{"answer": "-9", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-12-13-121-4d75563f43d7", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 12x + (-13) = -121.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract -13 from both sides: 12x = -108. Divide by 12: x = -9.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-9"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-9", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-2", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-6-5-17-d9a1f0e61df6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 6x + (-5) = -17.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract -5 from both sides: 6x = -12. Divide by 6: x = -2.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "8", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-4-14-18-cd69e732a817", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 4x + (-14) = 18.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract -14 from both sides: 4x = 32. Divide by 4: x = 8.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "8"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-3-17-29-8811afe7cf95", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 3x + (17) = 29.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract 17 from both sides: 3x = 12. Divide by 3: x = 4.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-7", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-2-19-33-9551e23d6a68", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 2x + (-19) = -33.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract -19 from both sides: 2x = -14. Divide by 2: x = -7.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-7"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "7", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-5-6-29-d8a32874f16a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 5x + (-6) = 29.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract -6 from both sides: 5x = 35. Divide by 5: x = 7.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "7"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "8", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-11-19-69-9b5871f15ef7", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 11x + (-19) = 69.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract -19 from both sides: 11x = 88. Divide by 11: x = 8.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "8"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-5-14-34-c72350530455", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 5x + (14) = 34.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract 14 from both sides: 5x = 20. Divide by 5: x = 4.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "9", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-5-8-53-a67a993358ce", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 5x + (8) = 53.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract 8 from both sides: 5x = 45. Divide by 5: x = 9.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "9"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "9", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-4", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-6-20-44-685abdb6f084", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 6x + (-20) = -44.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract -20 from both sides: 6x = -24. Divide by 6: x = -4.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-8-1-7-225524d6e9f4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.4250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 8x + (1) = -7.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract 1 from both sides: 8x = -8. Divide by 8: x = -1.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-4-7-3-71926b7af090", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.3000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 4x + (-7) = -3.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract -7 from both sides: 4x = 4. Divide by 4: x = 1.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-3-15-6-ad4a7a3f32d8", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 3.3000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 3x + (-15) = -6.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract -15 from both sides: 3x = 9. Divide by 3: x = 3.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "3"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": "python.variables", "constraints": ["Exact integer or rational solution", "Single real unknown"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-linear-3-2-8-187f98fcc790", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Move constants", "Divide by the coefficient of x", "Simplify"], "prompt": "Solve for x: 3x + (2) = 8.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Isolate the variable. Subtract 2 from both sides: 3x = 6. Divide by 3: x = 2.", "strategy": ["Move constants", "Divide by the coefficient of x", "Simplify"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-2, 3", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-3-2-b4a675fa78dc", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 - x - 6 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (3))(x - (-2)). The roots are 3 and -2.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-2, 3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1, 5", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-5-1-9dee00058d30", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 3.75}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 - 6*x + 5 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (5))(x - (1)). The roots are 5 and 1.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1, 5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-5, 0", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-0-5-96d620a8a17e", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.95}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 + 5*x = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (0))(x - (-5)). The roots are 0 and -5.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-5, 0", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3, 4", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-4-3-ec179f321d28", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 3.75}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 - 7*x + 12 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (4))(x - (3)). The roots are 4 and 3.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "3, 4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-3, 3", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-3-3-406a7891f49e", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.825}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 - 9 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (3))(x - (-3)). The roots are 3 and -3.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-3, 3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-6, 4", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-6-4-c6e4f7bc8bcc", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 4.125}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 + 2*x - 24 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (-6))(x - (4)). The roots are -6 and 4.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-6, 4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-2, 6", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-6-2-a00a277c1266", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 4.125}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 - 4*x - 12 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (6))(x - (-2)). The roots are 6 and -2.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-2, 6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-5, -3", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-2-3-5-d083f7947ef1", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.75, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 4.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of 2*x**2 + 16*x + 30 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (-3))(x - (-5)). The roots are -3 and -5.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-5, -3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-2, 1", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-2-1-cffaf993fa69", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 + x - 2 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (-2))(x - (1)). The roots are -2 and 1.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-2, 1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-4, -1", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-4-1-1ee58ae1f76e", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 4.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 + 5*x + 4 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (-4))(x - (-1)). The roots are -4 and -1.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-4, -1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-3, 4", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-3-4-148083f437f0", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 - x - 12 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (-3))(x - (4)). The roots are -3 and 4.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-3, 4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4, 5", "assumptions": [], "concept_id": null, "constraints": ["Work over the rationals", "Report every root"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-quad-1-5-4-f81dcf8debdb", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.275, "tests": 0.0, "total": 3.75}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "prompt": "Find all roots of x**2 - 9*x + 20 = 0.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The monic factorisation is proportional to (x - (5))(x - (4)). The roots are 5 and 4.", "strategy": ["Identify a quadratic", "Factor or use the quadratic formula", "Check by substitution"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4, 5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=4, y=5", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-2-5-2-2-33-18-fc71ffd8bdf9", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 2x + 5y = 33; 2x + 2y = 18.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = 4, y = 5.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=4, y=5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=2, y=1", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-3-5-2-3-11-7-6467f6b25338", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 3x + 5y = 11; 2x + 3y = 7.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = 2, y = 1.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=2, y=1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=-5, y=-2", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-1-3-4-3-11-26-e6c6912e2c1f", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 1x + 3y = -11; 4x + 3y = -26.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = -5, y = -2.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=-5, y=-2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=-4, y=-2", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-5-3-2-4-26-16-16b0e7c43370", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 5x + 3y = -26; 2x + 4y = -16.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = -4, y = -2.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=-4, y=-2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=1, y=5", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-4-2-3-2-14-13-28349a1d5883", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 4x + 2y = 14; 3x + 2y = 13.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = 1, y = 5.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=1, y=5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=-2, y=3", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-5-3-5-4-1-2-15b78eb33a54", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.5500000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 5x + 3y = -1; 5x + 4y = 2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = -2, y = 3.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=-2, y=3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=4, y=1", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-3-2-2-5-14-13-2af670d0cf68", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 3x + 2y = 14; 2x + 5y = 13.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = 4, y = 1.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=4, y=1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=2, y=-4", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-1-1-2-3-2-8-a8ccffa595f5", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 1x + 1y = -2; 2x + 3y = -8.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = 2, y = -4.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=2, y=-4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=5, y=1", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-5-1-4-4-26-24-a5446f13576b", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 5x + 1y = 26; 4x + 4y = 24.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = 5, y = 1.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=5, y=1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "x=4, y=2", "assumptions": [], "concept_id": null, "constraints": ["Unique real solution", "Integer coefficients"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sys-5-3-5-1-26-22-81f2be928ff4", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.325, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "prompt": "Solve the system: 5x + 3y = 26; 5x + 1y = 22.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use elimination or Cramer's rule. The unique solution of this invertible 2×2 system is x = 4, y = 2.", "strategy": ["Write the coefficient matrix", "Invert or eliminate", "Back-substitute"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "x=4, y=2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-5/3", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-2-6-6-3-9163098bad49", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.95}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 2/6 - 6/3 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 1/3 - 2 = -5/3.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-5/3"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-5/3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "7", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-7-4-8-2-688dc561faed", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.45}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 7/4 * 8/2 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 7/4 * 4 = 7.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "7"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "15/4", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-5-4-9-3-f81d9afa0fa1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.7}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 5/4 * 9/3 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 5/4 * 3 = 15/4.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "15/4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "15/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10/7", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-5-5-3-7-296aea2e4c66", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.7}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 5/5 + 3/7 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 1 + 3/7 = 10/7.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "10/7"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "10/7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "31/6", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-9-2-6-9-005f9744170e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.825}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 9/2 + 6/9 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 9/2 + 2/3 = 31/6.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "31/6"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "31/6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "9/7", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-2-7-5-5-ebfb99765ce4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.7}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 2/7 + 5/5 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 2/7 + 1 = 9/7.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "9/7"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "9/7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "14/9", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-4-3-2-9-f05a970eeffc", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.825}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 4/3 + 2/9 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 4/3 + 2/9 = 14/9.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "14/9"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "14/9", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3/4", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-9-4-3-9-a3669b96345a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.825}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 9/4 * 3/9 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 9/4 * 1/3 = 3/4.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "3/4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "3/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "13/8", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-3-6-9-8-cf4bfd5e67cd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.825}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 3/6 + 9/8 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 1/2 + 9/8 = 13/8.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "13/8"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "13/8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "9/8", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-9-5-5-8-f7a00e0e8b38", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.825}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 9/5 * 5/8 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 9/5 * 5/8 = 9/8.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "9/8"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "9/8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5/3", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-6-9-9-9-2615fee5a6cc", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.7}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 6/9 + 9/9 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 2/3 + 1 = 5/3.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5/3"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5/3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "38/35", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact arithmetic", "Lowest terms"], "context": {"method": "symbolic", "topic": "arithmetic"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-frac-4-5-2-7-11d89528186c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.225, "tests": 0.0, "total": 3.825}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic"}, "natural_language": "en", "observations": [], "plan": ["Write each term as a Rational", "Apply the operator", "Reduce"], "prompt": "Compute 4/5 + 2/7 as a simplified rational number.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Convert to rationals and simplify: 4/5 + 2/7 = 38/35.", "strategy": ["Write each term as a Rational", "Apply the operator", "Reduce"], "task_type": "arithmetic", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "38/35"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "38/35", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gcd-76-35-48608b070db3", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute GCD(76, 35).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(76, 35) = 1, so lcm(76, 35) = 76×35/gcd = 2660. Requested value: 1.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gcd-6-15-7be31cc9f5d6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute GCD(6, 15).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(6, 15) = 3, so lcm(6, 15) = 6×15/gcd = 30. Requested value: 3.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "7", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gcd-35-14-c329c9d125eb", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute GCD(35, 14).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(35, 14) = 7, so lcm(35, 14) = 35×14/gcd = 70. Requested value: 7.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gcd-48-15-77e905ec88a3", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute GCD(48, 15).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(48, 15) = 3, so lcm(48, 15) = 48×15/gcd = 240. Requested value: 3.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gcd-41-68-579bb3981027", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute GCD(41, 68).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(41, 68) = 1, so lcm(41, 68) = 41×68/gcd = 2788. Requested value: 1.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1650", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-lcm-75-22-3dcbe4b8e3a4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute LCM(75, 22).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(75, 22) = 1, so lcm(75, 22) = 75×22/gcd = 1650. Requested value: 1650.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "1650", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2442", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-lcm-37-66-3bb7bf18f34d", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute LCM(37, 66).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(37, 66) = 1, so lcm(37, 66) = 37×66/gcd = 2442. Requested value: 2442.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "2442", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "6", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gcd-30-18-92d939ac6981", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute GCD(30, 18).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(30, 18) = 6, so lcm(30, 18) = 30×18/gcd = 90. Requested value: 6.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3111", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-lcm-61-51-21c8fb0837b1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute LCM(61, 51).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(61, 51) = 1, so lcm(61, 51) = 61×51/gcd = 3111. Requested value: 3111.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "3111", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gcd-58-65-3ebcafba1ecf", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute GCD(58, 65).