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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 5.65 °C.
{ "id": "WUA_EARTH_25K_008401", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -3.10 °C.
{ "id": "WUA_EARTH_25K_008402", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 125.4 W/m²; Absorbed = 80.1 W/m².
{ "id": "WUA_EARTH_25K_008403", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.02024 kg/kg.
{ "id": "WUA_EARTH_25K_008404", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 987 hPa to Pa." ...
P = 98700 Pa.
{ "id": "WUA_EARTH_25K_008405", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 964 hPa to Pa." ...
P = 96400 Pa.
{ "id": "WUA_EARTH_25K_008406", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = -311.4 mm.
{ "id": "WUA_EARTH_25K_008407", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -1.14 °C.
{ "id": "WUA_EARTH_25K_008408", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01380 kg/kg.
{ "id": "WUA_EARTH_25K_008409", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = -453.8 mm.
{ "id": "WUA_EARTH_25K_008410", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 1697.7 mm.
{ "id": "WUA_EARTH_25K_008411", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 875 hPa to Pa." ...
P = 87500 Pa.
{ "id": "WUA_EARTH_25K_008412", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = -418.5 mm.
{ "id": "WUA_EARTH_25K_008413", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 63.8 W/m²; Absorbed = 213.7 W/m².
{ "id": "WUA_EARTH_25K_008414", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 148.4 W/m²; Absorbed = 1200.3 W/m².
{ "id": "WUA_EARTH_25K_008415", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 656.0 mm.
{ "id": "WUA_EARTH_25K_008416", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 1016 hPa to Pa."...
P = 101600 Pa.
{ "id": "WUA_EARTH_25K_008417", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 240.4 W/m²; Absorbed = 181.4 W/m².
{ "id": "WUA_EARTH_25K_008418", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 55.7 W/m²; Absorbed = 136.2 W/m².
{ "id": "WUA_EARTH_25K_008419", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 691.3 mm.
{ "id": "WUA_EARTH_25K_008420", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -10.55 °C.
{ "id": "WUA_EARTH_25K_008421", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 974 hPa to Pa." ...
P = 97400 Pa.
{ "id": "WUA_EARTH_25K_008422", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 58.6 mm.
{ "id": "WUA_EARTH_25K_008423", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 70.2 W/m²; Absorbed = 470.0 W/m².
{ "id": "WUA_EARTH_25K_008424", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 277.8 W/m²; Absorbed = 833.3 W/m².
{ "id": "WUA_EARTH_25K_008425", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 1893.2 mm.
{ "id": "WUA_EARTH_25K_008426", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01942 kg/kg.
{ "id": "WUA_EARTH_25K_008427", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 524.1 W/m²; Absorbed = 270.0 W/m².
{ "id": "WUA_EARTH_25K_008428", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 1000 hPa to Pa."...
P = 100000 Pa.
{ "id": "WUA_EARTH_25K_008429", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 1010 hPa to Pa."...
P = 101000 Pa.
{ "id": "WUA_EARTH_25K_008430", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 1050 hPa to Pa."...
P = 105000 Pa.
{ "id": "WUA_EARTH_25K_008431", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 63.2 W/m²; Absorbed = 42.2 W/m².
{ "id": "WUA_EARTH_25K_008432", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 629.4 mm.
{ "id": "WUA_EARTH_25K_008433", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 634.8 mm.
{ "id": "WUA_EARTH_25K_008434", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 108.1 W/m²; Absorbed = 209.7 W/m².
{ "id": "WUA_EARTH_25K_008435", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 985 hPa to Pa." ...
P = 98500 Pa.
{ "id": "WUA_EARTH_25K_008436", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -5.21 °C.
{ "id": "WUA_EARTH_25K_008437", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 756.4 W/m²; Absorbed = 93.5 W/m².
{ "id": "WUA_EARTH_25K_008438", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 321.6 mm.
{ "id": "WUA_EARTH_25K_008439", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 18.49 °C.
{ "id": "WUA_EARTH_25K_008440", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 146.4 W/m²; Absorbed = 171.8 W/m².
{ "id": "WUA_EARTH_25K_008441", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 54.2 W/m²; Absorbed = 720.3 W/m².
{ "id": "WUA_EARTH_25K_008442", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 219.3 W/m²; Absorbed = 48.2 W/m².
{ "id": "WUA_EARTH_25K_008443", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 1370.4 mm.
{ "id": "WUA_EARTH_25K_008444", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 938 hPa to Pa." ...
P = 93800 Pa.
{ "id": "WUA_EARTH_25K_008445", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 923 hPa to Pa." ...
P = 92300 Pa.
{ "id": "WUA_EARTH_25K_008446", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 212.7 W/m²; Absorbed = 319.0 W/m².
{ "id": "WUA_EARTH_25K_008447", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 876 hPa to Pa." ...
P = 87600 Pa.
{ "id": "WUA_EARTH_25K_008448", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.02055 kg/kg.
