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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 248700.59.
{ "id": "WUA_BIO_25K_016001", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 186.26 (same units as Vmax).
{ "id": "WUA_BIO_25K_016002", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.728 osmol/L.
{ "id": "WUA_BIO_25K_016003", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.02, comp...
p=0.980; 2pq=0.039; q^2=0.000.
{ "id": "WUA_BIO_25K_016004", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 110001.78.
{ "id": "WUA_BIO_25K_016005", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 161542.35.
{ "id": "WUA_BIO_25K_016006", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.67 each i...
Probability = p^n = 0.3008.
{ "id": "WUA_BIO_25K_016007", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.86 each i...
Probability = p^n = 0.5470.
{ "id": "WUA_BIO_25K_016008", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 120.45 (same units as Vmax).
{ "id": "WUA_BIO_25K_016009", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.66 each i...
Probability = p^n = 0.0827.
{ "id": "WUA_BIO_25K_016010", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.035, com...
p=0.965; 2pq=0.068; q^2=0.001.
{ "id": "WUA_BIO_25K_016011", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.406, com...
p=0.594; 2pq=0.482; q^2=0.165.
{ "id": "WUA_BIO_25K_016012", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 3535777.70.
{ "id": "WUA_BIO_25K_016013", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 3448.45.
{ "id": "WUA_BIO_25K_016014", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 40.73 (same units as Vmax).
{ "id": "WUA_BIO_25K_016015", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 1.926 osmol/L.
{ "id": "WUA_BIO_25K_016016", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 2991382.67.
{ "id": "WUA_BIO_25K_016017", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 1.389 osmol/L.
{ "id": "WUA_BIO_25K_016018", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.041, com...
p=0.959; 2pq=0.079; q^2=0.002.
{ "id": "WUA_BIO_25K_016019", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 2.42 h.
{ "id": "WUA_BIO_25K_016020", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.78 each i...
Probability = p^n = 0.4746.
{ "id": "WUA_BIO_25K_016021", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 36774.29.
{ "id": "WUA_BIO_25K_016022", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 14210.14.
{ "id": "WUA_BIO_25K_016023", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.21 h.
{ "id": "WUA_BIO_25K_016024", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 1.992 osmol/L.
{ "id": "WUA_BIO_25K_016025", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 48042070.08.
{ "id": "WUA_BIO_25K_016026", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.44 each i...
Probability = p^n = 0.1936.
{ "id": "WUA_BIO_25K_016027", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 420.45 (same units as Vmax).
{ "id": "WUA_BIO_25K_016028", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.45 each i...
Probability = p^n = 0.0008.
{ "id": "WUA_BIO_25K_016029", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.562 osmol/L.
{ "id": "WUA_BIO_25K_016030", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 4335.37.
{ "id": "WUA_BIO_25K_016031", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.63 each i...
Probability = p^n = 0.0156.
{ "id": "WUA_BIO_25K_016032", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.285, com...
p=0.715; 2pq=0.408; q^2=0.081.
{ "id": "WUA_BIO_25K_016033", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.08, comp...
p=0.920; 2pq=0.147; q^2=0.006.
{ "id": "WUA_BIO_25K_016034", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.76 each i...
Probability = p^n = 0.1927.
{ "id": "WUA_BIO_25K_016035", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 211.20 (same units as Vmax).
{ "id": "WUA_BIO_25K_016036", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 44050.58.
{ "id": "WUA_BIO_25K_016037", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 2.472 osmol/L.
{ "id": "WUA_BIO_25K_016038", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 154.90 (same units as Vmax).
{ "id": "WUA_BIO_25K_016039", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.85 each i...
Probability = p^n = 0.3206.
{ "id": "WUA_BIO_25K_016040", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.12, comp...
p=0.880; 2pq=0.211; q^2=0.014.
{ "id": "WUA_BIO_25K_016041", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 0.90 h.
{ "id": "WUA_BIO_25K_016042", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.313, com...
p=0.687; 2pq=0.430; q^2=0.098.
{ "id": "WUA_BIO_25K_016043", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 387.69 (same units as Vmax).
{ "id": "WUA_BIO_25K_016044", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.111, com...
p=0.889; 2pq=0.197; q^2=0.012.
{ "id": "WUA_BIO_25K_016045", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.183 osmol/L.
{ "id": "WUA_BIO_25K_016046", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.08 h.
{ "id": "WUA_BIO_25K_016047", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 13067674493.31.
{ "id": "WUA_BIO_25K_016048", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.02 h.
{ "id": "WUA_BIO_25K_016049", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.43 h.