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(58, 65) = 1, so lcm(58, 65) = 58×65/gcd = 3770. Requested value: 1.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "234", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-lcm-18-13-7f80658b0bb1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute LCM(18, 13).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(18, 13) = 1, so lcm(18, 13) = 18×13/gcd = 234. Requested value: 234.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "234", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Positive integers", "Exact integer result"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gcd-49-19-e02d5d09c85f", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.075, "tests": 0.0, "total": 2.4000000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "prompt": "Compute GCD(49, 19).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "gcd(49, 19) = 1, so lcm(49, 19) = 49×19/gcd = 931. Requested value: 1.", "strategy": ["Euclidean algorithm for gcd", "Use lcm = |ab|/gcd if needed"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-59-6-6-761abf1a023d", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 59^6 mod 6.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 59^6 ≡ 1 (mod 6).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-124-5-5-e591132ef5ea", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 124^5 mod 5.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 124^5 ≡ 4 (mod 5).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "0", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-56-5-7-23bc3a194338", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 56^5 mod 7.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 56^5 ≡ 0 (mod 7).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "0", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-73-2-16-8c3bd78aec20", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 73^2 mod 16.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 73^2 ≡ 1 (mod 16).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "6", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-123-8-15-43a69bdc790a", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 123^8 mod 15.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 123^8 ≡ 6 (mod 15).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "0", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-176-8-11-34e1440c4a1c", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 176^8 mod 11.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 176^8 ≡ 0 (mod 11).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "0", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-13-8-4-950aad5f41b1", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 13^8 mod 4.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 13^8 ≡ 1 (mod 4).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "0", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-70-5-5-01cec19e4b55", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 70^5 mod 5.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 70^5 ≡ 0 (mod 5).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "0", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-134-3-10-99486f50009c", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 134^3 mod 10.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 134^3 ≡ 4 (mod 10).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "15", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-112-2-17-0d8553c1b426", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 112^2 mod 17.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 112^2 ≡ 15 (mod 17).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "15", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": null, "constraints": ["Non-negative remainder in 0..m-1"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-mod-52-2-9-24dc9d75b7d1", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Reduce the base modulo m", "Square-and-multiply"], "prompt": "Compute 52^2 mod 9.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Use modular exponentiation: 52^2 ≡ 4 (mod 9).", "strategy": ["Reduce the base modulo m", "Square-and-multiply"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12*x**2 - 1", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-4-3-1-6-9edd8b34b7e5", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 5.1}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 4*x**3 - x + 6.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:15Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[4x^3] = 12x^2, plus -1. Derivative: 12*x**2 - 1.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12*x**2 - 1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12*x + 3", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-6-2-3-7-ec4251d9c600", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.75, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 4.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 6*x**2 + 3*x + 7.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[6x^2] = 12x^1, plus 3. Derivative: 12*x + 3.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12*x + 3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12*x**3 - 2", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-3-4-2-7-538dfb7eeefd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 5.225}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 3*x**4 - 2*x - 7.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[3x^4] = 12x^3, plus -2. Derivative: 12*x**3 - 2.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12*x**3 - 2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12*x", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-6-2-0-7-a8ddcb8214f1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.2, "tests": 0.0, "total": 4.050000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 6*x**2 - 7.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[6x^2] = 12x^1, plus 0. Derivative: 12*x.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12*x", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10*x + 3", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-5-2-3-3-b51720dae131", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.75, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 4.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 5*x**2 + 3*x - 3.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[5x^2] = 10x^1, plus 3. Derivative: 10*x + 3.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "10*x + 3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "8*x**3 - 4", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-2-4-4-6-6674b5e83bf8", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 5.225}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 2*x**4 - 4*x - 6.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[2x^4] = 8x^3, plus -4. Derivative: 8*x**3 - 4.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "8*x**3 - 4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "16*x**3 - 4", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-4-4-4-1-d6369c59bec1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 5.225}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 4*x**4 - 4*x - 1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[4x^4] = 16x^3, plus -4. Derivative: 16*x**3 - 4.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "16*x**3 - 4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "20*x**3 - 4", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-5-4-4-5-b46c62301853", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 5.225}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 5*x**4 - 4*x + 5.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[5x^4] = 20x^3, plus -4. Derivative: 20*x**3 - 4.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "20*x**3 - 4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "6*x - 2", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-3-2-2-2-6c9a23083f3c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 4.725}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 3*x**2 - 2*x + 2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[3x^2] = 6x^1, plus -2. Derivative: 6*x - 2.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "6*x - 2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12*x**2 - 3", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-4-3-3-1-e9a11fd78926", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 5.225}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: 4*x**3 - 3*x + 1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[4x^3] = 12x^2, plus -3. Derivative: 12*x**2 - 3.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12*x**2 - 3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4*x**3 - 5", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-1-4-5-6-bf034e01159d", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 5.1}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: x**4 - 5*x + 6.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[1x^4] = 4x^3, plus -5. Derivative: 4*x**3 - 5.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4*x**3 - 5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4*x**3 + 3", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Symbolic derivative", "Do not expand unnecessarily"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-deriv-1-4-3-2-3c27a1444afe", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 4.975}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "prompt": "Differentiate with respect to x: x**4 + 3*x - 2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Power rule: d/dx[1x^4] = 4x^3, plus 3. Derivative: 4*x**3 + 3.", "strategy": ["Apply the power rule termwise", "Differentiate the linear term", "Constant vanishes"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4*x**3 + 3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "320/3", "assumptions": [], "concept_id": "math.calculus", "constraints": ["Exact value", "Real interval"], "context": {"method": "symbolic", "topic": "calculus"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-int-5-2-0-4-ace17c68e7f1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 3.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "calculus"}, "natural_language": "en", "observations": [], "plan": ["Find an antiderivative", "Apply the fundamental theorem"], "prompt": "Evaluate the definite integral ∫_0^4 5*x**2 dx.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Antiderivative is 5x^3/3. Evaluate from 0 to 4: 320/3.", "strategy": ["Find an antiderivative", "Apply the fundamental theorem"], "task_type": "calculus", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "106.666666666667"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "320/3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "sqrt(3)/2", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact radical or rational form", "No decimal approximation"], "context": {"method": "symbolic", "topic": "trigonometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-trig-sin-pi-3-774653692b00", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.15, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trigonometry"}, "natural_language": "en", "observations": [], "plan": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "prompt": "Give the exact value of sin(pi/3).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "This is a standard unit-circle value: sin(pi/3) = sqrt(3)/2.", "strategy": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "task_type": "trigonometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "sqrt(3)/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "sqrt(3)/2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1/2", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact radical or rational form", "No decimal approximation"], "context": {"method": "symbolic", "topic": "trigonometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-trig-cos-2-pi-3-df51fd7b5d79", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.15, "tests": 0.0, "total": 3.875}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trigonometry"}, "natural_language": "en", "observations": [], "plan": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "prompt": "Give the exact value of cos(2*pi/3).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "This is a standard unit-circle value: cos(2*pi/3) = -1/2.", "strategy": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "task_type": "trigonometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1/2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1/2", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact radical or rational form", "No decimal approximation"], "context": {"method": "symbolic", "topic": "trigonometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-trig-cos-pi-3-ac44ef3f4df9", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.15, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trigonometry"}, "natural_language": "en", "observations": [], "plan": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "prompt": "Give the exact value of cos(pi/3).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "This is a standard unit-circle value: cos(pi/3) = 1/2.", "strategy": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "task_type": "trigonometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1/2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "sqrt(3)/2", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact radical or rational form", "No decimal approximation"], "context": {"method": "symbolic", "topic": "trigonometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-trig-cos-pi-6-312b5e3dc8ce", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.15, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trigonometry"}, "natural_language": "en", "observations": [], "plan": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "prompt": "Give the exact value of cos(pi/6).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "This is a standard unit-circle value: cos(pi/6) = sqrt(3)/2.", "strategy": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "task_type": "trigonometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "sqrt(3)/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "sqrt(3)/2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact radical or rational form", "No decimal approximation"], "context": {"method": "symbolic", "topic": "trigonometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-trig-tan-pi-4-bab92ad0ccd6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.15, "tests": 0.0, "total": 3.125}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trigonometry"}, "natural_language": "en", "observations": [], "plan": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "prompt": "Give the exact value of tan(pi/4).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "This is a standard unit-circle value: tan(pi/4) = 1.", "strategy": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "task_type": "trigonometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact radical or rational form", "No decimal approximation"], "context": {"method": "symbolic", "topic": "trigonometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-trig-sin-pi-2-ec9cc62be726", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.15, "tests": 0.0, "total": 3.125}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trigonometry"}, "natural_language": "en", "observations": [], "plan": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "prompt": "Give the exact value of sin(pi/2).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "This is a standard unit-circle value: sin(pi/2) = 1.", "strategy": ["Recall the unit circle", "Reduce the angle if needed", "Simplify"], "task_type": "trigonometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "20", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rect-5-4-5031addb7d9c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 2.9}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A rectangle has width 5 and height 4. What is its area?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Area = width × height = 5×4 = 20.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "20"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "20", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "16*pi", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-circle-4-59a9af41fd77", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 3.15}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A circle has radius 4. Give its area in terms of pi.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Area = πr2 = π·42 = 16*pi.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "16*pi"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "16*pi", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "sqrt(137)", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-hyp-11-4-ae751116b77a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 3.025}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A right triangle has legs 11 and 4. What is the hypotenuse?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Pythagoras: sqrt(112 + 42) = sqrt(137).", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "sqrt(137)"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "sqrt(137)", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "7*sqrt(39)/4", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-heron-7-10-4-ae3d00cd544b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.375, "tests": 0.0, "total": 3.975}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A triangle has side lengths 7, 10, and 4. Give its area using Heron's formula.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "s = 21/2. Area = sqrt(s(s-a)(s-b)(s-c)) = 7*sqrt(39)/4.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "7*sqrt(39)/4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "7*sqrt(39)/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "90", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rect-15-6-c04d01a8e563", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 2.9}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A rectangle has width 15 and height 6. What is its area?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Area = width × height = 15×6 = 90.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "90"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "90", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4*pi", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-circle-2-1a825fc995d5", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 3.15}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A circle has radius 2. Give its area in terms of pi.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Area = πr2 = π·22 = 4*pi.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "4*pi"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4*pi", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "sqrt(130)", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-hyp-7-9-f44bfa72f310", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 3.025}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A right triangle has legs 7 and 9. What is the hypotenuse?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Pythagoras: sqrt(72 + 92) = sqrt(130).", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "sqrt(130)"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "sqrt(130)", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "45", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rect-9-5-3954127617f7", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 2.9}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A rectangle has width 9 and height 5. What is its area?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Area = width × height = 9×5 = 45.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "45"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "45", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "49*pi", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-circle-7-3fa2291ecb4e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 3.15}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A circle has radius 7. Give its area in terms of pi.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Area = πr2 = π·72 = 49*pi.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "49*pi"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "49*pi", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3*sqrt(41)", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-hyp-15-12-9c59ce2eb82a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 3.275}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A right triangle has legs 15 and 12. What is the hypotenuse?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Pythagoras: sqrt(152 + 122) = 3*sqrt(41).", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "3*sqrt(41)"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "3*sqrt(41)", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3*sqrt(119)/4", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-heron-8-4-5-de607d2bbb30", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.375, "tests": 0.0, "total": 3.975}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A triangle has side lengths 8, 4, and 5. Give its area using Heron's formula.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "s = 17/2. Area = sqrt(s(s-a)(s-b)(s-c)) = 3*sqrt(119)/4.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "3*sqrt(119)/4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "3*sqrt(119)/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "49", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rect-7-7-6bd78ba8853e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 2.9}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A rectangle has width 7 and height 7. What is its area?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Area = width × height = 7×7 = 49.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "49"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "49", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "64*pi", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-circle-8-0d1409bb2370", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 3.15}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A circle has radius 8. Give its area in terms of pi.