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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 = 338.7 mm.
{ "id": "WUA_EARTH_25K_015201", "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 = 132.4 W/m²; Absorbed = 19.8 W/m².
{ "id": "WUA_EARTH_25K_015202", "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 = 284.8 mm.
{ "id": "WUA_EARTH_25K_015203", "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) ≈ 0.62 °C.
{ "id": "WUA_EARTH_25K_015204", "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 = 1435.7 mm.
{ "id": "WUA_EARTH_25K_015205", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -10.61 °C.
{ "id": "WUA_EARTH_25K_015206", "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) ≈ -4.57 °C.
{ "id": "WUA_EARTH_25K_015207", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 1.62 °C.
{ "id": "WUA_EARTH_25K_015208", "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 ≈ 0.01261 kg/kg.
{ "id": "WUA_EARTH_25K_015209", "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: 904 hPa to Pa." ...
P = 90400 Pa.
{ "id": "WUA_EARTH_25K_015210", "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: 983 hPa to Pa." ...
P = 98300 Pa.
{ "id": "WUA_EARTH_25K_015211", "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: 1014 hPa to Pa."...
P = 101400 Pa.
{ "id": "WUA_EARTH_25K_015212", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00921 kg/kg.
{ "id": "WUA_EARTH_25K_015213", "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 = 239.6 W/m²; Absorbed = 718.7 W/m².
{ "id": "WUA_EARTH_25K_015214", "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 = 181.4 mm.
{ "id": "WUA_EARTH_25K_015215", "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 ≈ 0.00361 kg/kg.
{ "id": "WUA_EARTH_25K_015216", "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: 949 hPa to Pa." ...
P = 94900 Pa.
{ "id": "WUA_EARTH_25K_015217", "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: 889 hPa to Pa." ...
P = 88900 Pa.
{ "id": "WUA_EARTH_25K_015218", "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: 1017 hPa to Pa."...
P = 101700 Pa.
{ "id": "WUA_EARTH_25K_015219", "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 = 489.0 W/m²; Absorbed = 416.6 W/m².
{ "id": "WUA_EARTH_25K_015220", "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 = 512.1 W/m²; Absorbed = 577.4 W/m².
{ "id": "WUA_EARTH_25K_015221", "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: 973 hPa to Pa." ...
P = 97300 Pa.
{ "id": "WUA_EARTH_25K_015222", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -10.26 °C.
{ "id": "WUA_EARTH_25K_015223", "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 = 320.1 W/m²; Absorbed = 43.6 W/m².
{ "id": "WUA_EARTH_25K_015224", "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 = -178.0 mm.
{ "id": "WUA_EARTH_25K_015225", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 1042.6 mm.
{ "id": "WUA_EARTH_25K_015226", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 999.1 mm.
{ "id": "WUA_EARTH_25K_015227", "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) ≈ 0.49 °C.
{ "id": "WUA_EARTH_25K_015228", "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 = 168.1 W/m²; Absorbed = 595.9 W/m².
{ "id": "WUA_EARTH_25K_015229", "domain": "master_scholars_academics", "subdomain": "earth_math::radiation", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ -11.21 °C.
{ "id": "WUA_EARTH_25K_015230", "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 = 1711.4 mm.
{ "id": "WUA_EARTH_25K_015231", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 1086.2 mm.
{ "id": "WUA_EARTH_25K_015232", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01695 kg/kg.
{ "id": "WUA_EARTH_25K_015233", "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: 996 hPa to Pa." ...
P = 99600 Pa.
{ "id": "WUA_EARTH_25K_015234", "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: 884 hPa to Pa." ...
P = 88400 Pa.
{ "id": "WUA_EARTH_25K_015235", "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 ≈ 0.00326 kg/kg.
{ "id": "WUA_EARTH_25K_015236", "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: 923 hPa to Pa." ...
P = 92300 Pa.
{ "id": "WUA_EARTH_25K_015237", "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: 906 hPa to Pa." ...
P = 90600 Pa.
{ "id": "WUA_EARTH_25K_015238", "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: 925 hPa to Pa." ...
P = 92500 Pa.
