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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=0.37 each i...
Probability = p^n = 0.0009.
{ "id": "WUA_BIO_25K_015901", "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) ≈ 10953.48.
{ "id": "WUA_BIO_25K_015902", "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 ≈ 147.50 (same units as Vmax).
{ "id": "WUA_BIO_25K_015903", "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 ≈ 291.90 (same units as Vmax).
{ "id": "WUA_BIO_25K_015904", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.540 osmol/L.
{ "id": "WUA_BIO_25K_015905", "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 ≈ 4.78 h.
{ "id": "WUA_BIO_25K_015906", "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=0.031, com...
p=0.969; 2pq=0.060; q^2=0.001.
{ "id": "WUA_BIO_25K_015907", "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=0.52 each i...
Probability = p^n = 0.0198.
{ "id": "WUA_BIO_25K_015908", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 337.07 (same units as Vmax).
{ "id": "WUA_BIO_25K_015909", "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=0.53 each i...
Probability = p^n = 0.0789.
{ "id": "WUA_BIO_25K_015910", "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 ≈ 89.31 (same units as Vmax).
{ "id": "WUA_BIO_25K_015911", "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=0.67 each i...
Probability = p^n = 0.3008.
{ "id": "WUA_BIO_25K_015912", "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=0.36, comp...
p=0.640; 2pq=0.461; q^2=0.130.
{ "id": "WUA_BIO_25K_015913", "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) ≈ 59870577.57.
{ "id": "WUA_BIO_25K_015914", "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=0.361, com...
p=0.639; 2pq=0.461; q^2=0.130.
{ "id": "WUA_BIO_25K_015915", "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 ≈ 1.894 osmol/L.
{ "id": "WUA_BIO_25K_015916", "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=0.23 each i...
Probability = p^n = 0.0000.
{ "id": "WUA_BIO_25K_015917", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.11 h.
{ "id": "WUA_BIO_25K_015918", "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 ≈ 246.27 (same units as Vmax).
{ "id": "WUA_BIO_25K_015919", "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) ≈ 17510.28.
{ "id": "WUA_BIO_25K_015920", "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) ≈ 219692813364.96.
{ "id": "WUA_BIO_25K_015921", "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 ≈ 202.68 (same units as Vmax).
{ "id": "WUA_BIO_25K_015922", "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) ≈ 15118.04.
{ "id": "WUA_BIO_25K_015923", "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) ≈ 3069.30.
{ "id": "WUA_BIO_25K_015924", "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=0.094, com...
p=0.906; 2pq=0.170; q^2=0.009.
{ "id": "WUA_BIO_25K_015925", "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) ≈ 96331.05.
{ "id": "WUA_BIO_25K_015926", "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 ≈ 240.83 (same units as Vmax).
{ "id": "WUA_BIO_25K_015927", "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 ≈ 85.73 (same units as Vmax).
{ "id": "WUA_BIO_25K_015928", "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 ≈ 7.79 h.
{ "id": "WUA_BIO_25K_015929", "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) ≈ 536694968.91.
{ "id": "WUA_BIO_25K_015930", "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 ≈ 1.270 osmol/L.
{ "id": "WUA_BIO_25K_015931", "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=0.39 each i...
Probability = p^n = 0.1521.
{ "id": "WUA_BIO_25K_015932", "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 ≈ 1.04 h.
{ "id": "WUA_BIO_25K_015933", "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 ≈ 2.216 osmol/L.
{ "id": "WUA_BIO_25K_015934", "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 ≈ 2.42 h.
{ "id": "WUA_BIO_25K_015935", "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) ≈ 6379.60.
{ "id": "WUA_BIO_25K_015936", "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 ≈ 2.229 osmol/L.
{ "id": "WUA_BIO_25K_015937", "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=0.6 each in...
Probability = p^n = 0.0778.
{ "id": "WUA_BIO_25K_015938", "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 ≈ 5.574 osmol/L.
{ "id": "WUA_BIO_25K_015939", "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 ≈ 283.69 (same units as Vmax).
{ "id": "WUA_BIO_25K_015940", "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 ≈ 56.67 (same units as Vmax).
{ "id": "WUA_BIO_25K_015941", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.642 osmol/L.
{ "id": "WUA_BIO_25K_015942", "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) ≈ 1639396.56.
{ "id": "WUA_BIO_25K_015943", "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) ≈ 13007134.73.
{ "id": "WUA_BIO_25K_015944", "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) ≈ 275511.24.
{ "id": "WUA_BIO_25K_015945", "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 ≈ 259.63 (same units as Vmax).
{ "id": "WUA_BIO_25K_015946", "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 ≈ 2.75 h.
{ "id": "WUA_BIO_25K_015947", "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 ≈ 2.068 osmol/L.
{ "id": "WUA_BIO_25K_015948", "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=0.73 each i...
Probability = p^n = 0.0589.
{ "id": "WUA_BIO_25K_015949", "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=0.341, com...
p=0.659; 2pq=0.449; q^2=0.116.
{ "id": "WUA_BIO_25K_015950", "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=0.277, com...
p=0.723; 2pq=0.401; q^2=0.077.
{ "id": "WUA_BIO_25K_015951", "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=0.194, com...
p=0.806; 2pq=0.313; q^2=0.038.
