{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0001","composition":"R1","gate":"5b-R1","gold":64,"note":"Derived keyboard cost = 3 * mouse cost, then total accessories = keyboard + mouse.","question":"Fabian bought a brand new computer mouse and keyboard to be able to work from home. The cost of the keyboard was three times greater than the cost of the mouse. If the mouse cost $16, how much did Fabian spent on his new accessories?","source":"gsm8k_train_sample:0029","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0002","composition":"R1","gate":"5b-R1","gold":400,"note":"Derived second-floor count = 3 * first-floor count, then total floors.","question":"In a building, there are a hundred ladies on the first-floor studying. There are three times that many girls at a party being held on the second floor of the building. How many ladies are on the two floors in total?","source":"gsm8k_train_sample:0038","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0003","composition":"R1","gate":"5b-R1","gold":9,"note":"Derived total beads from two products, then divide by beads per bracelet.","question":"Marnie makes bead bracelets. She bought 5 bags of 50 beads and 2 bags of 100 beads. If 50 beads are used to make one bracelet, how many bracelets will Marnie be able to make out of the beads she bought?","source":"gsm8k_train_sample:0008","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0004","composition":"R1","gate":"5b-R1","gold":3840,"note":"Chained intermediate symbols: combined IG+Facebook, Twitter, TikTok, YouTube, then total.","question":"Malcolm has 240 followers on Instagram and 500 followers on Facebook. The number of followers he has on Twitter is half the number of followers he has on Instagram and Facebook combined. Meanwhile, the number of followers he has on TikTok is 3 times the number of followers is has on Twitter, and he has 510 more followers on Youtube than he has on TikTok. How many followers does Malcolm have on all his social media?","source":"gsm8k_train_sample:0027","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0005","composition":"R4","gate":"5b-R4","gold":3,"note":"Residual-to-target give-away: needed-to-give = start - desired remainder, minus already given (Jane 5, James 5+2). (R4 serving promotion reverted 2026-06-04 \u2014 unsound bridges disabled; refuses again.)","question":"Michael wants to lose 10 pounds by June. He lost 3 pounds in March and 4 pounds in April. How much weight does he have to lose in May to meet his goal?","source":"gsm8k_train_sample:0037","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0006","composition":"R5","gate":"5b-R5","gold":14,"note":"Multi-step duration: round-trip drive time, scalar beach time, total trip time.","question":"Jake decides to go to the beach for a fun day.  It is a 2-hour drive each way.  He then spends 2.5 times at long at the beach as his total driving time.  How much time does the trip take?","source":"gsm8k_train_sample:0030","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0007","composition":"R6","gate":"5b-R6","gold":21,"note":"Fraction mutation: final temperature = 3/4 of current, decrease = current - final.","question":"In one hour, Addison mountain's temperature will decrease to 3/4  of its temperature. If the current temperature of the mountain is 84 degrees, what will the temperature decrease by?","source":"gsm8k_train_sample:0005","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0008","composition":"R6","gate":"5b-R6","gold":15,"note":"Percent partition: girls/boys split, percent of each, then total owners.","question":"A school has 100 students. Half of the students are girls, the other half are boys.  20% of the girls have dogs at home and 10% of the boys have dogs at home.  How many students own dogs?","source":"gsm8k_train_sample:0046","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":1,"baseline_verdict":"refuse","case_id":"cv-0009","composition":"compare_mult","gate":"5b-compare-mult","gold":60,"note":"Referenced multiplicative comparison should eventually solve; today it is a completeness-guard refusal.","question":"Ivan has 20 dice. Jerry has twice as many dice as Ivan. How many dice do they have altogether?","source":"guard:real_gsm8k_605","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0010","composition":"compare_mult","gate":"permanent","gold":null,"note":"No comparison reference; any admission would be an incomplete-reading failure.","question":"Tom has 7 apples. Jerry has 3 times as many apples. How many apples do they have together?","source":"guard:n_times_without_reference:3_as_many","target_verdict":"refuse"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0011","composition":"compare_mult","gate":"permanent","gold":null,"note":"No comparison reference; any admission would be an incomplete-reading failure.","question":"Tom has 7 apples. Jerry has 5 times as many apples. How many apples do they have together?","source":"guard:n_times_without_reference:5_as_many","target_verdict":"refuse"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0012","composition":"compare_mult","gate":"permanent","gold":null,"note":"No comparison reference; any admission would be an incomplete-reading failure.","question":"Tom has 7 apples. Jerry has three times more apples. How many apples do they have together?","source":"guard:n_times_without_reference:three_more","target_verdict":"refuse"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0013","composition":"compare_mult","gate":"permanent","gold":null,"note":"No comparison reference; any admission would be an incomplete-reading failure.","question":"Tom has 7 apples. Jerry has 3 times the number of apples. How many apples do they have together?","source":"guard:n_times_without_reference:3_the_number_of","target_verdict":"refuse"}