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Area = πr2 = π·82 = 64*pi.", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "64*pi"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "64*pi", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3*sqrt(5)", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-hyp-3-6-f1750d8df3cf", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.3, "tests": 0.0, "total": 3.275}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A right triangle has legs 3 and 6. What is the hypotenuse?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Pythagoras: sqrt(32 + 62) = 3*sqrt(5).", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "3*sqrt(5)"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "3*sqrt(5)", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10*sqrt(3)", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Exact value", "Euclidean plane"], "context": {"method": "symbolic", "topic": "geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-heron-7-8-5-1a14bcd7ea6a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.375, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometry"}, "natural_language": "en", "observations": [], "plan": ["Identify the formula", "Substitute", "Simplify"], "prompt": "A triangle has side lengths 7, 8, and 5. Give its area using Heron's formula.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "s = 10. Area = sqrt(s(s-a)(s-b)(s-c)) = 10*sqrt(3).", "strategy": ["Identify the formula", "Substitute", "Simplify"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "10*sqrt(3)"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "10*sqrt(3)", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "84", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-c-9-3-96705a068460", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute C(9, 3) = n choose k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k) = n! / (k!(n-k)!) = 84.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "84"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "84", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "110", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-p-11-2-2484a27a3181", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute P(11, 2) = n permute k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "P(n,k) = n! / (n-k)! = 110.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "110"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "110", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "336", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-p-8-3-cdc48634c80e", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute P(8, 3) = n permute k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "P(n,k) = n! / (n-k)! = 336.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "336"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "336", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "210", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-c-10-4-dac2dc886701", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute C(10, 4) = n choose k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k) = n! / (k!(n-k)!) = 210.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "210"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "210", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "28", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-c-8-2-ecad6b019cea", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute C(8, 2) = n choose k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k) = n! / (k!(n-k)!) = 28.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "28"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "28", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "7920", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-p-11-4-0d02f0dbc4f8", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute P(11, 4) = n permute k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "P(n,k) = n! / (n-k)! = 7920.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "7920"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "7920", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "360", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-p-6-4-ced875bf4eb9", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute P(6, 4) = n permute k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "P(n,k) = n! / (n-k)! = 360.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "360"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "360", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "330", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-c-11-4-e85821050b80", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute C(11, 4) = n choose k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k) = n! / (k!(n-k)!) = 330.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "330"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "330", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "15", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-c-6-4-1778498196c7", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute C(6, 4) = n choose k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k) = n! / (k!(n-k)!) = 15.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "15"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "15", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "36", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comb-c-9-2-b55bf6e229f2", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.175, "tests": 0.0, "total": 1.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply the factorial definition", "Simplify"], "prompt": "Compute C(9, 2) = n choose k.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k) = n! / (k!(n-k)!) = 36.", "strategy": ["Apply the factorial definition", "Simplify"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "36"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "36", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "256/2187", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-9-1-1-3-5f056efe4a23", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 1/3. In 9 independent trials, what is P(exactly 1 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(9,1) 1/3^1 (1-1/3)^8 = 256/2187.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "256/2187"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "256/2187", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1280/6561", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-10-2-1-3-204d33d77a12", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 1/3. In 10 independent trials, what is P(exactly 2 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(10,2) 1/3^2 (1-1/3)^8 = 1280/6561.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1280/6561"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1280/6561", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5103/16384", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-7-2-1-4-cbcae1049ed4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 1/4. In 7 independent trials, what is P(exactly 2 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(7,2) 1/4^2 (1-1/4)^5 = 5103/16384.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5103/16384"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5103/16384", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "512/2187", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-9-2-1-3-f3501729e8b0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 1/3. In 9 independent trials, what is P(exactly 2 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(9,2) 1/3^2 (1-1/3)^7 = 512/2187.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "512/2187"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "512/2187", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "405/1048576", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-10-2-3-4-e876383e7d71", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 3/4. In 10 independent trials, what is P(exactly 2 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(10,2) 3/4^2 (1-3/4)^8 = 405/1048576.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "405/1048576"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "405/1048576", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "236196/1953125", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-10-2-2-5-336fe3b3bafe", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 2/5. In 10 independent trials, what is P(exactly 2 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(10,2) 2/5^2 (1-2/5)^8 = 236196/1953125.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "236196/1953125"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "236196/1953125", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "432/3125", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-6-2-3-5-69cd9e543a20", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 3/5. In 6 independent trials, what is P(exactly 2 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(6,2) 3/5^2 (1-3/5)^4 = 432/3125.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "432/3125"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "432/3125", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "32805/131072", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-10-3-1-4-a8bf0fb39a53", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 1/4. In 10 independent trials, what is P(exactly 3 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(10,3) 1/4^3 (1-1/4)^7 = 32805/131072.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "32805/131072"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "32805/131072", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1701/8192", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-8-3-1-4-fa48fcb19d1c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 1/4. In 8 independent trials, what is P(exactly 3 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(8,3) 1/4^3 (1-1/4)^5 = 1701/8192.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1701/8192"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1701/8192", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "7/128", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-7-1-1-2-fd75508a6d9f", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 1/2. In 7 independent trials, what is P(exactly 1 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(7,1) 1/2^1 (1-1/2)^6 = 7/128.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "7/128"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "7/128", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "112/6561", "assumptions": [], "concept_id": "math.probability", "constraints": ["Independent trials", "Exact rational probability"], "context": {"method": "symbolic", "topic": "probability"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-8-2-2-3-7549a0d36182", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "probability"}, "natural_language": "en", "observations": [], "plan": ["Identify n, k, p", "Apply the binomial formula"], "prompt": "A Bernoulli trial succeeds with probability 2/3. In 8 independent trials, what is P(exactly 2 successes)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Binomial pmf: C(8,2) 2/3^2 (1-2/3)^6 = 112/6561.", "strategy": ["Identify n, k, p", "Apply the binomial formula"], "task_type": "probability", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "112/6561"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "112/6561", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-mean-6-3-10-17-20-11-3-1f164e952e35", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [6, 3, 10, 17, 20, 11, 3], compute the population mean (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 10; population variance = 264/7. Requested: 10.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "10"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "10", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "281/36", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-variance-8-7-5-1-2-8-a612dcbd518c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.45, "tests": 0.0, "total": 3.2750000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [8, 7, 5, 1, 2, 8], compute the population variance (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 31/6; population variance = 281/36. Requested: 281/36.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "281/36"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "281/36", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "299/16", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-variance-15-14-19-7-dce6c897d1f2", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.225}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [15, 14, 19, 7], compute the population variance (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 55/4; population variance = 299/16. Requested: 299/16.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "299/16"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "299/16", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "53/7", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-mean-13-8-5-1-4-14-8-70332d482c94", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 3.3000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [13, 8, 5, 1, 4, 14, 8], compute the population mean (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 53/7; population variance = 936/49. Requested: 53/7.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "53/7"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "53/7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1692/49", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-variance-2-18-8-4-15-5-15-2851cecd0370", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 3.3000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [2, 18, 8, 4, 15, 5, 15], compute the population variance (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 67/7; population variance = 1692/49. Requested: 1692/49.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1692/49"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1692/49", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "846/49", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-variance-20-17-14-18-15-6-16-e4cee6485c4f", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 3.3000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [20, 17, 14, 18, 15, 6, 16], compute the population variance (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 106/7; population variance = 846/49. Requested: 846/49.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "846/49"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "846/49", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "521/36", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-variance-8-9-17-16-8-9-c358b11dd3d4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.45, "tests": 0.0, "total": 3.2750000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [8, 9, 17, 16, 8, 9], compute the population variance (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 67/6; population variance = 521/36. Requested: 521/36.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "521/36"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "521/36", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5/4", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-variance-10-8-9-11-9d5031bd92c6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.225}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [10, 8, 9, 11], compute the population variance (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 19/2; population variance = 5/4. Requested: 5/4.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5/4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "31/4", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-mean-5-5-8-13-47a7fc785a7f", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.4, "tests": 0.0, "total": 3.225}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [5, 5, 8, 13], compute the population mean (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 31/4; population variance = 171/16. Requested: 31/4.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "31/4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "31/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "126/5", "assumptions": [], "concept_id": "math.statistics", "constraints": ["Population formulas", "Exact rational"], "context": {"method": "symbolic", "topic": "statistics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-stat-variance-3-14-14-11-18-3a91368fd6eb", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.8, "prompt_length": 0.425, "tests": 0.0, "total": 3.125}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "statistics"}, "natural_language": "en", "observations": [], "plan": ["Compute the mean", "If variance, average squared deviations"], "prompt": "For the sample [3, 14, 14, 11, 18], compute the population variance (divide by n, not n-1).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "mean = 12; population variance = 126/5. Requested: 126/5.", "strategy": ["Compute the mean", "If variance, average squared deviations"], "task_type": "statistics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "126/5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "126/5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-trace-1-5-2-1-b867f0df11b6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.4250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[1, -5], [-2, 1]]. Compute tr(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = 1·1 - -5·-2 = -9; trace = 1+1 = 2.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-trace-4-5-4-1-448c1e2aa08d", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.0500000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[4, -5], [4, 1]]. Compute tr(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = 4·1 - -5·4 = 24; trace = 4+1 = 5.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-4", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-trace-5-0-1-1-44bf34e32f13", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.8000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[-5, 0], [-1, 1]]. Compute tr(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = -5·1 - 0·-1 = -5; trace = -5+1 = -4.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-trace-3-3-4-2-b300f73c02e0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.3000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[3, 3], [4, -2]]. Compute tr(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = 3·-2 - 3·4 = -18; trace = 3+-2 = 1.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-3", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-det-2-1-1-2-3621cf206dcc", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[-2, -1], [1, 2]]. Compute det(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = -2·2 - -1·1 = -3; trace = -2+2 = 0.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-3"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "6", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-trace-1-0-5-5-8d4d2c6c83d8", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.8000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[1, 0], [5, 5]]. Compute tr(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = 1·5 - 0·5 = 5; trace = 1+5 = 6.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "6"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-6", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-det-3-2-3-4-0c653b8221a4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[-3, 2], [-3, 4]]. Compute det(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = -3·4 - 2·-3 = -6; trace = -3+4 = 1.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-6"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-11", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-det-1-4-4-5-57a0560e4255", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.0500000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[1, 4], [4, 5]]. Compute det(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = 1·5 - 4·4 = -11; trace = 1+5 = 6.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-11"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-11", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-7", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-trace-4-5-1-3-ad4813201baf", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.8000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[-4, 5], [1, -3]]. Compute tr(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = -4·-3 - 5·1 = 7; trace = -4+-3 = -7.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-7"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-2", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-trace-3-5-1-1-1acca34623cd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 4.050000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[-3, -5], [-1, 1]]. Compute tr(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = -3·1 - -5·-1 = -8; trace = -3+1 = -2.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-2", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-trace-2-2-0-0-908c3905de4e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.4250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[-2, 2], [0, 0]]. Compute tr(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = -2·0 - 2·0 = 0; trace = -2+0 = -2.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-5", "assumptions": [], "concept_id": "cs.concurrency", "constraints": ["2×2 matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-la-trace-1-1-1-4-35cd8edef7b6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 4.050000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "prompt": "Let A = [[-1, 1], [-1, -4]]. Compute tr(A).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "det = ad-bc = -1·-4 - 1·-1 = 5; trace = -1+-4 = -5.", "strategy": ["Write the matrix", "Apply det = ad-bc or tr = a+d"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "49/4", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-1-7-0-5f943bb86e6f", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.35, "tests": 0.0, "total": 4.575}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -x**2 - 7*x on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = -2*x - 7 = 0 at x = -7/2. f''(x) = -2 < 0, so this is a maximum, f = 49/4.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "-7/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "49/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "19/2", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-2-6-5-87fde53be6ab", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.875}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -2*x**2 - 6*x + 5 on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = -4*x - 6 = 0 at x = -3/2. f''(x) = -4 < 0, so this is a maximum, f = 19/2.