{ "id": "WUA_BIO_25K_016050", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 97.09 (same units as Vmax).
{ "id": "WUA_BIO_25K_016051", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.49 each i...
Probability = p^n = 0.0016.
{ "id": "WUA_BIO_25K_016052", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 35008.49.
{ "id": "WUA_BIO_25K_016053", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.68 each i...
Probability = p^n = 0.0211.
{ "id": "WUA_BIO_25K_016054", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 1.045 osmol/L.
{ "id": "WUA_BIO_25K_016055", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 156.87 (same units as Vmax).
{ "id": "WUA_BIO_25K_016056", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 2.290 osmol/L.
{ "id": "WUA_BIO_25K_016057", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 266.42 (same units as Vmax).
{ "id": "WUA_BIO_25K_016058", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 4.72 h.
{ "id": "WUA_BIO_25K_016059", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.51 each i...
Probability = p^n = 0.0677.
{ "id": "WUA_BIO_25K_016060", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 8.77 h.
{ "id": "WUA_BIO_25K_016061", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 21147.12.
{ "id": "WUA_BIO_25K_016062", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.800 osmol/L.
{ "id": "WUA_BIO_25K_016063", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 18167.64.
{ "id": "WUA_BIO_25K_016064", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.281, com...
p=0.719; 2pq=0.404; q^2=0.079.
{ "id": "WUA_BIO_25K_016065", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 119661481.10.
{ "id": "WUA_BIO_25K_016066", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.447 osmol/L.
{ "id": "WUA_BIO_25K_016067", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 4.848 osmol/L.
{ "id": "WUA_BIO_25K_016068", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 117.39 (same units as Vmax).
{ "id": "WUA_BIO_25K_016069", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.87 each i...
Probability = p^n = 0.2855.
{ "id": "WUA_BIO_25K_016070", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 0.89 h.
{ "id": "WUA_BIO_25K_016071", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 2.451 osmol/L.
{ "id": "WUA_BIO_25K_016072", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.261, com...
p=0.739; 2pq=0.386; q^2=0.068.
{ "id": "WUA_BIO_25K_016073", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.08 h.
{ "id": "WUA_BIO_25K_016074", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 115.69 (same units as Vmax).
{ "id": "WUA_BIO_25K_016075", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 36.91 (same units as Vmax).
{ "id": "WUA_BIO_25K_016076", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.485, com...
p=0.515; 2pq=0.500; q^2=0.235.
{ "id": "WUA_BIO_25K_016077", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.13, comp...
p=0.870; 2pq=0.226; q^2=0.017.
{ "id": "WUA_BIO_25K_016078", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.33 each i...
Probability = p^n = 0.1089.
{ "id": "WUA_BIO_25K_016079", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.44 h.
{ "id": "WUA_BIO_25K_016080", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 0.88 h.
{ "id": "WUA_BIO_25K_016081", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 9057938.02.
{ "id": "WUA_BIO_25K_016082", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 3.654 osmol/L.
{ "id": "WUA_BIO_25K_016083", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 169552.04.
{ "id": "WUA_BIO_25K_016084", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 1.156 osmol/L.
{ "id": "WUA_BIO_25K_016085", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 112.31 (same units as Vmax).
{ "id": "WUA_BIO_25K_016086", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.07 h.
{ "id": "WUA_BIO_25K_016087", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 23.31 (same units as Vmax).
{ "id": "WUA_BIO_25K_016088", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 74.53 (same units as Vmax).
{ "id": "WUA_BIO_25K_016089", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.395, com...
p=0.605; 2pq=0.478; q^2=0.156.
{ "id": "WUA_BIO_25K_016090", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.87 each i...
Probability = p^n = 0.4336.
{ "id": "WUA_BIO_25K_016091", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.174 osmol/L.
{ "id": "WUA_BIO_25K_016092", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.188 osmol/L.
{ "id": "WUA_BIO_25K_016093", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 7.15 h.
{ "id": "WUA_BIO_25K_016094", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 3564609649.97.
{ "id": "WUA_BIO_25K_016095", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 57962793.27.
{ "id": "WUA_BIO_25K_016096", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.041, com...
p=0.959; 2pq=0.079; q^2=0.002.
{ "id": "WUA_BIO_25K_016097", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 9439.14.
{ "id": "WUA_BIO_25K_016098", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 5.598 osmol/L.
{ "id": "WUA_BIO_25K_016099", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.069, com...
p=0.931; 2pq=0.128; q^2=0.005.
{ "id": "WUA_BIO_25K_016100", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
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