{ "id": "WUA_EARTH_25K_015239", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00665 kg/kg.
{ "id": "WUA_EARTH_25K_015240", "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) ≈ 22.14 °C.
{ "id": "WUA_EARTH_25K_015241", "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) ≈ -13.69 °C.
{ "id": "WUA_EARTH_25K_015242", "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: 850 hPa to Pa." ...
P = 85000 Pa.
{ "id": "WUA_EARTH_25K_015243", "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 = 642.3 W/m²; Absorbed = 754.0 W/m².
{ "id": "WUA_EARTH_25K_015244", "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 ≈ 0.02157 kg/kg.
{ "id": "WUA_EARTH_25K_015245", "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 = 378.5 W/m²; Absorbed = 252.3 W/m².
{ "id": "WUA_EARTH_25K_015246", "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: 1044 hPa to Pa."...
P = 104400 Pa.
{ "id": "WUA_EARTH_25K_015247", "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 ≈ 0.01493 kg/kg.
{ "id": "WUA_EARTH_25K_015248", "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) ≈ 12.08 °C.
{ "id": "WUA_EARTH_25K_015249", "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 ≈ 0.01297 kg/kg.
{ "id": "WUA_EARTH_25K_015250", "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 = 257.2 mm.
{ "id": "WUA_EARTH_25K_015251", "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 ≈ 0.01084 kg/kg.
{ "id": "WUA_EARTH_25K_015252", "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 ≈ 0.01128 kg/kg.
{ "id": "WUA_EARTH_25K_015253", "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 = 362.6 W/m²; Absorbed = 348.4 W/m².
{ "id": "WUA_EARTH_25K_015254", "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 ≈ 0.01790 kg/kg.
{ "id": "WUA_EARTH_25K_015255", "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 = 727.9 W/m²; Absorbed = 549.2 W/m².
{ "id": "WUA_EARTH_25K_015256", "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 = 717.8 W/m²; Absorbed = 107.2 W/m².
{ "id": "WUA_EARTH_25K_015257", "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: 1007 hPa to Pa."...
P = 100700 Pa.
{ "id": "WUA_EARTH_25K_015258", "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) ≈ -7.54 °C.
{ "id": "WUA_EARTH_25K_015259", "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: 900 hPa to Pa." ...
P = 90000 Pa.
{ "id": "WUA_EARTH_25K_015260", "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: 958 hPa to Pa." ...
P = 95800 Pa.
{ "id": "WUA_EARTH_25K_015261", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Water balance: Q = P - ET - ΔS. Gi...
Q = 460.4 mm.
{ "id": "WUA_EARTH_25K_015262", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Convert pressure: 860 hPa to Pa." ...
P = 86000 Pa.
{ "id": "WUA_EARTH_25K_015263", "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 = -595.9 mm.
{ "id": "WUA_EARTH_25K_015264", "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: 978 hPa to Pa." ...
P = 97800 Pa.
{ "id": "WUA_EARTH_25K_015265", "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 = 392.3 W/m²; Absorbed = 588.4 W/m².
{ "id": "WUA_EARTH_25K_015266", "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 = 118.6 W/m²; Absorbed = 320.6 W/m².
{ "id": "WUA_EARTH_25K_015267", "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 = 293.7 W/m²; Absorbed = 68.9 W/m².
{ "id": "WUA_EARTH_25K_015268", "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 = 41.1 W/m²; Absorbed = 644.2 W/m².
{ "id": "WUA_EARTH_25K_015269", "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) ≈ 27.06 °C.
{ "id": "WUA_EARTH_25K_015270", "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 ≈ 0.01499 kg/kg.
{ "id": "WUA_EARTH_25K_015271", "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 = 65.7 W/m²; Absorbed = 439.4 W/m².
{ "id": "WUA_EARTH_25K_015272", "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: 892 hPa to Pa." ...
P = 89200 Pa.
{ "id": "WUA_EARTH_25K_015273", "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 = 362.3 W/m²; Absorbed = 392.5 W/m².
{ "id": "WUA_EARTH_25K_015274", "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: 1028 hPa to Pa."...