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "-3/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "19/2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "14", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-1-8-2-d93c737cc212", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -x**2 - 8*x - 2 on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = -2*x - 8 = 0 at x = -4. f''(x) = -2 < 0, so this is a maximum, f = 14.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "-4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "14", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-2-8-4-2cf7bc06b5fe", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.5, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -2*x**2 - 8*x + 4 on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = -4*x - 8 = 0 at x = -2. f''(x) = -4 < 0, so this is a maximum, f = 12.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "-2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-23/8", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-2-1-3-02ae512c7d99", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 5.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -2*x**2 - x - 3 on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = -4*x - 1 = 0 at x = -1/4. f''(x) = -4 < 0, so this is a maximum, f = -23/8.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "-1/4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-23/8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "89/16", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-4-5-4-cc975f207843", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.875}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -4*x**2 - 5*x + 4 on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = -8*x - 5 = 0 at x = -5/8. f''(x) = -8 < 0, so this is a maximum, f = 89/16.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "-5/8"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "89/16", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "7/2", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-2-6-1-e31578ba154a", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -2*x**2 + 6*x - 1 on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = 6 - 4*x = 0 at x = 3/2. f''(x) = -4 < 0, so this is a maximum, f = 7/2.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "3/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "7/2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "19/4", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-3-3-4-990199f855b6", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.875, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.875}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -3*x**2 - 3*x + 4 on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = -6*x - 3 = 0 at x = -1/2. f''(x) = -6 < 0, so this is a maximum, f = 19/4.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "-1/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "19/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5/4", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-1-3-1-816f1fc2df37", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.75, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.75}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -x**2 - 3*x - 1 on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = -2*x - 3 = 0 at x = -3/2. f''(x) = -2 < 0, so this is a maximum, f = 5/4.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "-3/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "15", "assumptions": [], "concept_id": null, "constraints": ["Unconstrained real line", "Exact value"], "context": {"method": "symbolic", "topic": "optimization"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-opt-1-8-1-ef1089ce9ac6", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "optimization"}, "natural_language": "en", "observations": [], "plan": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "prompt": "Find the maximum value of f(x) = -x**2 - 8*x - 1 on the real line.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x) = -2*x - 8 = 0 at x = -4. f''(x) = -2 < 0, so this is a maximum, f = 15.", "strategy": ["Differentiate", "Solve f'=0", "Confirm with the second-derivative test"], "task_type": "optimization", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"argmax": "-4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "15", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "57", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-arithmetic-7-5-11-cb4f06afb4e9", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "An arithmetic sequence has first term 7 and common difference 5. What is term 11?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 + (k-1)d = 7 + (11-1)·5 = 57.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "57", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "62", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-arithmetic-2-6-11-1c8365c33465", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "An arithmetic sequence has first term 2 and common difference 6. What is term 11?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 + (k-1)d = 2 + (11-1)·6 = 62.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "62", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4096", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-2-7-12-8170dc5aa535", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 2 and common ratio 2. What is term 12?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 2·2^11 = 4096.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "4096", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "19683", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-1-4-10-4af46f9ef3e6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 1 and common ratio 3. What is term 10?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 1·3^9 = 19683.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "19683", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2048", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-2-6-11-38244863b661", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 2 and common ratio 2. What is term 11?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 2·2^10 = 2048.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "2048", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1701", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-7-5-6-cac2f40d2f32", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 7 and common ratio 3. What is term 6?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 7·3^5 = 1701.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "1701", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "512", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-8-7-7-8f3dba3a6a75", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 8 and common ratio 2. What is term 7?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 8·2^6 = 512.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "512", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "885735", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-5-6-12-cc20e4a859ab", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 5 and common ratio 3. What is term 12?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 5·3^11 = 885735.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "885735", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "137781", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-7-7-10-df653c5d9151", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 7 and common ratio 3. What is term 10?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 7·3^9 = 137781.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "137781", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "512", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-4-2-8-016eedd12e87", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 4 and common ratio 2. What is term 8?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 4·2^7 = 512.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "512", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "157464", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-8-6-10-3a42e14c27d9", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 8 and common ratio 3. What is term 10?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 8·3^9 = 157464.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "157464", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2048", "assumptions": [], "concept_id": "python.loops", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-seq-geometric-1-5-12-fae78cdee9cb", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.375, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Identify the closed form", "Substitute k"], "prompt": "A geometric sequence has first term 1 and common ratio 2. What is term 12?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_k = a1 · r^(k-1) = 1·2^11 = 2048.", "strategy": ["Identify the closed form", "Substitute k"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer", "passed": true, "result": "2048", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-5-125-0747fe161d19", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.05, "tests": 0.0, "total": 1.2750000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the argument as a power of the base"], "prompt": "Evaluate log_5(125).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "5^3 = 125, so the logarithm is 3.", "strategy": ["Write the argument as a power of the base"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "3"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-4-256-c11d2c050adb", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.05, "tests": 0.0, "total": 1.2750000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the argument as a power of the base"], "prompt": "Evaluate log_4(256).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "4^4 = 256, so the logarithm is 4.", "strategy": ["Write the argument as a power of the base"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-10-10000-ddc92cd60409", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.05, "tests": 0.0, "total": 1.2750000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the argument as a power of the base"], "prompt": "Evaluate log_10(10000).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "10^4 = 10000, so the logarithm is 4.", "strategy": ["Write the argument as a power of the base"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-10-100-78d3e0d9afba", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.05, "tests": 0.0, "total": 1.2750000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the argument as a power of the base"], "prompt": "Evaluate log_10(100).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "10^2 = 100, so the logarithm is 2.", "strategy": ["Write the argument as a power of the base"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-10-1000-9a82ad7ef91e", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.05, "tests": 0.0, "total": 1.2750000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the argument as a power of the base"], "prompt": "Evaluate log_10(1000).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "10^3 = 1000, so the logarithm is 3.", "strategy": ["Write the argument as a power of the base"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "3"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-2-8-25b0013fbdb9", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.05, "tests": 0.0, "total": 1.2750000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the argument as a power of the base"], "prompt": "Evaluate log_2(8).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "2^3 = 8, so the logarithm is 3.", "strategy": ["Write the argument as a power of the base"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "3"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-5-3125-8be33b96eefd", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.05, "tests": 0.0, "total": 1.2750000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Write the argument as a power of the base"], "prompt": "Evaluate log_5(3125).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "5^5 = 3125, so the logarithm is 5.", "strategy": ["Write the argument as a power of the base"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "-3/4", "assumptions": [], "concept_id": null, "constraints": ["a > 0 so the inequality direction is preserved"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-ineq-8-11-5-45770e32fc29", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 2.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Isolate x", "Divide by the positive coefficient"], "prompt": "Solve the inequality 8x + (11) > 5. Give the threshold x must exceed.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Subtract 11: 8x > -6. Divide by positive 8: x > -3/4.", "strategy": ["Isolate x", "Divide by the positive coefficient"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-3/4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-3/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "16/5", "assumptions": [], "concept_id": null, "constraints": ["a > 0 so the inequality direction is preserved"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-ineq-5-6-10-7ca8a7469ee2", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 2.475}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Isolate x", "Divide by the positive coefficient"], "prompt": "Solve the inequality 5x + (-6) > 10. Give the threshold x must exceed.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Subtract -6: 5x > 16. Divide by positive 5: x > 16/5.", "strategy": ["Isolate x", "Divide by the positive coefficient"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "16/5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "16/5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2.25", "assumptions": [], "concept_id": "python.loops", "constraints": ["One iteration only", "Use 64-bit floating point"], "context": {"method": "symbolic", "topic": "numerical_methods"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-newton-5-2-0-5808a0b2407c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 3.475}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "numerical_methods"}, "natural_language": "en", "observations": [], "plan": ["Evaluate f and f' at x0", "Apply the Newton update"], "prompt": "Perform one Newton iteration for f(x)=x^2-5=0 starting at x0=2. Report x1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x)=2x. x1 = x0 - f(x0)/f'(x0) = 2 - (2^2-5)/(2·2) = 2.25.", "strategy": ["Evaluate f and f' at x0", "Apply the Newton update"], "task_type": "numerical_methods", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": 2.25}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "2.25", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1.416666667", "assumptions": [], "concept_id": "python.loops", "constraints": ["One iteration only", "Use 64-bit floating point"], "context": {"method": "symbolic", "topic": "numerical_methods"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-newton-2-1-5-bacf818991b1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 3.475}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "numerical_methods"}, "natural_language": "en", "observations": [], "plan": ["Evaluate f and f' at x0", "Apply the Newton update"], "prompt": "Perform one Newton iteration for f(x)=x^2-2=0 starting at x0=1.5. Report x1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x)=2x. x1 = x0 - f(x0)/f'(x0) = 1.5 - (1.5^2-2)/(2·1.5) = 1.416666667.", "strategy": ["Evaluate f and f' at x0", "Apply the Newton update"], "task_type": "numerical_methods", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": 1.4166666666666665}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "1.416666667", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2.416666667", "assumptions": [], "concept_id": "python.loops", "constraints": ["One iteration only", "Use 64-bit floating point"], "context": {"method": "symbolic", "topic": "numerical_methods"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-newton-5-1-5-b02b57aac20a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 3.475}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "numerical_methods"}, "natural_language": "en", "observations": [], "plan": ["Evaluate f and f' at x0", "Apply the Newton update"], "prompt": "Perform one Newton iteration for f(x)=x^2-5=0 starting at x0=1.5. Report x1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x)=2x. x1 = x0 - f(x0)/f'(x0) = 1.5 - (1.5^2-5)/(2·1.5) = 2.416666667.", "strategy": ["Evaluate f and f' at x0", "Apply the Newton update"], "task_type": "numerical_methods", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": 2.416666666666667}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "2.416666667", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3", "assumptions": [], "concept_id": "python.loops", "constraints": ["One iteration only", "Use 64-bit floating point"], "context": {"method": "symbolic", "topic": "numerical_methods"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-newton-5-1-0-41a0afe68fe6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 3.475}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "numerical_methods"}, "natural_language": "en", "observations": [], "plan": ["Evaluate f and f' at x0", "Apply the Newton update"], "prompt": "Perform one Newton iteration for f(x)=x^2-5=0 starting at x0=1. Report x1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x)=2x. x1 = x0 - f(x0)/f'(x0) = 1 - (1^2-5)/(2·1) = 3.", "strategy": ["Evaluate f and f' at x0", "Apply the Newton update"], "task_type": "numerical_methods", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": 3.0}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4.083333333", "assumptions": [], "concept_id": "python.loops", "constraints": ["One iteration only", "Use 64-bit floating point"], "context": {"method": "symbolic", "topic": "numerical_methods"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-newton-10-1-5-42f43f6972c1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 3.475}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "numerical_methods"}, "natural_language": "en", "observations": [], "plan": ["Evaluate f and f' at x0", "Apply the Newton update"], "prompt": "Perform one Newton iteration for f(x)=x^2-10=0 starting at x0=1.5. Report x1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x)=2x. x1 = x0 - f(x0)/f'(x0) = 1.5 - (1.5^2-10)/(2·1.5) = 4.083333333.", "strategy": ["Evaluate f and f' at x0", "Apply the Newton update"], "task_type": "numerical_methods", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": 4.083333333333334}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "4.083333333", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1.5", "assumptions": [], "concept_id": "python.loops", "constraints": ["One iteration only", "Use 64-bit floating point"], "context": {"method": "symbolic", "topic": "numerical_methods"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-newton-2-2-0-3c7bcf523b9b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 3.475}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "numerical_methods"}, "natural_language": "en", "observations": [], "plan": ["Evaluate f and f' at x0", "Apply the Newton update"], "prompt": "Perform one Newton iteration for f(x)=x^2-2=0 starting at x0=2. Report x1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x)=2x. x1 = x0 - f(x0)/f'(x0) = 2 - (2^2-2)/(2·2) = 1.5.", "strategy": ["Evaluate f and f' at x0", "Apply the Newton update"], "task_type": "numerical_methods", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": 1.5}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "1.5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": "python.loops", "constraints": ["One iteration only", "Use 64-bit floating point"], "context": {"method": "symbolic", "topic": "numerical_methods"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-newton-3-3-0-73968823d8ad", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 3.475}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "numerical_methods"}, "natural_language": "en", "observations": [], "plan": ["Evaluate f and f' at x0", "Apply the Newton update"], "prompt": "Perform one Newton iteration for f(x)=x^2-3=0 starting at x0=3. Report x1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x)=2x. x1 = x0 - f(x0)/f'(x0) = 3 - (3^2-3)/(2·3) = 2.", "strategy": ["Evaluate f and f' at x0", "Apply the Newton update"], "task_type": "numerical_methods", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": 2.0}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1.5", "assumptions": [], "concept_id": "python.loops", "constraints": ["One iteration only", "Use 64-bit floating point"], "context": {"method": "symbolic", "topic": "numerical_methods"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-newton-2-1-0-a669c10fd1b1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 3.475}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "numerical_methods"}, "natural_language": "en", "observations": [], "plan": ["Evaluate f and f' at x0", "Apply the Newton update"], "prompt": "Perform one Newton iteration for f(x)=x^2-2=0 starting at x0=1. Report x1.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "f'(x)=2x. x1 = x0 - f(x0)/f'(x0) = 1 - (1^2-2)/(2·1) = 1.5.", "strategy": ["Evaluate f and f' at x0", "Apply the Newton update"], "task_type": "numerical_methods", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": 1.5}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "1.5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "240", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Proof over the integers", "Include the requested numeric check"], "context": {"method": "symbolic", "topic": "proofs"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-proof-0-0-79d495d11d43", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "proofs"}, "natural_language": "en", "observations": [], "plan": ["Write an algebraic factorisation or induction", "Evaluate the check instance"], "prompt": "Prove that for every integer n, n(n+1) is even. Then give the value of n(n+1) for n = 15 as a check.