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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 ≈ 419.67 (same units as Vmax).
{ "id": "WUA_BIO_25K_008701", "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=0.24 each i...
Probability = p^n = 0.0000.
{ "id": "WUA_BIO_25K_008702", "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 ≈ 1.564 osmol/L.
{ "id": "WUA_BIO_25K_008703", "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) ≈ 59787939.26.
{ "id": "WUA_BIO_25K_008704", "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) ≈ 20338454.30.
{ "id": "WUA_BIO_25K_008705", "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) ≈ 206015.85.
{ "id": "WUA_BIO_25K_008706", "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": "Hardy–Weinberg: p+q=1. Given q=0.272, com...
p=0.728; 2pq=0.396; q^2=0.074.
{ "id": "WUA_BIO_25K_008707", "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": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 100.23 (same units as Vmax).
{ "id": "WUA_BIO_25K_008708", "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 ≈ 1.131 osmol/L.
{ "id": "WUA_BIO_25K_008709", "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=0.251, com...
p=0.749; 2pq=0.376; q^2=0.063.
{ "id": "WUA_BIO_25K_008710", "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=0.269, com...
p=0.731; 2pq=0.393; q^2=0.072.
{ "id": "WUA_BIO_25K_008711", "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": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 102.90 (same units as Vmax).
{ "id": "WUA_BIO_25K_008712", "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=0.475, com...
p=0.525; 2pq=0.499; q^2=0.226.
{ "id": "WUA_BIO_25K_008713", "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) ≈ 59707415.95.
{ "id": "WUA_BIO_25K_008714", "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=0.28 each i...
Probability = p^n = 0.0005.
{ "id": "WUA_BIO_25K_008715", "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) ≈ 189343.44.
{ "id": "WUA_BIO_25K_008716", "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=0.54 each i...
Probability = p^n = 0.0072.
{ "id": "WUA_BIO_25K_008717", "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=0.296, com...
p=0.704; 2pq=0.417; q^2=0.088.
{ "id": "WUA_BIO_25K_008718", "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 ≈ 262.29 (same units as Vmax).
{ "id": "WUA_BIO_25K_008719", "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": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 1.206 osmol/L.
{ "id": "WUA_BIO_25K_008720", "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) ≈ 67435.52.
{ "id": "WUA_BIO_25K_008721", "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=0.83 each i...
Probability = p^n = 0.1869.
{ "id": "WUA_BIO_25K_008722", "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 ≈ 290.36 (same units as Vmax).
{ "id": "WUA_BIO_25K_008723", "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 ≈ 1.42 h.
{ "id": "WUA_BIO_25K_008724", "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=0.076, com...
p=0.924; 2pq=0.140; q^2=0.006.
{ "id": "WUA_BIO_25K_008725", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 213646243772.15.
{ "id": "WUA_BIO_25K_008726", "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=0.57 each i...
Probability = p^n = 0.0602.
{ "id": "WUA_BIO_25K_008727", "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) ≈ 3529081.89.
{ "id": "WUA_BIO_25K_008728", "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=0.134, com...
p=0.866; 2pq=0.232; q^2=0.018.
{ "id": "WUA_BIO_25K_008729", "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=0.412, com...
p=0.588; 2pq=0.485; q^2=0.170.
{ "id": "WUA_BIO_25K_008730", "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": "If an event has probability p=0.71 each i...
Probability = p^n = 0.0458.
{ "id": "WUA_BIO_25K_008731", "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) ≈ 11316.40.
{ "id": "WUA_BIO_25K_008732", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 187160067443.54.
{ "id": "WUA_BIO_25K_008733", "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=0.053, com...
p=0.947; 2pq=0.100; q^2=0.003.
{ "id": "WUA_BIO_25K_008734", "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 ≈ 0.544 osmol/L.
{ "id": "WUA_BIO_25K_008735", "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) ≈ 147590.12.
{ "id": "WUA_BIO_25K_008736", "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 ≈ 0.381 osmol/L.
{ "id": "WUA_BIO_25K_008737", "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": "If an event has probability p=0.54 each i...
Probability = p^n = 0.0850.
{ "id": "WUA_BIO_25K_008738", "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=0.3 each in...
Probability = p^n = 0.0024.
{ "id": "WUA_BIO_25K_008739", "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=0.088, com...
p=0.912; 2pq=0.161; q^2=0.008.
{ "id": "WUA_BIO_25K_008740", "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) ≈ 591692907.25.
{ "id": "WUA_BIO_25K_008741", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 627537558.41.
{ "id": "WUA_BIO_25K_008742", "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 ≈ 237.44 (same units as Vmax).
{ "id": "WUA_BIO_25K_008743", "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": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.08 h.
{ "id": "WUA_BIO_25K_008744", "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": "Hardy–Weinberg: p+q=1. Given q=0.43, comp...
p=0.570; 2pq=0.490; q^2=0.185.
{ "id": "WUA_BIO_25K_008745", "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=0.234, com...
p=0.766; 2pq=0.358; q^2=0.055.
{ "id": "WUA_BIO_25K_008746", "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": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.306 osmol/L.
{ "id": "WUA_BIO_25K_008747", "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=0.206, com...
p=0.794; 2pq=0.327; q^2=0.042.
{ "id": "WUA_BIO_25K_008748", "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": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 349.85 (same units as Vmax).
{ "id": "WUA_BIO_25K_008749", "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 ≈ 128.39 (same units as Vmax).
