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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 = 456.1 mm.
{ "id": "WUA_EARTH_25K_008601", "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) ≈ -19.66 °C.
{ "id": "WUA_EARTH_25K_008602", "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" } ]
{ "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 ≈ 0.00929 kg/kg.
{ "id": "WUA_EARTH_25K_008603", "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: 884 hPa to Pa." ...
P = 88400 Pa.
{ "id": "WUA_EARTH_25K_008604", "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: 940 hPa to Pa." ...
P = 94000 Pa.
{ "id": "WUA_EARTH_25K_008605", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 16.52 °C.
{ "id": "WUA_EARTH_25K_008606", "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 = -512.1 mm.
{ "id": "WUA_EARTH_25K_008607", "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: 922 hPa to Pa." ...
P = 92200 Pa.
{ "id": "WUA_EARTH_25K_008608", "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) ≈ 30.09 °C.
{ "id": "WUA_EARTH_25K_008609", "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" } ]
{ "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: 913 hPa to Pa." ...
P = 91300 Pa.
{ "id": "WUA_EARTH_25K_008610", "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 = 95.0 W/m²; Absorbed = 768.5 W/m².
{ "id": "WUA_EARTH_25K_008611", "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 = 223.1 W/m²; Absorbed = 1089.2 W/m².
{ "id": "WUA_EARTH_25K_008612", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 9.12 °C.
{ "id": "WUA_EARTH_25K_008613", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 23.21 °C.
{ "id": "WUA_EARTH_25K_008614", "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: 939 hPa to Pa." ...
P = 93900 Pa.
{ "id": "WUA_EARTH_25K_008615", "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 = 518.1 W/m²; Absorbed = 561.3 W/m².
{ "id": "WUA_EARTH_25K_008616", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ -13.10 °C.
{ "id": "WUA_EARTH_25K_008617", "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" } ]
{ "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 = 1596.7 mm.
{ "id": "WUA_EARTH_25K_008618", "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 = 244.5 W/m²; Absorbed = 1113.8 W/m².
{ "id": "WUA_EARTH_25K_008619", "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 = 816.7 mm.
{ "id": "WUA_EARTH_25K_008620", "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": "Convert pressure: 902 hPa to Pa." ...
P = 90200 Pa.
{ "id": "WUA_EARTH_25K_008621", "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 = 506.6 W/m²; Absorbed = 398.0 W/m².
{ "id": "WUA_EARTH_25K_008622", "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 = 446.5 W/m²; Absorbed = 273.6 W/m².
{ "id": "WUA_EARTH_25K_008623", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 14.54 °C.
{ "id": "WUA_EARTH_25K_008624", "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 = 930.0 W/m²; Absorbed = 458.1 W/m².
{ "id": "WUA_EARTH_25K_008625", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01043 kg/kg.
{ "id": "WUA_EARTH_25K_008626", "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" } ]
{ "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: 888 hPa to Pa." ...
P = 88800 Pa.
{ "id": "WUA_EARTH_25K_008627", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 13.43 °C.
{ "id": "WUA_EARTH_25K_008628", "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" } ]
{ "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) ≈ -1.40 °C.
{ "id": "WUA_EARTH_25K_008629", "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 = 167.8 W/m²; Absorbed = 1230.2 W/m².
{ "id": "WUA_EARTH_25K_008630", "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 = -755.8 mm.
{ "id": "WUA_EARTH_25K_008631", "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) ≈ 3.81 °C.
{ "id": "WUA_EARTH_25K_008632", "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 = 53.2 W/m²; Absorbed = 199.9 W/m².
{ "id": "WUA_EARTH_25K_008633", "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 = -73.7 mm.
{ "id": "WUA_EARTH_25K_008634", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00563 kg/kg.
{ "id": "WUA_EARTH_25K_008635", "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 = 97.3 W/m²; Absorbed = 263.1 W/m².
{ "id": "WUA_EARTH_25K_008636", "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 = 500.3 mm.
{ "id": "WUA_EARTH_25K_008637", "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 = 1184.0 mm.
{ "id": "WUA_EARTH_25K_008638", "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: 1006 hPa to Pa."...
P = 100600 Pa.
{ "id": "WUA_EARTH_25K_008639", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 6.73 °C.
{ "id": "WUA_EARTH_25K_008640", "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" } ]
{ "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) ≈ 11.38 °C.
{ "id": "WUA_EARTH_25K_008641", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 15.58 °C.
{ "id": "WUA_EARTH_25K_008642", "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" } ]
{ "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) ≈ -11.09 °C.
{ "id": "WUA_EARTH_25K_008643", "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 = 407.6 mm.
{ "id": "WUA_EARTH_25K_008644", "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 ≈ 0.01377 kg/kg.
{ "id": "WUA_EARTH_25K_008645", "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" } ]
{ "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 = -987.5 mm.
{ "id": "WUA_EARTH_25K_008646", "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 = 49.9 W/m²; Absorbed = 116.5 W/m².
{ "id": "WUA_EARTH_25K_008647", "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": "Convert pressure: 1031 hPa to Pa."...
P = 103100 Pa.
{ "id": "WUA_EARTH_25K_008648", "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: 864 hPa to Pa." ...
P = 86400 Pa.
{ "id": "WUA_EARTH_25K_008649", "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) ≈ -19.96 °C.