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "If n is even, n=2k and n(n+1)=2k(2k+1) is even. If n is odd, n+1 is even, so the product is even. Computational check: 15×16 = 240.", "strategy": ["Write an algebraic factorisation or induction", "Evaluate the check instance"], "task_type": "proof", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "240", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "81", "assumptions": [], "concept_id": "python.loops", "constraints": ["Proof over the integers", "Include the requested numeric check"], "context": {"method": "symbolic", "topic": "proofs"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-proof-1-1-0657efb199be", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.6, "tests": 0.0, "total": 3.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "proofs"}, "natural_language": "en", "observations": [], "plan": ["Write an algebraic factorisation or induction", "Evaluate the check instance"], "prompt": "Prove that the sum of the first m positive odd numbers is m^2. Then report the sum of the first 9 positive odd numbers.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The k-th odd number is 2k-1. Sum_{k=1..m}(2k-1) = 2·m(m+1)/2 - m = m^2. For m=9, the sum is 81.", "strategy": ["Write an algebraic factorisation or induction", "Evaluate the check instance"], "task_type": "proof", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "81", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "504", "assumptions": [], "concept_id": "python.loops", "constraints": ["Proof over the integers", "Include the requested numeric check"], "context": {"method": "symbolic", "topic": "proofs"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-proof-2-2-75b8369c58e4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 3.6500000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "proofs"}, "natural_language": "en", "observations": [], "plan": ["Write an algebraic factorisation or induction", "Evaluate the check instance"], "prompt": "Show that 3 divides n^3-n for every integer n. Report n^3-n for n=8.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "n^3-n = n(n-1)(n+1), three consecutive integers, hence divisible by 3. For n=8: 512-8=504.", "strategy": ["Write an algebraic factorisation or induction", "Evaluate the check instance"], "task_type": "proof", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "504", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1456", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric series"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-geomsum-4-3-6-4e906fce0402", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "prompt": "A geometric series has first term 4, ratio 3, and 6 terms. What is the sum?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S = a(r^n-1)/(r-1) = 4(3^6-1)/(3-1) = 1456.", "strategy": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1456"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1456", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "200", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric series"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-geomsum-5-3-4-f398f61a69f1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "prompt": "A geometric series has first term 5, ratio 3, and 4 terms. What is the sum?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S = a(r^n-1)/(r-1) = 5(3^4-1)/(3-1) = 200.", "strategy": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "200"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "200", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "728", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric series"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-geomsum-2-3-6-bec7fbf1518e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "prompt": "A geometric series has first term 2, ratio 3, and 6 terms. What is the sum?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S = a(r^n-1)/(r-1) = 2(3^6-1)/(3-1) = 728.", "strategy": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "728"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "728", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "126", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric series"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-geomsum-2-2-6-d40ebda32fe1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "prompt": "A geometric series has first term 2, ratio 2, and 6 terms. What is the sum?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S = a(r^n-1)/(r-1) = 2(2^6-1)/(2-1) = 126.", "strategy": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "126"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "126", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "35", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric series"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-geomsum-5-2-3-92e16c34c8ac", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "prompt": "A geometric series has first term 5, ratio 2, and 3 terms. What is the sum?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S = a(r^n-1)/(r-1) = 5(2^3-1)/(2-1) = 35.", "strategy": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "35"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "35", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "93", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric series"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-geomsum-3-2-5-1fb7da0a9428", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "prompt": "A geometric series has first term 3, ratio 2, and 5 terms. What is the sum?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S = a(r^n-1)/(r-1) = 3(2^5-1)/(2-1) = 93.", "strategy": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "93"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "93", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "14", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric series"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-geomsum-2-2-3-da4f643afcc9", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "prompt": "A geometric series has first term 2, ratio 2, and 3 terms. What is the sum?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S = a(r^n-1)/(r-1) = 2(2^3-1)/(2-1) = 14.", "strategy": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "14"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "14", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "315", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric series"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-geomsum-5-2-6-415e2cedb5dd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.4, "tests": 0.0, "total": 4.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "prompt": "A geometric series has first term 5, ratio 2, and 6 terms. What is the sum?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S = a(r^n-1)/(r-1) = 5(2^6-1)/(2-1) = 315.", "strategy": ["Write S=a(r^n-1)/(r-1)", "Substitute", "Simplify"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "315"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "315", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "175", "assumptions": [], "concept_id": "python.iterators", "constraints": ["No prefix", "Lowercase hex digits"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-125-8-639b22742cc6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.175, "tests": 0.0, "total": 2.775}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Divide by the base", "Collect remainders", "Reverse"], "prompt": "Write 125 in octal (no 0o prefix).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Repeated division by 8 yields 175, and int('175', 8) = 125.", "strategy": ["Divide by the base", "Collect remainders", "Reverse"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "175", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "56", "assumptions": [], "concept_id": "python.iterators", "constraints": ["No prefix", "Lowercase hex digits"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-86-16-eddfa9802908", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 2.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Divide by the base", "Collect remainders", "Reverse"], "prompt": "Write 86 in hexadecimal using lowercase letters (no 0x prefix).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Repeated division by 16 yields 56, and int('56', 16) = 86.", "strategy": ["Divide by the base", "Collect remainders", "Reverse"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "56", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "167", "assumptions": [], "concept_id": "python.iterators", "constraints": ["No prefix", "Lowercase hex digits"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-119-8-680d751b3efa", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.175, "tests": 0.0, "total": 2.775}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Divide by the base", "Collect remainders", "Reverse"], "prompt": "Write 119 in octal (no 0o prefix).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Repeated division by 8 yields 167, and int('167', 8) = 119.", "strategy": ["Divide by the base", "Collect remainders", "Reverse"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "167", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "9b", "assumptions": [], "concept_id": "python.iterators", "constraints": ["No prefix", "Lowercase hex digits"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-155-16-6603fa89ea1d", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 2.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Divide by the base", "Collect remainders", "Reverse"], "prompt": "Write 155 in hexadecimal using lowercase letters (no 0x prefix).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Repeated division by 16 yields 9b, and int('9b', 16) = 155.", "strategy": ["Divide by the base", "Collect remainders", "Reverse"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "9b", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "19", "assumptions": [], "concept_id": "python.iterators", "constraints": ["No prefix", "Lowercase hex digits"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-25-16-b5096015e61d", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 2.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Divide by the base", "Collect remainders", "Reverse"], "prompt": "Write 25 in hexadecimal using lowercase letters (no 0x prefix).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Repeated division by 16 yields 19, and int('19', 16) = 25.", "strategy": ["Divide by the base", "Collect remainders", "Reverse"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "19", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "11000111", "assumptions": [], "concept_id": "python.iterators", "constraints": ["No prefix", "Lowercase hex digits"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-199-2-cb14747933dc", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.175, "tests": 0.0, "total": 2.775}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Divide by the base", "Collect remainders", "Reverse"], "prompt": "Write 199 in binary (no 0b prefix).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Repeated division by 2 yields 11000111, and int('11000111', 2) = 199.", "strategy": ["Divide by the base", "Collect remainders", "Reverse"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "11000111", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3f", "assumptions": [], "concept_id": "python.iterators", "constraints": ["No prefix", "Lowercase hex digits"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-63-16-c4e8b483527c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.25, "tests": 0.0, "total": 2.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Divide by the base", "Collect remainders", "Reverse"], "prompt": "Write 63 in hexadecimal using lowercase letters (no 0x prefix).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Repeated division by 16 yields 3f, and int('3f', 16) = 63.", "strategy": ["Divide by the base", "Collect remainders", "Reverse"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "3f", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "100", "assumptions": [], "concept_id": "python.iterators", "constraints": ["No prefix", "Lowercase hex digits"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-64-8-2a3ac9c7b460", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 1.2000000000000002, "prompt_length": 0.175, "tests": 0.0, "total": 2.775}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Divide by the base", "Collect remainders", "Reverse"], "prompt": "Write 64 in octal (no 0o prefix).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Repeated division by 8 yields 100, and int('100', 8) = 64.", "strategy": ["Divide by the base", "Collect remainders", "Reverse"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "100", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "8", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rem-1-3-2-2-de6052027ee0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.7}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Evaluate p at the root of the divisor", "Report that value"], "prompt": "By the remainder theorem, what is the remainder when x**2 - 3*x - 2 is divided by (x - (-2))?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The remainder is p(-2) = 8.", "strategy": ["Evaluate p at the root of the divisor", "Report that value"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "8"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-5", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rem-1-3-5-0-24e3e35ceb51", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.7}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Evaluate p at the root of the divisor", "Report that value"], "prompt": "By the remainder theorem, what is the remainder when x**2 - 3*x - 5 is divided by (x - (0))?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The remainder is p(0) = -5.", "strategy": ["Evaluate p at the root of the divisor", "Report that value"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rem-4-4-2-1-1a70d312d29e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.825}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Evaluate p at the root of the divisor", "Report that value"], "prompt": "By the remainder theorem, what is the remainder when 4*x**2 + 4*x + 2 is divided by (x - (-1))?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The remainder is p(-1) = 2.", "strategy": ["Evaluate p at the root of the divisor", "Report that value"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rem-1-2-1-2-c9730377c1a8", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.7}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Evaluate p at the root of the divisor", "Report that value"], "prompt": "By the remainder theorem, what is the remainder when x**2 - 2*x - 1 is divided by (x - (2))?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The remainder is p(2) = -1.", "strategy": ["Evaluate p at the root of the divisor", "Report that value"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rem-3-2-4-2-54ad91095113", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.575}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Evaluate p at the root of the divisor", "Report that value"], "prompt": "By the remainder theorem, what is the remainder when 3*x**2 + 2*x - 4 is divided by (x - (2))?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The remainder is p(2) = 12.", "strategy": ["Evaluate p at the root of the divisor", "Report that value"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "12"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "6", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rem-2-1-5-1-73fe620f10eb", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.45}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Evaluate p at the root of the divisor", "Report that value"], "prompt": "By the remainder theorem, what is the remainder when 2*x**2 - x + 5 is divided by (x - (1))?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The remainder is p(1) = 6.", "strategy": ["Evaluate p at the root of the divisor", "Report that value"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "6"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rem-2-1-4-1-fbc392114605", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.7}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Evaluate p at the root of the divisor", "Report that value"], "prompt": "By the remainder theorem, what is the remainder when 2*x**2 + x - 4 is divided by (x - (1))?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The remainder is p(1) = -1.", "strategy": ["Evaluate p at the root of the divisor", "Report that value"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-6", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rem-2-5-3-1-2b87ef2bdc69", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 4.075}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Evaluate p at the root of the divisor", "Report that value"], "prompt": "By the remainder theorem, what is the remainder when 2*x**2 + 5*x - 3 is divided by (x - (-1))?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The remainder is p(-1) = -6.", "strategy": ["Evaluate p at the root of the divisor", "Report that value"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-6"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "77", "assumptions": [], "concept_id": "math.linear_algebra", "constraints": ["Report the square, not the square root"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vnorm-4-5-6-128b0353a713", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.5, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 3.3}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Square each component", "Add"], "prompt": "What is the squared Euclidean norm of the vector (-4, -5, -6)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "||v||^2 = -4^2+-5^2+-6^2 = 77.", "strategy": ["Square each component", "Add"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "77"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "77", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "56", "assumptions": [], "concept_id": "math.linear_algebra", "constraints": ["Report the square, not the square root"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vnorm-4-6-2-f549a013fc5a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 3.05}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Square each component", "Add"], "prompt": "What is the squared Euclidean norm of the vector (-4, 6, -2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "||v||^2 = -4^2+6^2+-2^2 = 56.", "strategy": ["Square each component", "Add"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "56"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "56", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "43", "assumptions": [], "concept_id": "math.linear_algebra", "constraints": ["Report the square, not the square root"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vnorm-3-5-3-65ff2e817658", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 2.55}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Square each component", "Add"], "prompt": "What is the squared Euclidean norm of the vector (3, 5, 3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "||v||^2 = 3^2+5^2+3^2 = 43.", "strategy": ["Square each component", "Add"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "43"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "43", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "30", "assumptions": [], "concept_id": "math.linear_algebra", "constraints": ["Report the square, not the square root"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vnorm-2-1-5-6c534713b149", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 3.05}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Square each component", "Add"], "prompt": "What is the squared Euclidean norm of the vector (-2, 1, -5)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "||v||^2 = -2^2+1^2+-5^2 = 30.", "strategy": ["Square each component", "Add"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "30"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "30", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "30", "assumptions": [], "concept_id": "math.linear_algebra", "constraints": ["Report the square, not the square root"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vnorm-1-5-2-695496aba490", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 2.8}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Square each component", "Add"], "prompt": "What is the squared Euclidean norm of the vector (1, 5, -2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "||v||^2 = 1^2+5^2+-2^2 = 30.", "strategy": ["Square each component", "Add"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "30"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "30", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "29", "assumptions": [], "concept_id": "math.linear_algebra", "constraints": ["Report the square, not the square root"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vnorm-5-0-2-a9341d9d2534", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 2.8}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Square each component", "Add"], "prompt": "What is the squared Euclidean norm of the vector (5, 0, -2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "||v||^2 = 5^2+0^2+-2^2 = 29.", "strategy": ["Square each component", "Add"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "29"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "29", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "9", "assumptions": [], "concept_id": "math.linear_algebra", "constraints": ["Report the square, not the square root"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vnorm-2-2-1-42840fbce502", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 2.55}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Square each component", "Add"], "prompt": "What is the squared Euclidean norm of the vector (2, 2, 1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "||v||^2 = 2^2+2^2+1^2 = 9.", "strategy": ["Square each component", "Add"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "9"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "9", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "35", "assumptions": [], "concept_id": "math.linear_algebra", "constraints": ["Report the square, not the square root"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vnorm-1-5-3-15be9000cc25", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 2.8}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Square each component", "Add"], "prompt": "What is the squared Euclidean norm of the vector (1, -5, 3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "||v||^2 = 1^2+-5^2+3^2 = 35.", "strategy": ["Square each component", "Add"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "35"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "35", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10", "assumptions": [], "concept_id": null, "constraints": ["Finite sets", "Exact cardinality"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inc-5-8-3-fe7e37532ea5", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.55}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply inclusion-exclusion for two sets"], "prompt": "|A|=5, |B|=8, |A ∩ B|=3. What is |A ∪ B|?