P = 102800 Pa.
{ "id": "WUA_EARTH_25K_015275", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": ...
[ { "source_title": "Self-contained in prompt", "source_url": "", "evidence_type": "self_contained", "accessed_at_utc": "2026-01-04T05:02:58" } ]
{ "max_tokens_hint": 220, "style_contract": "concise_formal" }
{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 22.11 °C.
{ "id": "WUA_EARTH_25K_015276", "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: 958 hPa to Pa." ...
P = 95800 Pa.
{ "id": "WUA_EARTH_25K_015277", "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: 1048 hPa to Pa."...
P = 104800 Pa.
{ "id": "WUA_EARTH_25K_015278", "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 = 591.2 W/m²; Absorbed = 304.5 W/m².
{ "id": "WUA_EARTH_25K_015279", "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: 923 hPa to Pa." ...
P = 92300 Pa.
{ "id": "WUA_EARTH_25K_015280", "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 = 572.7 W/m²; Absorbed = 70.8 W/m².
{ "id": "WUA_EARTH_25K_015281", "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 ≈ 0.01171 kg/kg.
{ "id": "WUA_EARTH_25K_015282", "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) ≈ 18.34 °C.
{ "id": "WUA_EARTH_25K_015283", "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 ≈ 0.01481 kg/kg.
{ "id": "WUA_EARTH_25K_015284", "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) ≈ 19.82 °C.
{ "id": "WUA_EARTH_25K_015285", "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) ≈ -2.15 °C.
{ "id": "WUA_EARTH_25K_015286", "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) ≈ -0.52 °C.
{ "id": "WUA_EARTH_25K_015287", "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) ≈ -20.33 °C.
{ "id": "WUA_EARTH_25K_015288", "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": "Convert pressure: 991 hPa to Pa." ...
P = 99100 Pa.
{ "id": "WUA_EARTH_25K_015289", "domain": "master_scholars_academics", "subdomain": "earth_math::units", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags": [ ...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00561 kg/kg.
{ "id": "WUA_EARTH_25K_015290", "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: 887 hPa to Pa." ...
P = 88700 Pa.
{ "id": "WUA_EARTH_25K_015291", "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": [ ...
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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 = 1056.0 mm.
{ "id": "WUA_EARTH_25K_015292", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "advanced", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tag...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Albedo: reflected = α·S; absorbed=...
Reflected = 124.2 W/m²; Absorbed = 831.0 W/m².
{ "id": "WUA_EARTH_25K_015293", "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": "Temperature with lapse rate: T(z)=...
T(z) ≈ 24.19 °C.
{ "id": "WUA_EARTH_25K_015294", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.00916 kg/kg.
{ "id": "WUA_EARTH_25K_015295", "domain": "master_scholars_academics", "subdomain": "earth_math::atmosphere", "task": "quantitative_reasoning", "difficulty": "core", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags":...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI Master Scholars Earth & Climate Science Quantitative Reasoning. Use the formula provided. Show minimal steps and give the final answer with units." }, { "role": "user", "content": "Temperature with lapse rate: T(z)=...
T(z) ≈ 31.28 °C.
{ "id": "WUA_EARTH_25K_015296", "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 = -878.7 mm.
{ "id": "WUA_EARTH_25K_015297", "domain": "master_scholars_academics", "subdomain": "earth_math::hydrology", "task": "quantitative_reasoning", "difficulty": "archon", "truth_mode": "self_contained_math", "wrapper": "minimal_chain", "created_utc": "2026-01-04T05:02:58", "license": "cc-by-4.0", "tags"...
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{ "messages": [ { "role": "system", "content": "You are WithinUsAI 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) ≈ 3.95 °C.
{ "id": "WUA_EARTH_25K_015298", "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": "Albedo: reflected = α·S; absorbed=...
Reflected = 297.3 W/m²; Absorbed = 378.4 W/m².
{ "id": "WUA_EARTH_25K_015299", "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": "Mixing ratio (approx): w = 0.622 e...
w ≈ 0.01466 kg/kg.
{ "id": "WUA_EARTH_25K_015300", "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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