prompt
dict
response
string
meta
dict
fact_sources
list
artifacts
dict
{ "messages": [ { "role": "system", "content": "You are 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=0.11 each i...
Probability = p^n = 0.0000.
{ "id": "WUA_BIO_25K_016701", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.14 h.
{ "id": "WUA_BIO_25K_016702", "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 ≈ 295.95 (same units as Vmax).
{ "id": "WUA_BIO_25K_016703", "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 ≈ 7.99 (same units as Vmax).
{ "id": "WUA_BIO_25K_016704", "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 ≈ 316.38 (same units as Vmax).
{ "id": "WUA_BIO_25K_016705", "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) ≈ 38362.97.
{ "id": "WUA_BIO_25K_016706", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Hardy–Weinberg: p+q=1. Given q=0.053, com...
p=0.947; 2pq=0.100; q^2=0.003.
{ "id": "WUA_BIO_25K_016707", "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 ≈ 1.05 h.
{ "id": "WUA_BIO_25K_016708", "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 ≈ 81.94 (same units as Vmax).
{ "id": "WUA_BIO_25K_016709", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.72 h.
{ "id": "WUA_BIO_25K_016710", "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) ≈ 4937117.25.
{ "id": "WUA_BIO_25K_016711", "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=0.49 each i...
Probability = p^n = 0.0008.
{ "id": "WUA_BIO_25K_016712", "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=0.54 each i...
Probability = p^n = 0.0072.
{ "id": "WUA_BIO_25K_016713", "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=0.47 each i...
Probability = p^n = 0.2209.
{ "id": "WUA_BIO_25K_016714", "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 ≈ 1.21 h.
{ "id": "WUA_BIO_25K_016715", "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=0.8 each in...
Probability = p^n = 0.1342.
{ "id": "WUA_BIO_25K_016716", "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 ≈ 1.480 osmol/L.
{ "id": "WUA_BIO_25K_016717", "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 ≈ 1.674 osmol/L.
{ "id": "WUA_BIO_25K_016718", "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=0.24 each i...
Probability = p^n = 0.0576.
{ "id": "WUA_BIO_25K_016719", "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 ≈ 360.11 (same units as Vmax).
{ "id": "WUA_BIO_25K_016720", "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 ≈ 0.087 osmol/L.
{ "id": "WUA_BIO_25K_016721", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 47425.23.
{ "id": "WUA_BIO_25K_016722", "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 ≈ 4.884 osmol/L.
{ "id": "WUA_BIO_25K_016723", "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 ≈ 108.74 (same units as Vmax).
{ "id": "WUA_BIO_25K_016724", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 0.90 h.
{ "id": "WUA_BIO_25K_016725", "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=0.19, comp...
p=0.810; 2pq=0.308; q^2=0.036.
{ "id": "WUA_BIO_25K_016726", "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=0.89 each i...
Probability = p^n = 0.5584.
{ "id": "WUA_BIO_25K_016727", "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 ≈ 216.52 (same units as Vmax).
{ "id": "WUA_BIO_25K_016728", "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 ≈ 201.57 (same units as Vmax).
{ "id": "WUA_BIO_25K_016729", "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=0.222, com...
p=0.778; 2pq=0.345; q^2=0.049.
{ "id": "WUA_BIO_25K_016730", "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 ≈ 1.996 osmol/L.
{ "id": "WUA_BIO_25K_016731", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 3186.88.
{ "id": "WUA_BIO_25K_016732", "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=0.096, com...
p=0.904; 2pq=0.174; q^2=0.009.
{ "id": "WUA_BIO_25K_016733", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 5.916 osmol/L.
{ "id": "WUA_BIO_25K_016734", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 16724.96.
{ "id": "WUA_BIO_25K_016735", "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=0.86 each i...
Probability = p^n = 0.2213.
{ "id": "WUA_BIO_25K_016736", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 2.62 h.
{ "id": "WUA_BIO_25K_016737", "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) ≈ 995266.10.
{ "id": "WUA_BIO_25K_016738", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.335 osmol/L.
{ "id": "WUA_BIO_25K_016739", "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 ≈ 264.26 (same units as Vmax).
{ "id": "WUA_BIO_25K_016740", "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 ≈ 208.40 (same units as Vmax).
{ "id": "WUA_BIO_25K_016741", "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) ≈ 103891.38.
{ "id": "WUA_BIO_25K_016742", "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) ≈ 14536.02.
{ "id": "WUA_BIO_25K_016743", "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) ≈ 2755.35.
{ "id": "WUA_BIO_25K_016744", "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 ≈ 1.27 h.
{ "id": "WUA_BIO_25K_016745", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 1.455 osmol/L.
{ "id": "WUA_BIO_25K_016746", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.468 osmol/L.
{ "id": "WUA_BIO_25K_016747", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 1176.87.
{ "id": "WUA_BIO_25K_016748", "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 ≈ 231.21 (same units as Vmax).
{ "id": "WUA_BIO_25K_016749", "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 ≈ 119.45 (same units as Vmax).
{ "id": "WUA_BIO_25K_016750", "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 ≈ 69.91 (same units as Vmax).
{ "id": "WUA_BIO_25K_016751", "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 ≈ 234.04 (same units as Vmax).
{ "id": "WUA_BIO_25K_016752", "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=0.227, com...
p=0.773; 2pq=0.351; q^2=0.052.
{ "id": "WUA_BIO_25K_016753", "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 ≈ 2.028 osmol/L.
{ "id": "WUA_BIO_25K_016754", "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 ≈ 1.52 h.
