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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) ≈ 31.85 °C.
{ "id": "WUA_EARTH_25K_012701", "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) ≈ -18.26 °C.
{ "id": "WUA_EARTH_25K_012702", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01319 kg/kg.
{ "id": "WUA_EARTH_25K_012703", "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) ≈ 1.67 °C.
{ "id": "WUA_EARTH_25K_012704", "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) ≈ -0.54 °C.
{ "id": "WUA_EARTH_25K_012705", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00929 kg/kg.
{ "id": "WUA_EARTH_25K_012706", "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: 1026 hPa to Pa."...
P = 102600 Pa.
{ "id": "WUA_EARTH_25K_012707", "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 = 253.0 W/m²; Absorbed = 449.8 W/m².
{ "id": "WUA_EARTH_25K_012708", "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 ≈ 0.00455 kg/kg.
{ "id": "WUA_EARTH_25K_012709", "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 = 988.7 mm.
{ "id": "WUA_EARTH_25K_012710", "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) ≈ 32.29 °C.
{ "id": "WUA_EARTH_25K_012711", "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 = 798.4 W/m²; Absorbed = 187.3 W/m².
{ "id": "WUA_EARTH_25K_012712", "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) ≈ 2.38 °C.
{ "id": "WUA_EARTH_25K_012713", "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) ≈ -3.83 °C.
{ "id": "WUA_EARTH_25K_012714", "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 = 323.3 mm.
{ "id": "WUA_EARTH_25K_012715", "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) ≈ -15.72 °C.
{ "id": "WUA_EARTH_25K_012716", "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 = 131.5 W/m²; Absorbed = 526.0 W/m².
{ "id": "WUA_EARTH_25K_012717", "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 = 145.9 W/m²; Absorbed = 145.9 W/m².
{ "id": "WUA_EARTH_25K_012718", "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) ≈ -5.81 °C.
{ "id": "WUA_EARTH_25K_012719", "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 ≈ 0.02200 kg/kg.
{ "id": "WUA_EARTH_25K_012720", "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 = 456.8 W/m²; Absorbed = 50.8 W/m².
{ "id": "WUA_EARTH_25K_012721", "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 = 142.6 W/m²; Absorbed = 1153.8 W/m².
{ "id": "WUA_EARTH_25K_012722", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01319 kg/kg.
{ "id": "WUA_EARTH_25K_012723", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00880 kg/kg.
{ "id": "WUA_EARTH_25K_012724", "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 = 13.4 W/m²; Absorbed = 254.9 W/m².
{ "id": "WUA_EARTH_25K_012725", "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) ≈ 2.65 °C.
{ "id": "WUA_EARTH_25K_012726", "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 = 382.9 W/m²; Absorbed = 651.9 W/m².
{ "id": "WUA_EARTH_25K_012727", "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 = 1430.3 mm.
{ "id": "WUA_EARTH_25K_012728", "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) ≈ 13.78 °C.
{ "id": "WUA_EARTH_25K_012729", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 655.7 W/m²; Absorbed = 174.3 W/m².
{ "id": "WUA_EARTH_25K_012730", "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 = 483.6 mm.
{ "id": "WUA_EARTH_25K_012731", "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": "Water balance: Q = P - ET - ΔS. Gi...
Q = -154.0 mm.
{ "id": "WUA_EARTH_25K_012732", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01321 kg/kg.
{ "id": "WUA_EARTH_25K_012733", "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 = -1093.1 mm.
{ "id": "WUA_EARTH_25K_012734", "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": "Convert pressure: 935 hPa to Pa." ...
P = 93500 Pa.
{ "id": "WUA_EARTH_25K_012735", "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 ≈ 0.00706 kg/kg.
{ "id": "WUA_EARTH_25K_012736", "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 = 1027.0 W/m²; Absorbed = 225.4 W/m².
{ "id": "WUA_EARTH_25K_012737", "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 = -491.5 mm.
{ "id": "WUA_EARTH_25K_012738", "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 = 704.1 W/m²; Absorbed = 154.5 W/m².
{ "id": "WUA_EARTH_25K_012739", "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) ≈ 24.24 °C.
{ "id": "WUA_EARTH_25K_012740", "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) ≈ 21.30 °C.
{ "id": "WUA_EARTH_25K_012741", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00969 kg/kg.
{ "id": "WUA_EARTH_25K_012742", "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 ≈ 0.00822 kg/kg.
{ "id": "WUA_EARTH_25K_012743", "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) ≈ -6.81 °C.
{ "id": "WUA_EARTH_25K_012744", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 143.6 W/m²; Absorbed = 40.5 W/m².
{ "id": "WUA_EARTH_25K_012745", "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 = 959.9 mm.
{ "id": "WUA_EARTH_25K_012746", "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: 875 hPa to Pa." ...
P = 87500 Pa.
{ "id": "WUA_EARTH_25K_012747", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 26.15 °C.
{ "id": "WUA_EARTH_25K_012748", "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) ≈ -26.19 °C.
{ "id": "WUA_EARTH_25K_012749", "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": "Water balance: Q = P - ET - ΔS. Gi...
Q = 224.2 mm.
{ "id": "WUA_EARTH_25K_012750", "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 = 260.8 mm.
{ "id": "WUA_EARTH_25K_012751", "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: 899 hPa to Pa." ...