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|A ∪ B| = |A|+|B|-|A ∩ B| = 5+8-3 = 10.", "strategy": ["Apply inclusion-exclusion for two sets"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "10"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "10", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "11", "assumptions": [], "concept_id": null, "constraints": ["Finite sets", "Exact cardinality"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inc-7-5-1-a8506554c12a", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.55}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply inclusion-exclusion for two sets"], "prompt": "|A|=7, |B|=5, |A ∩ B|=1. What is |A ∪ B|?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|A ∪ B| = |A|+|B|-|A ∩ B| = 7+5-1 = 11.", "strategy": ["Apply inclusion-exclusion for two sets"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "11"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "11", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10", "assumptions": [], "concept_id": null, "constraints": ["Finite sets", "Exact cardinality"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inc-7-8-5-925b9e86ccbf", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.55}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply inclusion-exclusion for two sets"], "prompt": "|A|=7, |B|=8, |A ∩ B|=5. What is |A ∪ B|?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|A ∪ B| = |A|+|B|-|A ∩ B| = 7+8-5 = 10.", "strategy": ["Apply inclusion-exclusion for two sets"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "10"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "10", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "10", "assumptions": [], "concept_id": null, "constraints": ["Finite sets", "Exact cardinality"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inc-8-4-2-234a4d248015", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.55}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply inclusion-exclusion for two sets"], "prompt": "|A|=8, |B|=4, |A ∩ B|=2. What is |A ∪ B|?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|A ∪ B| = |A|+|B|-|A ∩ B| = 8+4-2 = 10.", "strategy": ["Apply inclusion-exclusion for two sets"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "10"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "10", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "15", "assumptions": [], "concept_id": null, "constraints": ["Finite sets", "Exact cardinality"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inc-9-10-4-380945d96e9a", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.55}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply inclusion-exclusion for two sets"], "prompt": "|A|=9, |B|=10, |A ∩ B|=4. What is |A ∪ B|?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|A ∪ B| = |A|+|B|-|A ∩ B| = 9+10-4 = 15.", "strategy": ["Apply inclusion-exclusion for two sets"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "15"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "15", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12", "assumptions": [], "concept_id": null, "constraints": ["Finite sets", "Exact cardinality"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inc-9-8-5-c92c4f4d3cd5", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.55}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply inclusion-exclusion for two sets"], "prompt": "|A|=9, |B|=8, |A ∩ B|=5. What is |A ∪ B|?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|A ∪ B| = |A|+|B|-|A ∩ B| = 9+8-5 = 12.", "strategy": ["Apply inclusion-exclusion for two sets"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "12"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "16", "assumptions": [], "concept_id": null, "constraints": ["Finite sets", "Exact cardinality"], "context": {"method": "symbolic", "topic": "discrete_mathematics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inc-9-11-4-fb2a4cdbcd45", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.55}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "discrete_mathematics"}, "natural_language": "en", "observations": [], "plan": ["Apply inclusion-exclusion for two sets"], "prompt": "|A|=9, |B|=11, |A ∩ B|=4. What is |A ∪ B|?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|A ∪ B| = |A|+|B|-|A ∩ B| = 9+11-4 = 16.", "strategy": ["Apply inclusion-exclusion for two sets"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "16"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "16", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "26", "assumptions": [], "concept_id": null, "constraints": ["Exact integer", "i^2 = -1"], "context": {"method": "symbolic", "topic": "complex"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cmod-5-1-32a32b683bb0", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 3.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "complex"}, "natural_language": "en", "observations": [], "plan": ["Identify a and b", "Compute a^2+b^2"], "prompt": "Let z = -5 + 1i. What is |z|^2 (the square of the modulus)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|z|^2 = a^2+b^2 = -5^2+1^2 = 26.", "strategy": ["Identify a and b", "Compute a^2+b^2"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "26"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "26", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": null, "constraints": ["Exact integer", "i^2 = -1"], "context": {"method": "symbolic", "topic": "complex"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cmod-1-0-ce2941f53af7", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 3.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "complex"}, "natural_language": "en", "observations": [], "plan": ["Identify a and b", "Compute a^2+b^2"], "prompt": "Let z = -1 + 0i. What is |z|^2 (the square of the modulus)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|z|^2 = a^2+b^2 = -1^2+0^2 = 1.", "strategy": ["Identify a and b", "Compute a^2+b^2"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": null, "constraints": ["Exact integer", "i^2 = -1"], "context": {"method": "symbolic", "topic": "complex"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cmod-1-1-b7a5e0582961", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 4.175000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "complex"}, "natural_language": "en", "observations": [], "plan": ["Identify a and b", "Compute a^2+b^2"], "prompt": "Let z = -1 + -1i. What is |z|^2 (the square of the modulus)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|z|^2 = a^2+b^2 = -1^2+-1^2 = 2.", "strategy": ["Identify a and b", "Compute a^2+b^2"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "41", "assumptions": [], "concept_id": null, "constraints": ["Exact integer", "i^2 = -1"], "context": {"method": "symbolic", "topic": "complex"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cmod-4-5-2741cda7c0e7", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 3.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "complex"}, "natural_language": "en", "observations": [], "plan": ["Identify a and b", "Compute a^2+b^2"], "prompt": "Let z = 4 + -5i. What is |z|^2 (the square of the modulus)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|z|^2 = a^2+b^2 = 4^2+-5^2 = 41.", "strategy": ["Identify a and b", "Compute a^2+b^2"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "41"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "41", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "17", "assumptions": [], "concept_id": null, "constraints": ["Exact integer", "i^2 = -1"], "context": {"method": "symbolic", "topic": "complex"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cmod-4-1-94671e81983b", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 4.175000000000001}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "complex"}, "natural_language": "en", "observations": [], "plan": ["Identify a and b", "Compute a^2+b^2"], "prompt": "Let z = -4 + -1i. What is |z|^2 (the square of the modulus)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|z|^2 = a^2+b^2 = -4^2+-1^2 = 17.", "strategy": ["Identify a and b", "Compute a^2+b^2"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "17"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "17", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "25", "assumptions": [], "concept_id": null, "constraints": ["Exact integer", "i^2 = -1"], "context": {"method": "symbolic", "topic": "complex"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cmod-0-5-754abfb7ceb4", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 3.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "complex"}, "natural_language": "en", "observations": [], "plan": ["Identify a and b", "Compute a^2+b^2"], "prompt": "Let z = 0 + 5i. What is |z|^2 (the square of the modulus)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|z|^2 = a^2+b^2 = 0^2+5^2 = 25.", "strategy": ["Identify a and b", "Compute a^2+b^2"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "25"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "25", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5", "assumptions": [], "concept_id": null, "constraints": ["Exact integer", "i^2 = -1"], "context": {"method": "symbolic", "topic": "complex"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cmod-1-2-c5691233c8f4", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 3.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "complex"}, "natural_language": "en", "observations": [], "plan": ["Identify a and b", "Compute a^2+b^2"], "prompt": "Let z = 1 + -2i. What is |z|^2 (the square of the modulus)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|z|^2 = a^2+b^2 = 1^2+-2^2 = 5.", "strategy": ["Identify a and b", "Compute a^2+b^2"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "16", "assumptions": [], "concept_id": null, "constraints": ["Exact integer", "i^2 = -1"], "context": {"method": "symbolic", "topic": "complex"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cmod-4-0-10dedb874a0a", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 3.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "complex"}, "natural_language": "en", "observations": [], "plan": ["Identify a and b", "Compute a^2+b^2"], "prompt": "Let z = 4 + 0i. What is |z|^2 (the square of the modulus)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "|z|^2 = a^2+b^2 = 4^2+0^2 = 16.", "strategy": ["Identify a and b", "Compute a^2+b^2"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "16"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "16", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "36", "assumptions": [], "concept_id": "python.context_managers", "constraints": ["Exact integer", "Combinations, not permutations"], "context": {"method": "symbolic", "topic": "combinatorics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-9-2-d7d3e36a3c97", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "combinatorics"}, "natural_language": "en", "observations": [], "plan": ["Write the binomial formula", "Evaluate"], "prompt": "What is C(9,2), the number of ways to choose 2 items from 9 distinct items without regard to order?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k)=n!/(k!(n-k)!) = 36.", "strategy": ["Write the binomial formula", "Evaluate"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "36", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "28", "assumptions": [], "concept_id": "python.context_managers", "constraints": ["Exact integer", "Combinations, not permutations"], "context": {"method": "symbolic", "topic": "combinatorics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-8-2-4f6d6a27da4b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "combinatorics"}, "natural_language": "en", "observations": [], "plan": ["Write the binomial formula", "Evaluate"], "prompt": "What is C(8,2), the number of ways to choose 2 items from 8 distinct items without regard to order?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k)=n!/(k!(n-k)!) = 28.", "strategy": ["Write the binomial formula", "Evaluate"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "28", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "35", "assumptions": [], "concept_id": "python.context_managers", "constraints": ["Exact integer", "Combinations, not permutations"], "context": {"method": "symbolic", "topic": "combinatorics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-7-3-7fb0721938f0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "combinatorics"}, "natural_language": "en", "observations": [], "plan": ["Write the binomial formula", "Evaluate"], "prompt": "What is C(7,3), the number of ways to choose 3 items from 7 distinct items without regard to order?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k)=n!/(k!(n-k)!) = 35.", "strategy": ["Write the binomial formula", "Evaluate"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "35", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "21", "assumptions": [], "concept_id": "python.context_managers", "constraints": ["Exact integer", "Combinations, not permutations"], "context": {"method": "symbolic", "topic": "combinatorics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-7-2-90973cb0897a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "combinatorics"}, "natural_language": "en", "observations": [], "plan": ["Write the binomial formula", "Evaluate"], "prompt": "What is C(7,2), the number of ways to choose 2 items from 7 distinct items without regard to order?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k)=n!/(k!(n-k)!) = 21.", "strategy": ["Write the binomial formula", "Evaluate"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "21", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "70", "assumptions": [], "concept_id": "python.context_managers", "constraints": ["Exact integer", "Combinations, not permutations"], "context": {"method": "symbolic", "topic": "combinatorics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-8-4-7669790fa1a5", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "combinatorics"}, "natural_language": "en", "observations": [], "plan": ["Write the binomial formula", "Evaluate"], "prompt": "What is C(8,4), the number of ways to choose 4 items from 8 distinct items without regard to order?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k)=n!/(k!(n-k)!) = 70.", "strategy": ["Write the binomial formula", "Evaluate"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "70", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5", "assumptions": [], "concept_id": "python.context_managers", "constraints": ["Exact integer", "Combinations, not permutations"], "context": {"method": "symbolic", "topic": "combinatorics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-5-4-01c0109cc80a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "combinatorics"}, "natural_language": "en", "observations": [], "plan": ["Write the binomial formula", "Evaluate"], "prompt": "What is C(5,4), the number of ways to choose 4 items from 5 distinct items without regard to order?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k)=n!/(k!(n-k)!) = 5.", "strategy": ["Write the binomial formula", "Evaluate"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "84", "assumptions": [], "concept_id": "python.context_managers", "constraints": ["Exact integer", "Combinations, not permutations"], "context": {"method": "symbolic", "topic": "combinatorics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-bin-9-3-edf57de186bb", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.475, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "combinatorics"}, "natural_language": "en", "observations": [], "plan": ["Write the binomial formula", "Evaluate"], "prompt": "What is C(9,3), the number of ways to choose 3 items from 9 distinct items without regard to order?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "C(n,k)=n!/(k!(n-k)!) = 84.", "strategy": ["Write the binomial formula", "Evaluate"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "84", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-7", "assumptions": [], "concept_id": "python.loops", "constraints": ["2×2 determinant", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-det2-1-4-1-3-7c1e76977e43", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Apply ad-bc"], "prompt": "What is det([[-1, 4], [1, 3]]) for a 2×2 matrix?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "ad-bc = -1·3 - 4·1 = -7.", "strategy": ["Apply ad-bc"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-7"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-4", "assumptions": [], "concept_id": "python.loops", "constraints": ["2×2 determinant", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-det2-3-4-1-0-fa6da1964252", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 3.175}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Apply ad-bc"], "prompt": "What is det([[3, -4], [-1, 0]]) for a 2×2 matrix?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "ad-bc = 3·0 - -4·-1 = -4.", "strategy": ["Apply ad-bc"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12", "assumptions": [], "concept_id": "python.loops", "constraints": ["2×2 determinant", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-det2-4-2-0-3-f3e3179f4463", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.675}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Apply ad-bc"], "prompt": "What is det([[4, -2], [0, 3]]) for a 2×2 matrix?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "ad-bc = 4·3 - -2·0 = 12.", "strategy": ["Apply ad-bc"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "12"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-15", "assumptions": [], "concept_id": "python.loops", "constraints": ["2×2 determinant", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-det2-3-3-4-1-5218e762667d", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 3.425}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Apply ad-bc"], "prompt": "What is det([[3, -3], [-4, -1]]) for a 2×2 matrix?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "ad-bc = 3·-1 - -3·-4 = -15.", "strategy": ["Apply ad-bc"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-15"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-15", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "8", "assumptions": [], "concept_id": "python.loops", "constraints": ["2×2 determinant", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-det2-2-0-4-4-af1ced45af79", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Apply ad-bc"], "prompt": "What is det([[-2, 0], [4, -4]]) for a 2×2 matrix?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "ad-bc = -2·-4 - 0·4 = 8.", "strategy": ["Apply ad-bc"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "8"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": "python.loops", "constraints": ["2×2 determinant", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-det2-4-2-3-1-512d5a43b473", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Apply ad-bc"], "prompt": "What is det([[4, 2], [-3, -1]]) for a 2×2 matrix?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "ad-bc = 4·-1 - 2·-3 = 2.", "strategy": ["Apply ad-bc"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "15", "assumptions": [], "concept_id": "python.loops", "constraints": ["2×2 determinant", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-det2-3-3-3-2-216ea037f0f3", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 3.175}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Apply ad-bc"], "prompt": "What is det([[-3, 3], [-3, -2]]) for a 2×2 matrix?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "ad-bc = -3·-2 - 3·-3 = 15.", "strategy": ["Apply ad-bc"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "15"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "15", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "0", "assumptions": [], "concept_id": "python.loops", "constraints": ["2×2 determinant", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-det2-3-0-4-0-2818836d718d", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.25, "tests": 0.0, "total": 2.425}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Apply ad-bc"], "prompt": "What is det([[3, 0], [4, 0]]) for a 2×2 matrix?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "ad-bc = 3·0 - 0·4 = 0.", "strategy": ["Apply ad-bc"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "0"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "0", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "8", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Coprime to the modulus", "Least positive residue"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inv-15-17-35e45567ce7e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.4250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Extended Euclid or trial", "Check a·inv ≡ 1"], "prompt": "Find the inverse of 15 modulo 17 in 1..16.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "15·8 ≡ 1 (mod 17).", "strategy": ["Extended Euclid or trial", "Check a·inv ≡ 1"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Coprime to the modulus", "Least positive residue"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inv-9-17-95ee5c65825b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.4250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Extended Euclid or trial", "Check a·inv ≡ 1"], "prompt": "Find the inverse of 9 modulo 17 in 1..16.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "9·2 ≡ 1 (mod 17).", "strategy": ["Extended Euclid or trial", "Check a·inv ≡ 1"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "5", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Coprime to the modulus", "Least positive residue"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inv-8-13-7cc8da88a1fd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.4250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Extended Euclid or trial", "Check a·inv ≡ 1"], "prompt": "Find the inverse of 8 modulo 13 in 1..12.