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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": "If an event has probability p=0.78 each i...
Probability = p^n = 0.2887.
{ "id": "WUA_BIO_25K_016201", "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) ≈ 902855.66.
{ "id": "WUA_BIO_25K_016202", "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) ≈ 53847980748.56.
{ "id": "WUA_BIO_25K_016203", "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=0.417, com...
p=0.583; 2pq=0.486; q^2=0.174.
{ "id": "WUA_BIO_25K_016204", "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 ≈ 1.24 h.
{ "id": "WUA_BIO_25K_016205", "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=0.51 each i...
Probability = p^n = 0.0012.
{ "id": "WUA_BIO_25K_016206", "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=0.244, com...
p=0.756; 2pq=0.369; q^2=0.060.
{ "id": "WUA_BIO_25K_016207", "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 ≈ 1.85 h.
{ "id": "WUA_BIO_25K_016208", "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) ≈ 107967107.25.
{ "id": "WUA_BIO_25K_016209", "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 ≈ 6.19 h.
{ "id": "WUA_BIO_25K_016210", "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) ≈ 9167438573.64.
{ "id": "WUA_BIO_25K_016211", "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=0.048, com...
p=0.952; 2pq=0.091; q^2=0.002.
{ "id": "WUA_BIO_25K_016212", "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": "Hardy–Weinberg: p+q=1. Given q=0.084, com...
p=0.916; 2pq=0.154; q^2=0.007.
{ "id": "WUA_BIO_25K_016213", "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) ≈ 31795064294.26.
{ "id": "WUA_BIO_25K_016214", "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 ≈ 210.94 (same units as Vmax).
{ "id": "WUA_BIO_25K_016215", "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": "Hardy–Weinberg: p+q=1. Given q=0.191, com...
p=0.809; 2pq=0.309; q^2=0.036.
{ "id": "WUA_BIO_25K_016216", "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=0.69 each i...
Probability = p^n = 0.0514.
{ "id": "WUA_BIO_25K_016217", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 6622000505.41.
{ "id": "WUA_BIO_25K_016218", "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=0.82 each i...
Probability = p^n = 0.2493.
{ "id": "WUA_BIO_25K_016219", "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 ≈ 412.87 (same units as Vmax).
{ "id": "WUA_BIO_25K_016220", "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 ≈ 1.880 osmol/L.
{ "id": "WUA_BIO_25K_016221", "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": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 341.88 (same units as Vmax).
{ "id": "WUA_BIO_25K_016222", "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) ≈ 8060.97.
{ "id": "WUA_BIO_25K_016223", "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) ≈ 6174.43.
{ "id": "WUA_BIO_25K_016224", "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=0.75 each i...
Probability = p^n = 0.1335.
{ "id": "WUA_BIO_25K_016225", "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=0.5 each in...
Probability = p^n = 0.0039.
{ "id": "WUA_BIO_25K_016226", "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 ≈ 0.532 osmol/L.
{ "id": "WUA_BIO_25K_016227", "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": "If an event has probability p=0.55 each i...
Probability = p^n = 0.0277.
{ "id": "WUA_BIO_25K_016228", "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": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 3.696 osmol/L.
{ "id": "WUA_BIO_25K_016229", "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=0.446, com...
p=0.554; 2pq=0.494; q^2=0.199.
{ "id": "WUA_BIO_25K_016230", "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=0.381, com...
p=0.619; 2pq=0.472; q^2=0.145.
{ "id": "WUA_BIO_25K_016231", "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=0.333, com...
p=0.667; 2pq=0.444; q^2=0.111.
{ "id": "WUA_BIO_25K_016232", "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) ≈ 619557.49.
{ "id": "WUA_BIO_25K_016233", "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) ≈ 2563235.89.
{ "id": "WUA_BIO_25K_016234", "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=0.28 each i...
Probability = p^n = 0.0220.
{ "id": "WUA_BIO_25K_016235", "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": "If an event has probability p=0.17 each i...
Probability = p^n = 0.0049.
{ "id": "WUA_BIO_25K_016236", "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=0.387, com...
p=0.613; 2pq=0.474; q^2=0.150.
{ "id": "WUA_BIO_25K_016237", "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=0.85 each i...
Probability = p^n = 0.7225.
{ "id": "WUA_BIO_25K_016238", "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 ≈ 1.38 h.
{ "id": "WUA_BIO_25K_016239", "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 ≈ 427.71 (same units as Vmax).
{ "id": "WUA_BIO_25K_016240", "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 ≈ 4.44 h.
{ "id": "WUA_BIO_25K_016241", "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 ≈ 4.143 osmol/L.
{ "id": "WUA_BIO_25K_016242", "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": "If an event has probability p=0.61 each i...
Probability = p^n = 0.2270.
{ "id": "WUA_BIO_25K_016243", "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) ≈ 437575816.74.
{ "id": "WUA_BIO_25K_016244", "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) ≈ 21206122.69.
{ "id": "WUA_BIO_25K_016245", "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 ≈ 3.462 osmol/L.
{ "id": "WUA_BIO_25K_016246", "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=0.321, com...
p=0.679; 2pq=0.436; q^2=0.103.
{ "id": "WUA_BIO_25K_016247", "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 ≈ 70.34 (same units as Vmax).
{ "id": "WUA_BIO_25K_016248", "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 ≈ 1.33 h.
{ "id": "WUA_BIO_25K_016249", "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) ≈ 100271.22.