P = 89900 Pa.
{ "id": "WUA_EARTH_25K_012752", "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": "Water balance: Q = P - ET - ΔS. Gi...
Q = 1422.0 mm.
{ "id": "WUA_EARTH_25K_012753", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01774 kg/kg.
{ "id": "WUA_EARTH_25K_012754", "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 = 416.8 mm.
{ "id": "WUA_EARTH_25K_012755", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 83.6 W/m²; Absorbed = 380.7 W/m².
{ "id": "WUA_EARTH_25K_012756", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 279.1 W/m²; Absorbed = 88.2 W/m².
{ "id": "WUA_EARTH_25K_012757", "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 ≈ 0.01411 kg/kg.
{ "id": "WUA_EARTH_25K_012758", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 294.0 W/m²; Absorbed = 188.0 W/m².
{ "id": "WUA_EARTH_25K_012759", "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": "Water balance: Q = P - ET - ΔS. Gi...
Q = -629.8 mm.
{ "id": "WUA_EARTH_25K_012760", "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": "Water balance: Q = P - ET - ΔS. Gi...
Q = -595.7 mm.
{ "id": "WUA_EARTH_25K_012761", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01555 kg/kg.
{ "id": "WUA_EARTH_25K_012762", "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 = 539.4 W/m²; Absorbed = 110.5 W/m².
{ "id": "WUA_EARTH_25K_012763", "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": "Convert pressure: 960 hPa to Pa." ...
P = 96000 Pa.
{ "id": "WUA_EARTH_25K_012764", "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 ≈ 0.00703 kg/kg.
{ "id": "WUA_EARTH_25K_012765", "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) ≈ -4.23 °C.
{ "id": "WUA_EARTH_25K_012766", "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 ≈ 0.01347 kg/kg.
{ "id": "WUA_EARTH_25K_012767", "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 ≈ 0.01495 kg/kg.
{ "id": "WUA_EARTH_25K_012768", "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) ≈ 20.79 °C.
{ "id": "WUA_EARTH_25K_012769", "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 = 98.5 mm.
{ "id": "WUA_EARTH_25K_012770", "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": "Water balance: Q = P - ET - ΔS. Gi...
Q = -758.6 mm.
{ "id": "WUA_EARTH_25K_012771", "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 ≈ 0.00674 kg/kg.
{ "id": "WUA_EARTH_25K_012772", "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 = 367.0 W/m²; Absorbed = 943.6 W/m².
{ "id": "WUA_EARTH_25K_012773", "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 = -1015.1 mm.
{ "id": "WUA_EARTH_25K_012774", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00912 kg/kg.
{ "id": "WUA_EARTH_25K_012775", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 670.4 W/m²; Absorbed = 428.6 W/m².
{ "id": "WUA_EARTH_25K_012776", "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 = 871.1 W/m²; Absorbed = 322.2 W/m².
{ "id": "WUA_EARTH_25K_012777", "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: 898 hPa to Pa." ...
P = 89800 Pa.
{ "id": "WUA_EARTH_25K_012778", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00624 kg/kg.
{ "id": "WUA_EARTH_25K_012779", "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 = 436.4 W/m²; Absorbed = 205.4 W/m².
{ "id": "WUA_EARTH_25K_012780", "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 = -571.3 mm.
{ "id": "WUA_EARTH_25K_012781", "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 = 868.2 W/m²; Absorbed = 408.5 W/m².
{ "id": "WUA_EARTH_25K_012782", "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 ≈ 0.00380 kg/kg.
{ "id": "WUA_EARTH_25K_012783", "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 = -418.4 mm.
{ "id": "WUA_EARTH_25K_012784", "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": "Water balance: Q = P - ET - ΔS. Gi...
Q = 737.7 mm.
{ "id": "WUA_EARTH_25K_012785", "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) ≈ -21.62 °C.
{ "id": "WUA_EARTH_25K_012786", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01395 kg/kg.
{ "id": "WUA_EARTH_25K_012787", "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: 904 hPa to Pa." ...
P = 90400 Pa.
{ "id": "WUA_EARTH_25K_012788", "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: 1026 hPa to Pa."...
P = 102600 Pa.
{ "id": "WUA_EARTH_25K_012789", "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 ≈ 0.01325 kg/kg.
{ "id": "WUA_EARTH_25K_012790", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 459.6 W/m²; Absorbed = 661.3 W/m².
{ "id": "WUA_EARTH_25K_012791", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 747.1 W/m²; Absorbed = 320.2 W/m².
{ "id": "WUA_EARTH_25K_012792", "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 = -699.4 mm.
{ "id": "WUA_EARTH_25K_012793", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.02077 kg/kg.
{ "id": "WUA_EARTH_25K_012794", "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) ≈ -1.43 °C.
{ "id": "WUA_EARTH_25K_012795", "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 ≈ 0.00735 kg/kg.
{ "id": "WUA_EARTH_25K_012796", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01901 kg/kg.
{ "id": "WUA_EARTH_25K_012797", "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": "Water balance: Q = P - ET - ΔS. Gi...
Q = 207.3 mm.
{ "id": "WUA_EARTH_25K_012798", "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) ≈ -17.62 °C.
{ "id": "WUA_EARTH_25K_012799", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00872 kg/kg.
{ "id": "WUA_EARTH_25K_012800", "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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