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "8·5 ≡ 1 (mod 13).", "strategy": ["Extended Euclid or trial", "Check a·inv ≡ 1"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Coprime to the modulus", "Least positive residue"], "context": {"method": "symbolic", "topic": "number_theory"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-inv-10-13-c87bbf184e65", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.4250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "number_theory"}, "natural_language": "en", "observations": [], "plan": ["Extended Euclid or trial", "Check a·inv ≡ 1"], "prompt": "Find the inverse of 10 modulo 13 in 1..12.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "10·4 ≡ 1 (mod 13).", "strategy": ["Extended Euclid or trial", "Check a·inv ≡ 1"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12", "assumptions": [], "concept_id": "javascript.promises", "constraints": ["Composition is f(g(x)), not g(f(x))"], "context": {"method": "symbolic", "topic": "functions"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comp-4-1-2-feac199769ab", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "functions"}, "natural_language": "en", "observations": [], "plan": ["Evaluate g first", "Apply f"], "prompt": "Let f(x)=4x and g(x)=1x+1. What is (f ∘ g)(2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "g(2)=3, then f of that is 12.", "strategy": ["Evaluate g first", "Apply f"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "12"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "20", "assumptions": [], "concept_id": "javascript.promises", "constraints": ["Composition is f(g(x)), not g(f(x))"], "context": {"method": "symbolic", "topic": "functions"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comp-4-4-1-6fe299057862", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "functions"}, "natural_language": "en", "observations": [], "plan": ["Evaluate g first", "Apply f"], "prompt": "Let f(x)=4x and g(x)=4x+1. What is (f ∘ g)(1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "g(1)=5, then f of that is 20.", "strategy": ["Evaluate g first", "Apply f"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "20"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "20", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "45", "assumptions": [], "concept_id": "javascript.promises", "constraints": ["Composition is f(g(x)), not g(f(x))"], "context": {"method": "symbolic", "topic": "functions"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comp-5-4-2-688b4d00c118", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "functions"}, "natural_language": "en", "observations": [], "plan": ["Evaluate g first", "Apply f"], "prompt": "Let f(x)=5x and g(x)=4x+1. What is (f ∘ g)(2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "g(2)=9, then f of that is 45.", "strategy": ["Evaluate g first", "Apply f"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "45"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "45", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "52", "assumptions": [], "concept_id": "javascript.promises", "constraints": ["Composition is f(g(x)), not g(f(x))"], "context": {"method": "symbolic", "topic": "functions"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comp-4-4-3-4ef247827231", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "functions"}, "natural_language": "en", "observations": [], "plan": ["Evaluate g first", "Apply f"], "prompt": "Let f(x)=4x and g(x)=4x+1. What is (f ∘ g)(3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "g(3)=13, then f of that is 52.", "strategy": ["Evaluate g first", "Apply f"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "52"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "52", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "35", "assumptions": [], "concept_id": "javascript.promises", "constraints": ["Composition is f(g(x)), not g(f(x))"], "context": {"method": "symbolic", "topic": "functions"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comp-5-2-3-d7086734c255", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "functions"}, "natural_language": "en", "observations": [], "plan": ["Evaluate g first", "Apply f"], "prompt": "Let f(x)=5x and g(x)=2x+1. What is (f ∘ g)(3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "g(3)=7, then f of that is 35.", "strategy": ["Evaluate g first", "Apply f"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "35"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "35", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "20", "assumptions": [], "concept_id": "javascript.promises", "constraints": ["Composition is f(g(x)), not g(f(x))"], "context": {"method": "symbolic", "topic": "functions"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comp-2-3-3-b31650c1f48f", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "functions"}, "natural_language": "en", "observations": [], "plan": ["Evaluate g first", "Apply f"], "prompt": "Let f(x)=2x and g(x)=3x+1. What is (f ∘ g)(3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "g(3)=10, then f of that is 20.", "strategy": ["Evaluate g first", "Apply f"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "20"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "20", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "25", "assumptions": [], "concept_id": "javascript.promises", "constraints": ["Composition is f(g(x)), not g(f(x))"], "context": {"method": "symbolic", "topic": "functions"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-comp-5-4-1-775378ca4230", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 1.85}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "functions"}, "natural_language": "en", "observations": [], "plan": ["Evaluate g first", "Apply f"], "prompt": "Let f(x)=5x and g(x)=4x+1. What is (f ∘ g)(1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "g(1)=5, then f of that is 25.", "strategy": ["Evaluate g first", "Apply f"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "25"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "25", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "-1/3", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Distinct linear factors", "Cover-up method"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-pf-3-6-99605d057e26", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 4.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Cover-up at x=a", "Simplify A"], "prompt": "Decompose 1/((x-3)(x-6)) into partial fractions A/(x-3)+B/(x-6). Report A as a simplified rational.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A=1/(3-6)=-1/3. Check: B=1/(6-3)=1/3.", "strategy": ["Cover-up at x=a", "Simplify A"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1/3"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1/3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1/4", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Distinct linear factors", "Cover-up method"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-pf-2-6-b3959b6a801c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 4.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Cover-up at x=a", "Simplify A"], "prompt": "Decompose 1/((x-2)(x-6)) into partial fractions A/(x-2)+B/(x-6). Report A as a simplified rational.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A=1/(2-6)=-1/4. Check: B=1/(6-2)=1/4.", "strategy": ["Cover-up at x=a", "Simplify A"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1/4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1/4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1/2", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Distinct linear factors", "Cover-up method"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-pf-2-4-e61fd09644e3", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 4.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Cover-up at x=a", "Simplify A"], "prompt": "Decompose 1/((x-2)(x-4)) into partial fractions A/(x-2)+B/(x-4). Report A as a simplified rational.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A=1/(2-4)=-1/2. Check: B=1/(4-2)=1/2.", "strategy": ["Cover-up at x=a", "Simplify A"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1/2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1/2", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Distinct linear factors", "Cover-up method"], "context": {"method": "symbolic", "topic": "algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-pf-5-7-229b75198fdf", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 2.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 4.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "algebra"}, "natural_language": "en", "observations": [], "plan": ["Cover-up at x=a", "Simplify A"], "prompt": "Decompose 1/((x-5)(x-7)) into partial fractions A/(x-5)+B/(x-7). Report A as a simplified rational.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A=1/(5-7)=-1/2. Check: B=1/(7-5)=1/2.", "strategy": ["Cover-up at x=a", "Simplify A"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1/2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1/2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "8281", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Closed form", "Exact integer"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sigma-cubes-13-95160bedaf75", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Recall the formula", "Substitute n"], "prompt": "What is sum_{k=1}^{13} k^3?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "(n(n+1)/2)^2 = 8281.", "strategy": ["Recall the formula", "Substitute n"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "8281", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "289", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Closed form", "Exact integer"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sigma-odds-17-ad5725f35806", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 2.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Recall the formula", "Substitute n"], "prompt": "What is the sum of the first 17 positive odd numbers?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The sum is n^2 = 289.", "strategy": ["Recall the formula", "Substitute n"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "289", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "23409", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Closed form", "Exact integer"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sigma-cubes-17-05aa47f77a6c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.1, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Recall the formula", "Substitute n"], "prompt": "What is sum_{k=1}^{17} k^3?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "(n(n+1)/2)^2 = 23409.", "strategy": ["Recall the formula", "Substitute n"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "23409", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "400", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Closed form", "Exact integer"], "context": {"method": "symbolic", "topic": "sequences"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sigma-odds-20-56a0a45e4035", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.275, "tests": 0.0, "total": 2.6}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sequences"}, "natural_language": "en", "observations": [], "plan": ["Recall the formula", "Substitute n"], "prompt": "What is the sum of the first 20 positive odd numbers?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "The sum is n^2 = 400.", "strategy": ["Recall the formula", "Substitute n"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "400", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "-3", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Diagonal matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-eig-1-3-4c829817de4e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 2.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.8, "prompt_length": 0.425, "tests": 0.0, "total": 5.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Read the diagonal", "Multiply"], "prompt": "The diagonal matrix diag(1, -3) has eigenvalues 1 and -3. What is the product of the eigenvalues?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Product of eigenvalues equals det = 1·-3 = -3.", "strategy": ["Read the diagonal", "Multiply"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-3"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-6", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Diagonal matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-eig-2-3-281cf73ac634", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 2.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.8, "prompt_length": 0.425, "tests": 0.0, "total": 5.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Read the diagonal", "Multiply"], "prompt": "The diagonal matrix diag(-2, 3) has eigenvalues -2 and 3. What is the product of the eigenvalues?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Product of eigenvalues equals det = -2·3 = -6.", "strategy": ["Read the diagonal", "Multiply"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-6"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Diagonal matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-eig-1-4-57812a707dde", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 2.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.425, "tests": 0.0, "total": 4.75}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Read the diagonal", "Multiply"], "prompt": "The diagonal matrix diag(1, 4) has eigenvalues 1 and 4. What is the product of the eigenvalues?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Product of eigenvalues equals det = 1·4 = 4.", "strategy": ["Read the diagonal", "Multiply"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-15", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Diagonal matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-eig-5-3-595dc808e5d0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 2.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.8, "prompt_length": 0.425, "tests": 0.0, "total": 5.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Read the diagonal", "Multiply"], "prompt": "The diagonal matrix diag(5, -3) has eigenvalues 5 and -3. What is the product of the eigenvalues?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Product of eigenvalues equals det = 5·-3 = -15.", "strategy": ["Read the diagonal", "Multiply"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-15"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-15", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "0", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Diagonal matrix", "Exact integer"], "context": {"method": "symbolic", "topic": "linear_algebra"}, "difficulty": "intermediate", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-eig-3-0-e4796da90a5d", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 2.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.8, "prompt_length": 0.425, "tests": 0.0, "total": 5.125}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "linear_algebra"}, "natural_language": "en", "observations": [], "plan": ["Read the diagonal", "Multiply"], "prompt": "The diagonal matrix diag(-3, 0) has eigenvalues -3 and 0. What is the product of the eigenvalues?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Product of eigenvalues equals det = -3·0 = 0.", "strategy": ["Read the diagonal", "Multiply"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "0"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "0", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "840", "assumptions": [], "concept_id": "math.functions", "constraints": ["Order matters", "No repetition"], "context": {"method": "symbolic", "topic": "combinatorics"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-perm-7-4-fd830e751e1b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 2.95}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "combinatorics"}, "natural_language": "en", "observations": [], "plan": ["Write n(n-1)...(n-k+1)", "Evaluate"], "prompt": "How many injective functions are there from a set of 4 elements to a set of 7 elements? Equivalently P(7,4).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "P(n,k)=n!/(n-k)! = 840.", "strategy": ["Write n(n-1)...(n-k+1)", "Evaluate"], "task_type": "discrete_mathematics", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "840", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": null, "constraints": ["Integer logarithm", "Exact power"], "context": {"method": "symbolic", "topic": "logarithms"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-2-1-0094d087c48f", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.15, "tests": 0.0, "total": 2.0749999999999997}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "logarithms"}, "natural_language": "en", "observations": [], "plan": ["Recognize the matching power"], "prompt": "What is log2(2) as an integer?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "2^1 = 2.", "strategy": ["Recognize the matching power"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3", "assumptions": [], "concept_id": null, "constraints": ["Integer logarithm", "Exact power"], "context": {"method": "symbolic", "topic": "logarithms"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-27-3-4046d7a2153a", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.15, "tests": 0.0, "total": 2.0749999999999997}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "logarithms"}, "natural_language": "en", "observations": [], "plan": ["Recognize the matching power"], "prompt": "What is log3(27) as an integer?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "3^3 = 27.", "strategy": ["Recognize the matching power"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3", "assumptions": [], "concept_id": null, "constraints": ["Integer logarithm", "Exact power"], "context": {"method": "symbolic", "topic": "logarithms"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-8-3-2396a47cc813", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.15, "tests": 0.0, "total": 2.0749999999999997}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "logarithms"}, "natural_language": "en", "observations": [], "plan": ["Recognize the matching power"], "prompt": "What is log2(8) as an integer?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "2^3 = 8.", "strategy": ["Recognize the matching power"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1", "assumptions": [], "concept_id": null, "constraints": ["Integer logarithm", "Exact power"], "context": {"method": "symbolic", "topic": "logarithms"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-5-1-276e70ee90c1", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.15, "tests": 0.0, "total": 2.0749999999999997}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "logarithms"}, "natural_language": "en", "observations": [], "plan": ["Recognize the matching power"], "prompt": "What is log5(5) as an integer?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "5^1 = 5.", "strategy": ["Recognize the matching power"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": null, "constraints": ["Integer logarithm", "Exact power"], "context": {"method": "symbolic", "topic": "logarithms"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-log-9-2-e181dc82d5e1", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.15, "tests": 0.0, "total": 2.0749999999999997}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "logarithms"}, "natural_language": "en", "observations": [], "plan": ["Recognize the matching power"], "prompt": "What is log3(9) as an integer?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "3^2 = 9.", "strategy": ["Recognize the matching power"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "9", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-5-0-4-1-9e5f01cb3431", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.675}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 5x^2 + (0)x + (4) is divided by (x - -1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(-1) = 5(-1)^2+(0)(-1)+(4) = 9.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "9"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "9", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-2", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-1-4-2-4-cf804eb6f76a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 1x^2 + (-4)x + (-2) is divided by (x - 4)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(4) = 1(4)^2+(-4)(4)+(-2) = -2.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-1-1-5-1-cd3c091f084f", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.675}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 1x^2 + (1)x + (5) is divided by (x - -1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(-1) = 1(-1)^2+(1)(-1)+(5) = 5.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "8", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-1-0-1-3-98adeab5b09b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.425}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 1x^2 + (0)x + (-1) is divided by (x - 3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(3) = 1(3)^2+(0)(3)+(-1) = 8.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "8"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-2-1-4-2-48c79f2ca780", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.675}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 2x^2 + (-1)x + (-4) is divided by (x - 2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(2) = 2(2)^2+(-1)(2)+(-4) = 2.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-5-4-2-1-50f96037ffdf", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 4.175}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 5x^2 + (4)x + (-2) is divided by (x - -1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(-1) = 5(-1)^2+(4)(-1)+(-2) = -1.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-3-3-6-1-c8d947295d9a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.175}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 3x^2 + (3)x + (6) is divided by (x - 1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(1) = 3(1)^2+(3)(1)+(6) = 12.