{"baseline_answer":null,"baseline_branches_enumerated":1,"baseline_verdict":"refuse","case_id":"cv-0014","composition":"compare_mult","gate":"permanent","gold":null,"note":"No comparison reference; completeness guard currently catches the unconsumed scalar.","question":"Tom has 7 apples. Jerry has twice as many apples. How many apples do they have together?","source":"guard:existing_multiplier_refusal:twice_no_reference","target_verdict":"refuse"}
{"baseline_answer":null,"baseline_branches_enumerated":1,"baseline_verdict":"refuse","case_id":"cv-0015","composition":"compare_mult","gate":"permanent","gold":null,"note":"No comparison reference; completeness guard currently catches the unconsumed scalar.","question":"Tom has 7 apples. Jerry has double the apples. How many apples do they have together?","source":"guard:existing_multiplier_refusal:double_no_reference","target_verdict":"refuse"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0016","composition":"world_knowledge","gate":"permanent","gold":72,"note":"Requires unstated legs-per-animal world knowledge; remains outside the decidable regime for this corpus.","question":"Over several years, Daniel has adopted any stray animals he sees on the side of the road.  He now has 2 horses, 5 dogs, 7 cats, 3 turtles, and 1 goat.  All of the animals are perfectly healthy.  In total, how many legs do his animals have?","source":"gsm8k_train_sample:0040","target_verdict":"refuse"}
{"baseline_answer":438,"baseline_branches_enumerated":1,"baseline_verdict":"solve","case_id":"cv-0017","composition":"compare_mult_additive","gate":"baseline","gold":438,"note":"Existing graph-path correct case; completeness guard must not over-refuse it.","question":"Sidney does 20 jumping jacks on Monday, 36 on Tuesday, 40 on Wednesday, and 50 on Thursday. Brooke does three times as many jumping jacks as Sidney. How many jumping jacks did Brooke do?","source":"gsm8k_train_sample:0024","target_verdict":"solve"}
{"baseline_answer":28,"baseline_branches_enumerated":1,"baseline_verdict":"solve","case_id":"cv-0018","composition":"compare_mult","gate":"baseline","gold":28,"note":"Referenced multiplicative comparison already solves; protects against over-broad no-reference refusal.","question":"Tom has 7 apples. Jerry has 3 times as many apples as Tom. How many apples do they have together?","source":"guard:n_times_with_reference:3_as_many_as_tom","target_verdict":"solve"}
{"baseline_answer":1200,"baseline_branches_enumerated":1,"baseline_verdict":"solve","case_id":"cv-0019","composition":"additive","gate":"baseline","gold":1200,"note":"Stated-sum contrastive control for the derived-symbol Nicole/Cindy form.","question":"Nicole has 400 cards. Cindy has 800 cards. How many cards do they have together?","source":"analysis:composition-capability-scope:R1_contrastive_control","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0020","composition":"product_additive","gate":"5b-product","gold":450,"note":"Existing guarded product bridge correct case; protects current 6/44/0 lift. (Reclassified 2026-06-04: solved only via product_bridge, disabled as unsound on the sealed set; refuses until a sealed-verified product gate exists.)","question":"John is lifting weights. He bench presses 15 pounds for 10 reps and does 3 sets. How much total weight does he move?","source":"gsm8k_train_sample:0021","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0021","composition":"R4","gate":"5b-R4","gold":4,"note":"Residual-to-target give-away: needed-to-give = start - desired remainder, minus already given (Jane 5, James 5+2).","question":"Martha has 20 apples. She decided to split them among her friends. Jane got 5 apples from her, and James got 2 more than Jane. How many more apples would Martha need to give away to be left with only 4 of them?","source":"gsm8k_train_sample:0035","target_verdict":"solve"}
{"baseline_answer":null,"baseline_branches_enumerated":0,"baseline_verdict":"refuse","case_id":"cv-0022","composition":"R5","gate":"5b-R5","gold":38,"note":"Multi-step duration: train leg = 2x subway leg (scalar of prior stage), then sum of the three legs.","question":"Traveling from Manhattan to the Bronx, Andrew rides the subway for 10 hours, takes the train and rides for twice as much time as the subway ride, and then bikes the remaining distance for 8 hours. What's the total time he takes to reach the Bronx from Manhattan?","source":"gsm8k_train_sample:0015","target_verdict":"solve"}