{ "id": "WUA_BIO_25K_008750", "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=0.14, comp...
p=0.860; 2pq=0.241; q^2=0.020.
{ "id": "WUA_BIO_25K_008751", "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=0.42 each i...
Probability = p^n = 0.0010.
{ "id": "WUA_BIO_25K_008752", "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) ≈ 768374.75.
{ "id": "WUA_BIO_25K_008753", "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) ≈ 1094.08.
{ "id": "WUA_BIO_25K_008754", "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 ≈ 108.26 (same units as Vmax).
{ "id": "WUA_BIO_25K_008755", "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) ≈ 1824.07.
{ "id": "WUA_BIO_25K_008756", "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 ≈ 0.812 osmol/L.
{ "id": "WUA_BIO_25K_008757", "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 ≈ 3.854 osmol/L.
{ "id": "WUA_BIO_25K_008758", "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 ≈ 189.90 (same units as Vmax).
{ "id": "WUA_BIO_25K_008759", "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": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.15 h.
{ "id": "WUA_BIO_25K_008760", "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=0.029, com...
p=0.971; 2pq=0.056; q^2=0.001.
{ "id": "WUA_BIO_25K_008761", "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": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 165.07 (same units as Vmax).
{ "id": "WUA_BIO_25K_008762", "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: doubling time t_d = l...
t_d ≈ 1.40 h.
{ "id": "WUA_BIO_25K_008763", "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=0.056, com...
p=0.944; 2pq=0.106; q^2=0.003.
{ "id": "WUA_BIO_25K_008764", "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: doubling time t_d = l...
t_d ≈ 2.56 h.
{ "id": "WUA_BIO_25K_008765", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 2787.96.
{ "id": "WUA_BIO_25K_008766", "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=0.5 each in...
Probability = p^n = 0.0039.
{ "id": "WUA_BIO_25K_008767", "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: doubling time t_d = l...
t_d ≈ 7.70 h.
{ "id": "WUA_BIO_25K_008768", "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 ≈ 406.38 (same units as Vmax).
{ "id": "WUA_BIO_25K_008769", "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 ≈ 94.53 (same units as Vmax).
{ "id": "WUA_BIO_25K_008770", "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=0.87 each i...
Probability = p^n = 0.3773.
{ "id": "WUA_BIO_25K_008771", "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": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.22 h.
{ "id": "WUA_BIO_25K_008772", "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 ≈ 187.66 (same units as Vmax).
{ "id": "WUA_BIO_25K_008773", "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 ≈ 324.86 (same units as Vmax).
{ "id": "WUA_BIO_25K_008774", "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 ≈ 425.87 (same units as Vmax).
{ "id": "WUA_BIO_25K_008775", "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": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 1816.67.
{ "id": "WUA_BIO_25K_008776", "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) ≈ 3332.31.
{ "id": "WUA_BIO_25K_008777", "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 ≈ 0.90 h.
{ "id": "WUA_BIO_25K_008778", "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=0.402, com...
p=0.598; 2pq=0.481; q^2=0.162.
{ "id": "WUA_BIO_25K_008779", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 1189242728.45.
{ "id": "WUA_BIO_25K_008780", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 2931.26.
{ "id": "WUA_BIO_25K_008781", "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 ≈ 2.127 osmol/L.
{ "id": "WUA_BIO_25K_008782", "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": "If an event has probability p=0.69 each i...
Probability = p^n = 0.1079.
{ "id": "WUA_BIO_25K_008783", "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": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 12.70 (same units as Vmax).
{ "id": "WUA_BIO_25K_008784", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 2476812157.91.
{ "id": "WUA_BIO_25K_008785", "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: doubling time t_d = l...
t_d ≈ 1.59 h.
{ "id": "WUA_BIO_25K_008786", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 20094.73.
{ "id": "WUA_BIO_25K_008787", "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": "Hardy–Weinberg: p+q=1. Given q=0.369, com...
p=0.631; 2pq=0.466; q^2=0.136.
{ "id": "WUA_BIO_25K_008788", "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 ≈ 1.02 h.
{ "id": "WUA_BIO_25K_008789", "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 ≈ 1.04 h.
{ "id": "WUA_BIO_25K_008790", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 2955870.90.
{ "id": "WUA_BIO_25K_008791", "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=0.306, com...
p=0.694; 2pq=0.425; q^2=0.094.
{ "id": "WUA_BIO_25K_008792", "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=0.182, com...
p=0.818; 2pq=0.298; q^2=0.033.
{ "id": "WUA_BIO_25K_008793", "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=0.32, comp...
p=0.680; 2pq=0.435; q^2=0.102.
{ "id": "WUA_BIO_25K_008794", "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=0.479, com...
p=0.521; 2pq=0.499; q^2=0.229.
{ "id": "WUA_BIO_25K_008795", "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": "If an event has probability p=0.85 each i...
Probability = p^n = 0.4437.
{ "id": "WUA_BIO_25K_008796", "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: doubling time t_d = l...
t_d ≈ 1.14 h.
{ "id": "WUA_BIO_25K_008797", "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 ≈ 182.92 (same units as Vmax).
{ "id": "WUA_BIO_25K_008798", "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": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 145.40 (same units as Vmax).
{ "id": "WUA_BIO_25K_008799", "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=0.86 each i...
Probability = p^n = 0.2573.
{ "id": "WUA_BIO_25K_008800", "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" } ]
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