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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: 958 hPa to Pa." ...
P = 95800 Pa.
{ "id": "WUA_EARTH_25K_008901", "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 = 118.6 W/m²; Absorbed = 290.5 W/m².
{ "id": "WUA_EARTH_25K_008902", "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 = -280.5 mm.
{ "id": "WUA_EARTH_25K_008903", "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 ≈ 0.00558 kg/kg.
{ "id": "WUA_EARTH_25K_008904", "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 = 371.5 W/m²; Absorbed = 721.1 W/m².
{ "id": "WUA_EARTH_25K_008905", "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 ≈ 0.01857 kg/kg.
{ "id": "WUA_EARTH_25K_008906", "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 = 235.1 W/m²; Absorbed = 32.1 W/m².
{ "id": "WUA_EARTH_25K_008907", "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": "Convert pressure: 1002 hPa to Pa."...
P = 100200 Pa.
{ "id": "WUA_EARTH_25K_008908", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00636 kg/kg.
{ "id": "WUA_EARTH_25K_008909", "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) ≈ -23.69 °C.
{ "id": "WUA_EARTH_25K_008910", "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 ≈ 0.01604 kg/kg.
{ "id": "WUA_EARTH_25K_008911", "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 = 441.4 mm.
{ "id": "WUA_EARTH_25K_008912", "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: 969 hPa to Pa." ...
P = 96900 Pa.
{ "id": "WUA_EARTH_25K_008913", "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": "Convert pressure: 930 hPa to Pa." ...
P = 93000 Pa.
{ "id": "WUA_EARTH_25K_008914", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00770 kg/kg.
{ "id": "WUA_EARTH_25K_008915", "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 ≈ 0.01242 kg/kg.
{ "id": "WUA_EARTH_25K_008916", "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: 929 hPa to Pa." ...
P = 92900 Pa.
{ "id": "WUA_EARTH_25K_008917", "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 = 656.1 W/m²; Absorbed = 353.3 W/m².
{ "id": "WUA_EARTH_25K_008918", "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) ≈ 16.62 °C.
{ "id": "WUA_EARTH_25K_008919", "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 = 1222.0 W/m²; Absorbed = 135.8 W/m².
{ "id": "WUA_EARTH_25K_008920", "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) ≈ 15.95 °C.
{ "id": "WUA_EARTH_25K_008921", "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: 891 hPa to Pa." ...
P = 89100 Pa.
{ "id": "WUA_EARTH_25K_008922", "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: 1040 hPa to Pa."...
P = 104000 Pa.
{ "id": "WUA_EARTH_25K_008923", "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": "Convert pressure: 930 hPa to Pa." ...
P = 93000 Pa.
{ "id": "WUA_EARTH_25K_008924", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = -295.1 mm.
{ "id": "WUA_EARTH_25K_008925", "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: 1022 hPa to Pa."...
P = 102200 Pa.
{ "id": "WUA_EARTH_25K_008926", "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) ≈ -9.93 °C.
{ "id": "WUA_EARTH_25K_008927", "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 = 189.3 mm.
{ "id": "WUA_EARTH_25K_008928", "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 ≈ 0.01208 kg/kg.
{ "id": "WUA_EARTH_25K_008929", "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 = -29.2 mm.
{ "id": "WUA_EARTH_25K_008930", "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) ≈ -9.88 °C.
{ "id": "WUA_EARTH_25K_008931", "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) ≈ 23.44 °C.
{ "id": "WUA_EARTH_25K_008932", "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 = 474.8 W/m²; Absorbed = 474.8 W/m².
{ "id": "WUA_EARTH_25K_008933", "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) ≈ 8.60 °C.
{ "id": "WUA_EARTH_25K_008934", "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: 871 hPa to Pa." ...
P = 87100 Pa.
{ "id": "WUA_EARTH_25K_008935", "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 = 955.5 mm.
{ "id": "WUA_EARTH_25K_008936", "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: 992 hPa to Pa." ...
P = 99200 Pa.
{ "id": "WUA_EARTH_25K_008937", "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": "Convert pressure: 866 hPa to Pa." ...
P = 86600 Pa.
{ "id": "WUA_EARTH_25K_008938", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00882 kg/kg.
{ "id": "WUA_EARTH_25K_008939", "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 = 991.7 mm.
{ "id": "WUA_EARTH_25K_008940", "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 = 697.9 mm.
{ "id": "WUA_EARTH_25K_008941", "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: 888 hPa to Pa." ...
P = 88800 Pa.
{ "id": "WUA_EARTH_25K_008942", "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: 926 hPa to Pa." ...
P = 92600 Pa.
{ "id": "WUA_EARTH_25K_008943", "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": "Convert pressure: 916 hPa to Pa." ...
P = 91600 Pa.
{ "id": "WUA_EARTH_25K_008944", "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 = 697.3 W/m²; Absorbed = 328.1 W/m².
{ "id": "WUA_EARTH_25K_008945", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 886 hPa to Pa." ...
P = 88600 Pa.
{ "id": "WUA_EARTH_25K_008946", "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": "Convert pressure: 993 hPa to Pa." ...
P = 99300 Pa.
{ "id": "WUA_EARTH_25K_008947", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01634 kg/kg.
{ "id": "WUA_EARTH_25K_008948", "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 = 1285.8 mm.