{ "id": "WUA_BIO_25K_016250", "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 ≈ 6.80 h.
{ "id": "WUA_BIO_25K_016251", "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=0.356, com...
p=0.644; 2pq=0.459; q^2=0.127.
{ "id": "WUA_BIO_25K_016252", "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": "Hardy–Weinberg: p+q=1. Given q=0.197, com...
p=0.803; 2pq=0.316; q^2=0.039.
{ "id": "WUA_BIO_25K_016253", "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 ≈ 19.98 (same units as Vmax).
{ "id": "WUA_BIO_25K_016254", "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 ≈ 375.14 (same units as Vmax).
{ "id": "WUA_BIO_25K_016255", "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 ≈ 0.713 osmol/L.
{ "id": "WUA_BIO_25K_016256", "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 ≈ 8.89 h.
{ "id": "WUA_BIO_25K_016257", "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 ≈ 4.50 h.
{ "id": "WUA_BIO_25K_016258", "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 ≈ 1.37 h.
{ "id": "WUA_BIO_25K_016259", "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 ≈ 24.51 (same units as Vmax).
{ "id": "WUA_BIO_25K_016260", "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=0.81 each i...
Probability = p^n = 0.3487.
{ "id": "WUA_BIO_25K_016261", "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 ≈ 80.97 (same units as Vmax).
{ "id": "WUA_BIO_25K_016262", "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 ≈ 1.110 osmol/L.
{ "id": "WUA_BIO_25K_016263", "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": "If an event has probability p=0.17 each i...
Probability = p^n = 0.0049.
{ "id": "WUA_BIO_25K_016264", "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 ≈ 313.32 (same units as Vmax).
{ "id": "WUA_BIO_25K_016265", "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 ≈ 4.206 osmol/L.
{ "id": "WUA_BIO_25K_016266", "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 ≈ 1.41 h.
{ "id": "WUA_BIO_25K_016267", "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 ≈ 2.508 osmol/L.
{ "id": "WUA_BIO_25K_016268", "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 ≈ 9.63 h.
{ "id": "WUA_BIO_25K_016269", "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 ≈ 57.33 (same units as Vmax).
{ "id": "WUA_BIO_25K_016270", "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=0.245, com...
p=0.755; 2pq=0.370; q^2=0.060.
{ "id": "WUA_BIO_25K_016271", "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=0.33 each i...
Probability = p^n = 0.0001.
{ "id": "WUA_BIO_25K_016272", "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 ≈ 2.292 osmol/L.
{ "id": "WUA_BIO_25K_016273", "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": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 229.90 (same units as Vmax).
{ "id": "WUA_BIO_25K_016274", "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": "Hardy–Weinberg: p+q=1. Given q=0.048, com...
p=0.952; 2pq=0.091; q^2=0.002.
{ "id": "WUA_BIO_25K_016275", "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": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 3.591 osmol/L.
{ "id": "WUA_BIO_25K_016276", "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 ≈ 2.670 osmol/L.
{ "id": "WUA_BIO_25K_016277", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 3673.18.
{ "id": "WUA_BIO_25K_016278", "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=0.206, com...
p=0.794; 2pq=0.327; q^2=0.042.
{ "id": "WUA_BIO_25K_016279", "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=0.72 each i...
Probability = p^n = 0.3732.
{ "id": "WUA_BIO_25K_016280", "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 ≈ 52.00 (same units as Vmax).
{ "id": "WUA_BIO_25K_016281", "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=0.19 each i...
Probability = p^n = 0.0013.
{ "id": "WUA_BIO_25K_016282", "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": "If an event has probability p=0.3 each in...
Probability = p^n = 0.0000.
{ "id": "WUA_BIO_25K_016283", "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: N(t)=N0·e^(rt). Given...
N(t) ≈ 9513.37.
{ "id": "WUA_BIO_25K_016284", "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 ≈ 122.12 (same units as Vmax).
{ "id": "WUA_BIO_25K_016285", "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 ≈ 229.15 (same units as Vmax).
{ "id": "WUA_BIO_25K_016286", "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=0.53 each i...
Probability = p^n = 0.0062.
{ "id": "WUA_BIO_25K_016287", "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) ≈ 358621542.75.
{ "id": "WUA_BIO_25K_016288", "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=0.42 each i...
Probability = p^n = 0.0023.
{ "id": "WUA_BIO_25K_016289", "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 ≈ 0.780 osmol/L.
{ "id": "WUA_BIO_25K_016290", "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) ≈ 10991.87.
{ "id": "WUA_BIO_25K_016291", "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 ≈ 0.98 h.
{ "id": "WUA_BIO_25K_016292", "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) ≈ 995970.82.
{ "id": "WUA_BIO_25K_016293", "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=0.499, com...
p=0.501; 2pq=0.500; q^2=0.249.
{ "id": "WUA_BIO_25K_016294", "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 ≈ 366.60 (same units as Vmax).
{ "id": "WUA_BIO_25K_016295", "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) ≈ 4376.94.
{ "id": "WUA_BIO_25K_016296", "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 ≈ 4.41 h.
{ "id": "WUA_BIO_25K_016297", "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=0.49 each i...
Probability = p^n = 0.1176.
{ "id": "WUA_BIO_25K_016298", "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) ≈ 156528921.80.
{ "id": "WUA_BIO_25K_016299", "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 ≈ 53.63 (same units as Vmax).
{ "id": "WUA_BIO_25K_016300", "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" }