{ "id": "WUA_BIO_25K_015952", "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) ≈ 101933.02.
{ "id": "WUA_BIO_25K_015953", "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 ≈ 75.63 (same units as Vmax).
{ "id": "WUA_BIO_25K_015954", "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) ≈ 22066869.73.
{ "id": "WUA_BIO_25K_015955", "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 ≈ 1.36 h.
{ "id": "WUA_BIO_25K_015956", "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=0.347, com...
p=0.653; 2pq=0.453; q^2=0.120.
{ "id": "WUA_BIO_25K_015957", "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) ≈ 22108802846.04.
{ "id": "WUA_BIO_25K_015958", "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) ≈ 3401407.43.
{ "id": "WUA_BIO_25K_015959", "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 ≈ 179.37 (same units as Vmax).
{ "id": "WUA_BIO_25K_015960", "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=0.46 each i...
Probability = p^n = 0.0020.
{ "id": "WUA_BIO_25K_015961", "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=0.012, com...
p=0.988; 2pq=0.024; q^2=0.000.
{ "id": "WUA_BIO_25K_015962", "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 ≈ 122.92 (same units as Vmax).
{ "id": "WUA_BIO_25K_015963", "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) ≈ 33407.53.
{ "id": "WUA_BIO_25K_015964", "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=0.62 each i...
Probability = p^n = 0.0084.
{ "id": "WUA_BIO_25K_015965", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.53 h.
{ "id": "WUA_BIO_25K_015966", "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 ≈ 1.17 h.
{ "id": "WUA_BIO_25K_015967", "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=0.339, com...
p=0.661; 2pq=0.448; q^2=0.115.
{ "id": "WUA_BIO_25K_015968", "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 ≈ 12.84 h.
{ "id": "WUA_BIO_25K_015969", "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 ≈ 299.23 (same units as Vmax).
{ "id": "WUA_BIO_25K_015970", "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 ≈ 178.80 (same units as Vmax).
{ "id": "WUA_BIO_25K_015971", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.116 osmol/L.
{ "id": "WUA_BIO_25K_015972", "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=0.419, com...
p=0.581; 2pq=0.487; q^2=0.176.
{ "id": "WUA_BIO_25K_015973", "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=0.175, com...
p=0.825; 2pq=0.289; q^2=0.031.
{ "id": "WUA_BIO_25K_015974", "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 ≈ 29.18 (same units as Vmax).
{ "id": "WUA_BIO_25K_015975", "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) ≈ 106292.15.
{ "id": "WUA_BIO_25K_015976", "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 ≈ 367.26 (same units as Vmax).
{ "id": "WUA_BIO_25K_015977", "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) ≈ 274987.67.
{ "id": "WUA_BIO_25K_015978", "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=0.014, com...
p=0.986; 2pq=0.028; q^2=0.000.
{ "id": "WUA_BIO_25K_015979", "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 ≈ 91.68 (same units as Vmax).
{ "id": "WUA_BIO_25K_015980", "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 ≈ 88.26 (same units as Vmax).
{ "id": "WUA_BIO_25K_015981", "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 ≈ 1.797 osmol/L.
{ "id": "WUA_BIO_25K_015982", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 202.29 (same units as Vmax).
{ "id": "WUA_BIO_25K_015983", "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=0.384, com...
p=0.616; 2pq=0.473; q^2=0.147.
{ "id": "WUA_BIO_25K_015984", "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=0.73 each i...
Probability = p^n = 0.0430.
{ "id": "WUA_BIO_25K_015985", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ...
v ≈ 139.94 (same units as Vmax).
{ "id": "WUA_BIO_25K_015986", "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=0.314, com...
p=0.686; 2pq=0.431; q^2=0.099.
{ "id": "WUA_BIO_25K_015987", "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=0.07, comp...
p=0.930; 2pq=0.130; q^2=0.005.
{ "id": "WUA_BIO_25K_015988", "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 ≈ 3.668 osmol/L.
{ "id": "WUA_BIO_25K_015989", "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=0.72 each i...
Probability = p^n = 0.0374.
{ "id": "WUA_BIO_25K_015990", "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 ≈ 140.72 (same units as Vmax).
{ "id": "WUA_BIO_25K_015991", "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 ≈ 334.87 (same units as Vmax).
{ "id": "WUA_BIO_25K_015992", "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 ≈ 2.86 (same units as Vmax).
{ "id": "WUA_BIO_25K_015993", "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) ≈ 28234514.91.
{ "id": "WUA_BIO_25K_015994", "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) ≈ 319221.97.
{ "id": "WUA_BIO_25K_015995", "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) ≈ 5941881.27.
{ "id": "WUA_BIO_25K_015996", "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=0.279, com...
p=0.721; 2pq=0.402; q^2=0.078.
{ "id": "WUA_BIO_25K_015997", "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) ≈ 85280.36.
{ "id": "WUA_BIO_25K_015998", "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=0.072, com...
p=0.928; 2pq=0.134; q^2=0.005.
{ "id": "WUA_BIO_25K_015999", "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 ≈ 1.674 osmol/L.
{ "id": "WUA_BIO_25K_016000", "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" }