{ "id": "WUA_EARTH_25K_008949", "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 ≈ 0.00423 kg/kg.
{ "id": "WUA_EARTH_25K_008950", "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 = 9.6 W/m²; Absorbed = 182.5 W/m².
{ "id": "WUA_EARTH_25K_008951", "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: 891 hPa to Pa." ...
P = 89100 Pa.
{ "id": "WUA_EARTH_25K_008952", "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 = 55.6 W/m²; Absorbed = 150.3 W/m².
{ "id": "WUA_EARTH_25K_008953", "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) ≈ 3.25 °C.
{ "id": "WUA_EARTH_25K_008954", "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 = 427.0 W/m²; Absorbed = 462.6 W/m².
{ "id": "WUA_EARTH_25K_008955", "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) ≈ 24.77 °C.
{ "id": "WUA_EARTH_25K_008956", "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 = 365.2 W/m²; Absorbed = 464.9 W/m².
{ "id": "WUA_EARTH_25K_008957", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 123.6 W/m²; Absorbed = 648.9 W/m².
{ "id": "WUA_EARTH_25K_008958", "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 = 1138.2 W/m²; Absorbed = 170.1 W/m².
{ "id": "WUA_EARTH_25K_008959", "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) ≈ 8.62 °C.
{ "id": "WUA_EARTH_25K_008960", "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 ≈ 0.01960 kg/kg.
{ "id": "WUA_EARTH_25K_008961", "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: 866 hPa to Pa." ...
P = 86600 Pa.
{ "id": "WUA_EARTH_25K_008962", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01442 kg/kg.
{ "id": "WUA_EARTH_25K_008963", "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 = 299.1 mm.
{ "id": "WUA_EARTH_25K_008964", "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 = 260.7 mm.
{ "id": "WUA_EARTH_25K_008965", "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) ≈ -27.71 °C.
{ "id": "WUA_EARTH_25K_008966", "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 ≈ 0.01337 kg/kg.
{ "id": "WUA_EARTH_25K_008967", "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: 878 hPa to Pa." ...
P = 87800 Pa.
{ "id": "WUA_EARTH_25K_008968", "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: 1043 hPa to Pa."...
P = 104300 Pa.
{ "id": "WUA_EARTH_25K_008969", "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 = 412.1 W/m²; Absorbed = 84.4 W/m².
{ "id": "WUA_EARTH_25K_008970", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 1049 hPa to Pa."...
P = 104900 Pa.
{ "id": "WUA_EARTH_25K_008971", "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: 882 hPa to Pa." ...
P = 88200 Pa.
{ "id": "WUA_EARTH_25K_008972", "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: 1003 hPa to Pa."...
P = 100300 Pa.
{ "id": "WUA_EARTH_25K_008973", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00881 kg/kg.
{ "id": "WUA_EARTH_25K_008974", "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) ≈ 4.04 °C.
{ "id": "WUA_EARTH_25K_008975", "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) ≈ 15.63 °C.
{ "id": "WUA_EARTH_25K_008976", "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: 974 hPa to Pa." ...
P = 97400 Pa.
{ "id": "WUA_EARTH_25K_008977", "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 = 134.7 W/m²; Absorbed = 574.4 W/m².
{ "id": "WUA_EARTH_25K_008978", "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 = 578.2 W/m²; Absorbed = 182.6 W/m².
{ "id": "WUA_EARTH_25K_008979", "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) ≈ -10.55 °C.
{ "id": "WUA_EARTH_25K_008980", "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) ≈ -9.01 °C.
{ "id": "WUA_EARTH_25K_008981", "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 ≈ 0.01268 kg/kg.
{ "id": "WUA_EARTH_25K_008982", "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 ≈ 0.01762 kg/kg.
{ "id": "WUA_EARTH_25K_008983", "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 ≈ 0.00819 kg/kg.
{ "id": "WUA_EARTH_25K_008984", "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 = 1046.5 mm.
{ "id": "WUA_EARTH_25K_008985", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 321.7 W/m²; Absorbed = 482.5 W/m².
{ "id": "WUA_EARTH_25K_008986", "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 = 1129.0 mm.
{ "id": "WUA_EARTH_25K_008987", "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 = 1581.7 mm.
{ "id": "WUA_EARTH_25K_008988", "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 = 723.5 mm.
{ "id": "WUA_EARTH_25K_008989", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ -17.67 °C.
{ "id": "WUA_EARTH_25K_008990", "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 = 70.2 mm.
{ "id": "WUA_EARTH_25K_008991", "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) ≈ -18.13 °C.
{ "id": "WUA_EARTH_25K_008992", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 1697.5 mm.
{ "id": "WUA_EARTH_25K_008993", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00972 kg/kg.
{ "id": "WUA_EARTH_25K_008994", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 941 hPa to Pa." ...
P = 94100 Pa.
{ "id": "WUA_EARTH_25K_008995", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ -1.08 °C.
{ "id": "WUA_EARTH_25K_008996", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "ta...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 21.95 °C.
{ "id": "WUA_EARTH_25K_008997", "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 = 491.7 W/m²; Absorbed = 242.2 W/m².
{ "id": "WUA_EARTH_25K_008998", "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"...
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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 = -517.2 mm.
{ "id": "WUA_EARTH_25K_008999", "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 = 101.3 mm.
{ "id": "WUA_EARTH_25K_009000", "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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