{ "id": "WUA_EARTH_25K_008650", "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 = 718.6 W/m²; Absorbed = 404.2 W/m².
{ "id": "WUA_EARTH_25K_008651", "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 = 705.1 mm.
{ "id": "WUA_EARTH_25K_008652", "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 = -603.0 mm.
{ "id": "WUA_EARTH_25K_008653", "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 ≈ 0.01377 kg/kg.
{ "id": "WUA_EARTH_25K_008654", "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" } ]
{ "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 = -168.8 mm.
{ "id": "WUA_EARTH_25K_008655", "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 = 741.7 mm.
{ "id": "WUA_EARTH_25K_008656", "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: 926 hPa to Pa." ...
P = 92600 Pa.
{ "id": "WUA_EARTH_25K_008657", "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 = 241.0 mm.
{ "id": "WUA_EARTH_25K_008658", "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) ≈ -2.78 °C.
{ "id": "WUA_EARTH_25K_008659", "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" } ]
{ "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 = 38.7 W/m²; Absorbed = 606.7 W/m².
{ "id": "WUA_EARTH_25K_008660", "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 ≈ 0.01646 kg/kg.
{ "id": "WUA_EARTH_25K_008661", "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" } ]
{ "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 ≈ 0.00703 kg/kg.
{ "id": "WUA_EARTH_25K_008662", "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" } ]
{ "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) ≈ 29.89 °C.
{ "id": "WUA_EARTH_25K_008663", "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 = 550.9 mm.
{ "id": "WUA_EARTH_25K_008664", "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) ≈ 5.46 °C.
{ "id": "WUA_EARTH_25K_008665", "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" } ]
{ "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 ≈ 0.01433 kg/kg.
{ "id": "WUA_EARTH_25K_008666", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 1.89 °C.
{ "id": "WUA_EARTH_25K_008667", "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 ≈ 0.00974 kg/kg.
{ "id": "WUA_EARTH_25K_008668", "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" } ]
{ "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 = -383.0 mm.
{ "id": "WUA_EARTH_25K_008669", "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 = -259.1 mm.
{ "id": "WUA_EARTH_25K_008670", "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 = 71.3 mm.
{ "id": "WUA_EARTH_25K_008671", "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) ≈ 19.10 °C.
{ "id": "WUA_EARTH_25K_008672", "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 ≈ 0.01357 kg/kg.
{ "id": "WUA_EARTH_25K_008673", "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 = 38.2 W/m²; Absorbed = 598.3 W/m².
{ "id": "WUA_EARTH_25K_008674", "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 = 787.2 mm.
{ "id": "WUA_EARTH_25K_008675", "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) ≈ 8.24 °C.
{ "id": "WUA_EARTH_25K_008676", "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" } ]
{ "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 = 51.5 mm.
{ "id": "WUA_EARTH_25K_008677", "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 ≈ 0.00429 kg/kg.
{ "id": "WUA_EARTH_25K_008678", "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: 1031 hPa to Pa."...
P = 103100 Pa.
{ "id": "WUA_EARTH_25K_008679", "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 = 294.1 W/m²; Absorbed = 132.1 W/m².
{ "id": "WUA_EARTH_25K_008680", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ -16.01 °C.
{ "id": "WUA_EARTH_25K_008681", "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" } ]
{ "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 = 133.1 W/m²; Absorbed = 282.8 W/m².
{ "id": "WUA_EARTH_25K_008682", "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) ≈ -2.98 °C.
{ "id": "WUA_EARTH_25K_008683", "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" } ]
{ "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 = -17.7 mm.
{ "id": "WUA_EARTH_25K_008684", "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) ≈ 15.11 °C.
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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: 888 hPa to Pa." ...
P = 88800 Pa.
{ "id": "WUA_EARTH_25K_008686", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01729 kg/kg.
{ "id": "WUA_EARTH_25K_008687", "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": "Water balance: Q = P - ET - ΔS. Gi...
Q = -185.0 mm.
{ "id": "WUA_EARTH_25K_008688", "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 = -838.8 mm.
{ "id": "WUA_EARTH_25K_008689", "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...
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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) ≈ -2.55 °C.
{ "id": "WUA_EARTH_25K_008690", "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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{ "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 ≈ 0.00339 kg/kg.
{ "id": "WUA_EARTH_25K_008691", "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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{ "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 = 246.0 W/m²; Absorbed = 872.0 W/m².
{ "id": "WUA_EARTH_25K_008692", "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...
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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 = 1121.9 mm.
{ "id": "WUA_EARTH_25K_008693", "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...
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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 = 97.9 W/m²; Absorbed = 990.3 W/m².
{ "id": "WUA_EARTH_25K_008694", "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...
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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 = 719.6 W/m²; Absorbed = 179.9 W/m².
{ "id": "WUA_EARTH_25K_008695", "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...
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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: 978 hPa to Pa." ...
P = 97800 Pa.
{ "id": "WUA_EARTH_25K_008696", "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": [ ...
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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 ≈ 0.01190 kg/kg.
{ "id": "WUA_EARTH_25K_008697", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00383 kg/kg.
{ "id": "WUA_EARTH_25K_008698", "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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{ "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 = 647.9 W/m²; Absorbed = 72.0 W/m².
{ "id": "WUA_EARTH_25K_008699", "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...
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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 = -836.9 mm.
{ "id": "WUA_EARTH_25K_008700", "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"...
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