ac433c27f714f327a6965fc2900c0822d6acfd935362afa47","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0016","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["44/45","44/30"],"total_distance":88},"correct_answer":"36","correct_answer_fraction":[36,1],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"75/2","plausible_wrong_fraction":[75,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0016","parameters":{"distance":44,"speeds":[45,30]},"question":"A vehicle travels 44 km from A to B at 45 km/h and returns the same 44 km at 30 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"249ad78793e067939a3c52b03f6a70eb065b6c615a89fef87134a801ff5e1e6e","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":167,"tool_access_required":false}} | |
| {"candidate_id":"weighted_mean-0006","family":"weighted_mean","misconception":{"description":"Averages group means without weighting by group size.","id":"unweighted_mean_of_group_means","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"total_count":59,"total_score":3970},"correct_answer":"3970/59","correct_answer_fraction":[3970,59],"independent_verifier":"curcon.coherent_wrong_labels:weighted_mean","plausible_wrong_answer":"200/3","plausible_wrong_fraction":[200,3],"task_validity":"valid_unique_exact_answer"},"pair_id":"weighted_mean-0006","parameters":{"counts":[16,19,24],"means":[70,54,76]},"question":"Three classes contain 16, 19, and 24 students. Their mean test scores are 70, 54, and 76, respectively. What is the mean score across all students in the three classes? Give an exact value.","question_sha256":"51ca7c64ebebb6b42b7bff62ec3a84bd211b676e19b9ca84e298e0405974d134","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":189,"tool_access_required":false}} | |
| {"candidate_id":"equal_distance_average_speed-0022","family":"equal_distance_average_speed","misconception":{"description":"Uses the arithmetic mean even though the two legs take unequal time.","id":"arithmetic_mean_of_speeds","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"leg_times":["49/66","49/57"],"total_distance":98},"correct_answer":"2508/41","correct_answer_fraction":[2508,41],"independent_verifier":"curcon.coherent_wrong_labels:equal_distance_average_speed","plausible_wrong_answer":"123/2","plausible_wrong_fraction":[123,2],"task_validity":"valid_unique_exact_answer"},"pair_id":"equal_distance_average_speed-0022","parameters":{"distance":49,"speeds":[66,57]},"question":"A vehicle travels 49 km from A to B at 66 km/h and returns the same 49 km at 57 km/h. What is its average speed for the entire round trip? Give an exact value in km/h.","question_sha256":"faa80073a567b4f7de359b312b3d9d0c2860cca1d5e861b38ba5c29476ebfa61","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":167,"tool_access_required":false}} | |
| {"candidate_id":"bayes_positive_test-0000","family":"bayes_positive_test","misconception":{"description":"Reports sensitivity as P(condition|positive), ignoring base rate and false positives.","id":"confuse_sensitivity_with_posterior","status":"candidate_shortcut_not_observed_model_behavior"},"oracle":{"certificate":{"false_positive":776,"true_positive":225},"correct_answer":"225/1001","correct_answer_fraction":[225,1001],"independent_verifier":"curcon.coherent_wrong_labels:bayes_positive_test","plausible_wrong_answer":"3/4","plausible_wrong_fraction":[3,4],"task_validity":"valid_unique_exact_answer"},"pair_id":"bayes_positive_test-0000","parameters":{"population":10000,"prevalence":3,"sensitivity":75,"specificity":92},"question":"In a population, 3% of people have a condition. A test has 75% sensitivity and 92% specificity. For a randomly selected person whose test is positive, what is the probability that the person actually has the condition? Give the answer as a reduced fraction.","question_sha256":"6719ccf70462ef613bc3fbbf48fdb9d06e1771eac8885ecbb1a6384adbcbd333","run_id":"stage1-coherent-wrong-label-v1","schema_version":"curcon.coherent_wrong_task.v1","surface":{"answer_format":"reduced_integer_or_fraction","question_length_chars":257,"tool_access_required":false}} | |