{ "id": "WUA_BIO_25K_016755", "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=0.65 each i...
Probability = p^n = 0.2746.
{ "id": "WUA_BIO_25K_016756", "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) ≈ 567060192.13.
{ "id": "WUA_BIO_25K_016757", "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=0.28, comp...
p=0.720; 2pq=0.403; q^2=0.078.
{ "id": "WUA_BIO_25K_016758", "domain": "master_scholars_academics", "subdomain": "bio_math::population_genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "If an event has probability p=0.25 each i...
Probability = p^n = 0.0000.
{ "id": "WUA_BIO_25K_016759", "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 ≈ 0.709 osmol/L.
{ "id": "WUA_BIO_25K_016760", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.49 h.
{ "id": "WUA_BIO_25K_016761", "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 ≈ 63.60 (same units as Vmax).
{ "id": "WUA_BIO_25K_016762", "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=0.154, com...
p=0.846; 2pq=0.261; q^2=0.024.
{ "id": "WUA_BIO_25K_016763", "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 ≈ 0.99 h.
{ "id": "WUA_BIO_25K_016764", "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=0.66 each i...
Probability = p^n = 0.4356.
{ "id": "WUA_BIO_25K_016765", "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 ≈ 3.48 h.
{ "id": "WUA_BIO_25K_016766", "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=0.71 each i...
Probability = p^n = 0.0458.
{ "id": "WUA_BIO_25K_016767", "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 ≈ 6.30 h.
{ "id": "WUA_BIO_25K_016768", "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=0.15 each i...
Probability = p^n = 0.0005.
{ "id": "WUA_BIO_25K_016769", "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=0.207, com...
p=0.793; 2pq=0.328; q^2=0.043.
{ "id": "WUA_BIO_25K_016770", "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=0.29 each i...
Probability = p^n = 0.0002.
{ "id": "WUA_BIO_25K_016771", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 129637.26.
{ "id": "WUA_BIO_25K_016772", "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 ≈ 164.64 (same units as Vmax).
{ "id": "WUA_BIO_25K_016773", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 1.101 osmol/L.
{ "id": "WUA_BIO_25K_016774", "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 ≈ 207.54 (same units as Vmax).
{ "id": "WUA_BIO_25K_016775", "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 ≈ 0.849 osmol/L.
{ "id": "WUA_BIO_25K_016776", "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=0.12 each i...
Probability = p^n = 0.0000.
{ "id": "WUA_BIO_25K_016777", "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=0.21 each i...
Probability = p^n = 0.0093.
{ "id": "WUA_BIO_25K_016778", "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=0.433, com...
p=0.567; 2pq=0.491; q^2=0.187.
{ "id": "WUA_BIO_25K_016779", "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 ≈ 207.68 (same units as Vmax).
{ "id": "WUA_BIO_25K_016780", "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=0.65 each i...
Probability = p^n = 0.0490.
{ "id": "WUA_BIO_25K_016781", "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 ≈ 5.673 osmol/L.
{ "id": "WUA_BIO_25K_016782", "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=0.84 each i...
Probability = p^n = 0.1749.
{ "id": "WUA_BIO_25K_016783", "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) ≈ 97122.88.
{ "id": "WUA_BIO_25K_016784", "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=0.62 each i...
Probability = p^n = 0.0135.
{ "id": "WUA_BIO_25K_016785", "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 ≈ 5.013 osmol/L.
{ "id": "WUA_BIO_25K_016786", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.20 h.
{ "id": "WUA_BIO_25K_016787", "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=0.168, com...
p=0.832; 2pq=0.280; q^2=0.028.
{ "id": "WUA_BIO_25K_016788", "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=0.1 each in...
Probability = p^n = 0.0001.
{ "id": "WUA_BIO_25K_016789", "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=0.46 each i...
Probability = p^n = 0.0020.
{ "id": "WUA_BIO_25K_016790", "domain": "master_scholars_academics", "subdomain": "bio_math::genetics", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 72756141.99.
{ "id": "WUA_BIO_25K_016791", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "core", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", "t...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.034 osmol/L.
{ "id": "WUA_BIO_25K_016792", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.392 osmol/L.
{ "id": "WUA_BIO_25K_016793", "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) ≈ 4266.35.
{ "id": "WUA_BIO_25K_016794", "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 ≈ 1.418 osmol/L.
{ "id": "WUA_BIO_25K_016795", "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 ≈ 0.68 (same units as Vmax).
{ "id": "WUA_BIO_25K_016796", "domain": "master_scholars_academics", "subdomain": "bio_math::biochemistry", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: doubling time t_d = l...
t_d ≈ 1.62 h.
{ "id": "WUA_BIO_25K_016797", "domain": "master_scholars_academics", "subdomain": "bio_math::population", "task": "quantitative_or_structured_reasoning", "difficulty": "advanced", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv...
Osmolarity ≈ 0.479 osmol/L.
{ "id": "WUA_BIO_25K_016798", "domain": "master_scholars_academics", "subdomain": "bio_math::physiology", "task": "quantitative_or_structured_reasoning", "difficulty": "archon", "truth_mode": "self_contained", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:12:40", "license": "cc-by-4.0", ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:12:40" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer." }, { "role": "user", "content": "Exponential growth: N(t)=N0·e^(rt). Given...
N(t) ≈ 326629557.70.
{ "id": "WUA_BIO_25K_016799", "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=0.038, com...
p=0.962; 2pq=0.073; q^2=0.001.
{ "id": "WUA_BIO_25K_016800", "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" }