{ "id": "WUA_EARTH_25K_008449", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -5.43 °C.
{ "id": "WUA_EARTH_25K_008450", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 862 hPa to Pa." ...
P = 86200 Pa.
{ "id": "WUA_EARTH_25K_008451", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 220.7 W/m²; Absorbed = 124.2 W/m².
{ "id": "WUA_EARTH_25K_008452", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 148.5 W/m²; Absorbed = 422.7 W/m².
{ "id": "WUA_EARTH_25K_008453", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 7.56 °C.
{ "id": "WUA_EARTH_25K_008454", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = -1209.6 mm.
{ "id": "WUA_EARTH_25K_008455", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 50.3 mm.
{ "id": "WUA_EARTH_25K_008456", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 78.9 W/m²; Absorbed = 72.8 W/m².
{ "id": "WUA_EARTH_25K_008457", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 861.3 W/m²; Absorbed = 189.1 W/m².
{ "id": "WUA_EARTH_25K_008458", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 872 hPa to Pa." ...
P = 87200 Pa.
{ "id": "WUA_EARTH_25K_008459", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00566 kg/kg.
{ "id": "WUA_EARTH_25K_008460", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 182.5 W/m²; Absorbed = 102.6 W/m².
{ "id": "WUA_EARTH_25K_008461", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 116.7 W/m²; Absorbed = 717.0 W/m².
{ "id": "WUA_EARTH_25K_008462", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 173.5 W/m²; Absorbed = 336.9 W/m².
{ "id": "WUA_EARTH_25K_008463", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 698.0 mm.
{ "id": "WUA_EARTH_25K_008464", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 317.6 W/m²; Absorbed = 540.8 W/m².
{ "id": "WUA_EARTH_25K_008465", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00413 kg/kg.
{ "id": "WUA_EARTH_25K_008466", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01595 kg/kg.
{ "id": "WUA_EARTH_25K_008467", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 1030 hPa to Pa."...
P = 103000 Pa.
{ "id": "WUA_EARTH_25K_008468", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 1015 hPa to Pa."...
P = 101500 Pa.
{ "id": "WUA_EARTH_25K_008469", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -25.20 °C.
{ "id": "WUA_EARTH_25K_008470", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01769 kg/kg.
{ "id": "WUA_EARTH_25K_008471", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 53.1 W/m²; Absorbed = 389.1 W/m².
{ "id": "WUA_EARTH_25K_008472", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00912 kg/kg.
{ "id": "WUA_EARTH_25K_008473", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01878 kg/kg.
{ "id": "WUA_EARTH_25K_008474", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = -209.0 mm.
{ "id": "WUA_EARTH_25K_008475", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 56.7 mm.
{ "id": "WUA_EARTH_25K_008476", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 402.2 W/m²; Absorbed = 113.5 W/m².
{ "id": "WUA_EARTH_25K_008477", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 734.5 mm.
{ "id": "WUA_EARTH_25K_008478", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 17.68 °C.
{ "id": "WUA_EARTH_25K_008479", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 988 hPa to Pa." ...
P = 98800 Pa.
{ "id": "WUA_EARTH_25K_008480", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 240.9 W/m²; Absorbed = 619.3 W/m².
{ "id": "WUA_EARTH_25K_008481", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -11.94 °C.
{ "id": "WUA_EARTH_25K_008482", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 1013 hPa to Pa."...
P = 101300 Pa.
{ "id": "WUA_EARTH_25K_008483", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 19.27 °C.
{ "id": "WUA_EARTH_25K_008484", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = -699.7 mm.
{ "id": "WUA_EARTH_25K_008485", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 675.4 mm.
{ "id": "WUA_EARTH_25K_008486", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01800 kg/kg.
{ "id": "WUA_EARTH_25K_008487", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -17.48 °C.
{ "id": "WUA_EARTH_25K_008488", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -12.18 °C.
{ "id": "WUA_EARTH_25K_008489", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -7.75 °C.
{ "id": "WUA_EARTH_25K_008490", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 32.1 mm.
{ "id": "WUA_EARTH_25K_008491", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 89.9 mm.
{ "id": "WUA_EARTH_25K_008492", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -16.04 °C.
{ "id": "WUA_EARTH_25K_008493", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 14.04 °C.
{ "id": "WUA_EARTH_25K_008494", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 12.60 °C.
{ "id": "WUA_EARTH_25K_008495", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 15.45 °C.
{ "id": "WUA_EARTH_25K_008496", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 26.91 °C.
{ "id": "WUA_EARTH_25K_008497", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 897 hPa to Pa." ...
P = 89700 Pa.
{ "id": "WUA_EARTH_25K_008498", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 55.4 W/m²; Absorbed = 102.8 W/m².
{ "id": "WUA_EARTH_25K_008499", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -17.26 °C.
{ "id": "WUA_EARTH_25K_008500", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags...
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