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "12"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "12", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "19", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-3-3-1-2-fb8b25eef6c3", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 3x^2 + (-3)x + (1) is divided by (x - -2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(-2) = 3(-2)^2+(-3)(-2)+(1) = 19.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "19"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "19", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "19", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-2-1-4-3-8b783ba28ec3", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.425}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 2x^2 + (-1)x + (4) is divided by (x - 3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(3) = 2(3)^2+(-1)(3)+(4) = 19.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "19"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "19", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "43", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-5-1-5-3-a1a4f0d6e892", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.425}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 5x^2 + (1)x + (-5) is divided by (x - 3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(3) = 5(3)^2+(1)(3)+(-5) = 43.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "43"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "43", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "6", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-1-0-2-2-f4f436a22029", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.675}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 1x^2 + (0)x + (2) is divided by (x - -2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(-2) = 1(-2)^2+(0)(-2)+(2) = 6.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "6"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "9", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-4-1-4-1-2aca9b7db18e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.175}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 4x^2 + (1)x + (4) is divided by (x - 1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(1) = 4(1)^2+(1)(1)+(4) = 9.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "9"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "9", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "28", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-5-2-4-2-129f05887529", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.175}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 5x^2 + (2)x + (4) is divided by (x - 2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(2) = 5(2)^2+(2)(2)+(4) = 28.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "28"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "28", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "13", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-1-1-1-3-a4d0a1f1ea18", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 1x^2 + (-1)x + (1) is divided by (x - -3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(-3) = 1(-3)^2+(-1)(-3)+(1) = 13.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "13"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "13", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-5-4-1-0-01045af93a66", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.675}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 5x^2 + (4)x + (-1) is divided by (x - 0)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(0) = 5(0)^2+(4)(0)+(-1) = -1.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-1"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "9", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-1-3-5-1-6425699f8f1f", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.175}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 1x^2 + (3)x + (5) is divided by (x - 1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(1) = 1(1)^2+(3)(1)+(5) = 9.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "9"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "9", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "41", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-4-3-4-3-2fa3cd71e72e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 4.175}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 4x^2 + (-3)x + (-4) is divided by (x - -3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(-3) = 4(-3)^2+(-3)(-3)+(-4) = 41.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "41"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "41", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-1-0-1-2-de5fb03a6c8c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.675}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 1x^2 + (0)x + (1) is divided by (x - -2)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(-2) = 1(-2)^2+(0)(-2)+(1) = 5.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-1-1-2-1-a8d60f914433", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 1x^2 + (-1)x + (2) is divided by (x - -1)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(-1) = 1(-1)^2+(-1)(-1)+(2) = 4.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "4"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "44", "assumptions": [], "concept_id": "math.number_theory", "constraints": ["Polynomial division over the integers", "Exact remainder"], "context": {"method": "symbolic", "topic": "remainder-theorem"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-rt-4-3-1-3-ad4c24460f1c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.425}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "remainder-theorem"}, "natural_language": "en", "observations": [], "plan": ["Evaluate the polynomial at the root of the divisor"], "prompt": "By the remainder theorem, what is the remainder when 4x^2 + (3)x + (-1) is divided by (x - 3)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Remainder = p(3) = 4(3)^2+(3)(3)+(-1) = 44.", "strategy": ["Evaluate the polynomial at the root of the divisor"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "44"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "44", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-13", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-9-2-12-4aee4a5752fb", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 9 and common difference -2. What is the 12th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 9 + (12-1)·-2 = -13.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-13", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-25", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-11-3-13-669b5abf1172", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 11 and common difference -3. What is the 13th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 11 + (13-1)·-3 = -25.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-25", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "55", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-10-5-10-1bf44b4695dd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 10 and common difference 5. What is the 10th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 10 + (10-1)·5 = 55.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "55", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "24", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-8-4-9-7716c8537dc9", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term -8 and common difference 4. What is the 9th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = -8 + (9-1)·4 = 24.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "24", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "61", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-5-7-9-736a5bc37a06", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 5 and common difference 7. What is the 9th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 5 + (9-1)·7 = 61.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "61", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-43", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-2-3-16-401eb998eaa4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 2 and common difference -3. What is the 16th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 2 + (16-1)·-3 = -43.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-43", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "22", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-2-4-6-b15729689a6e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 2 and common difference 4. What is the 6th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 2 + (6-1)·4 = 22.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "22", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "27", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-3-3-9-4a6284bb8be4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 3 and common difference 3. What is the 9th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 3 + (9-1)·3 = 27.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "27", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "36", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-6-7-7-3980e33e26f0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term -6 and common difference 7. What is the 7th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = -6 + (7-1)·7 = 36.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "36", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "42", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-12-2-16-fb60e8f29b9b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 12 and common difference 2. What is the 16th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 12 + (16-1)·2 = 42.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "42", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-14", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-11-5-6-31baa7e9bfd0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 11 and common difference -5. What is the 6th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 11 + (6-1)·-5 = -14.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-14", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "15", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-1-2-8-ea9b36406fca", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 1 and common difference 2. What is the 8th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 1 + (8-1)·2 = 15.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "15", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "21", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-9-2-7-547bf19e7bf0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 9 and common difference 2. What is the 7th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 9 + (7-1)·2 = 21.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "21", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "36", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-8-2-15-979b63d78a8c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 8 and common difference 2. What is the 15th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 8 + (15-1)·2 = 36.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "36", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "17", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-3-2-11-d3a14e27cee1", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term -3 and common difference 2. What is the 11th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = -3 + (11-1)·2 = 17.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "17", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-50", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-5-5-10-edf0438dc824", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.75}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term -5 and common difference -5. What is the 10th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = -5 + (10-1)·-5 = -50.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-50", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-31", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-5-2-14-69e86fac0307", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.75}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term -5 and common difference -2. What is the 14th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = -5 + (14-1)·-2 = -31.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-31", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-13", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-1-2-7-47f5b575841a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.75}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term -1 and common difference -2. What is the 7th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = -1 + (7-1)·-2 = -13.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-13", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-23", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-12-5-8-f8605a235325", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term 12 and common difference -5. What is the 8th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = 12 + (8-1)·-5 = -23.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-23", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "59", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Exact integer term"], "context": {"method": "symbolic", "topic": "arithmetic-sequence"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-aseq-9-4-18-00f59fe23425", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "arithmetic-sequence"}, "natural_language": "en", "observations": [], "plan": ["Apply a_n = a_1+(n-1)d"], "prompt": "An arithmetic sequence has first term -9 and common difference 4. What is the 18th term?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "a_n = a_1 + (n-1)d = -9 + (18-1)·4 = 59.", "strategy": ["Apply a_n = a_1+(n-1)d"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "59", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-42", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-2-2-6-b2ad0db49fc0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 6 terms of the geometric series with first term 2 and common ratio -2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 2(-2^6-1)/(-2-1) = -42.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-42", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "63", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-1-2-6-be9c1f4621de", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.3}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 6 terms of the geometric series with first term 1 and common ratio 2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 1(2^6-1)/(2-1) = 63.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "63", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "127", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-1-2-7-930a4a4611c4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.3}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 7 terms of the geometric series with first term 1 and common ratio 2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 1(2^7-1)/(2-1) = 127.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "127", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-5", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-1-2-4-f11798dcfc4c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 4 terms of the geometric series with first term 1 and common ratio -2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 1(-2^4-1)/(-2-1) = -5.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1820", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-5-3-6-a0bdd77981fd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.3}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 6 terms of the geometric series with first term 5 and common ratio 3.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 5(3^6-1)/(3-1) = 1820.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "1820", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "121", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-1-3-5-7c72bea7fe92", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.3}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 5 terms of the geometric series with first term 1 and common ratio 3.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 1(3^5-1)/(3-1) = 121.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "121", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-21", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-1-2-6-22052ea300bb", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 6 terms of the geometric series with first term 1 and common ratio -2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 1(-2^6-1)/(-2-1) = -21.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-21", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-25", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-5-2-4-32d84683f2d0", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 4 terms of the geometric series with first term 5 and common ratio -2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 5(-2^4-1)/(-2-1) = -25.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-25", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1093", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-1-3-7-b9a55f925954", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.3}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 7 terms of the geometric series with first term 1 and common ratio 3.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 1(3^7-1)/(3-1) = 1093.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "1093", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "215", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-5-2-7-120004984c82", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.675}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 7 terms of the geometric series with first term 5 and common ratio -2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 5(-2^7-1)/(-2-1) = 215.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "215", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "62", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-2-2-5-0ddc307bf0e3", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.3}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 2(2^5-1)/(2-1) = 62.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "62", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-63", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-3-2-6-2adc2f571bb9", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 6 terms of the geometric series with first term 3 and common ratio -2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 3(-2^6-1)/(-2-1) = -63.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-63", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-105", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-5-2-6-d89c7dfec6cd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.925}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 6 terms of the geometric series with first term 5 and common ratio -2.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 5(-2^6-1)/(-2-1) = -105.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-105", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2186", "assumptions": [], "concept_id": "math.sequences", "constraints": ["Exact integer", "Finite geometric sum"], "context": {"method": "symbolic", "topic": "geometric-series"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-gsum-2-3-7-43fba932db6b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.5, "tests": 0.0, "total": 3.3}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "geometric-series"}, "natural_language": "en", "observations": [], "plan": ["Use the closed geometric-sum formula"], "prompt": "Find the sum of the first 7 terms of the geometric series with first term 2 and common ratio 3.", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "S_n = a(r^n-1)/(r-1) = 2(3^7-1)/(3-1) = 2186.", "strategy": ["Use the closed geometric-sum formula"], "task_type": "sequences", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "2186", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": "python.loops", "constraints": ["Vertex form", "Exact integer"], "context": {"method": "symbolic", "topic": "parabola"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vert-1-1-2-76a13e1bac33", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.45, "tests": 0.0, "total": 3.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "parabola"}, "natural_language": "en", "observations": [], "plan": ["Read k from vertex form"], "prompt": "The parabola y = -1(x - (1))^2 + (2) opens down. What is the y-coordinate of the vertex?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Vertex form y=a(x-h)^2+k has vertex (h,k)=(1,2).", "strategy": ["Read k from vertex form"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "2"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5", "assumptions": [], "concept_id": "python.loops", "constraints": ["Vertex form", "Exact integer"], "context": {"method": "symbolic", "topic": "parabola"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vert-2-1-5-d1e98131d6ab", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.45, "tests": 0.0, "total": 3.125}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "parabola"}, "natural_language": "en", "observations": [], "plan": ["Read k from vertex form"], "prompt": "The parabola y = 2(x - (1))^2 + (5) opens up. What is the y-coordinate of the vertex?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Vertex form y=a(x-h)^2+k has vertex (h,k)=(1,5).", "strategy": ["Read k from vertex form"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5", "assumptions": [], "concept_id": "python.loops", "constraints": ["Vertex form", "Exact integer"], "context": {"method": "symbolic", "topic": "parabola"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vert-2-0-5-9b04a585f3cf", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.45, "tests": 0.0, "total": 3.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "parabola"}, "natural_language": "en", "observations": [], "plan": ["Read k from vertex form"], "prompt": "The parabola y = -2(x - (0))^2 + (5) opens down. What is the y-coordinate of the vertex?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Vertex form y=a(x-h)^2+k has vertex (h,k)=(0,5).", "strategy": ["Read k from vertex form"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "7", "assumptions": [], "concept_id": "python.loops", "constraints": ["Vertex form", "Exact integer"], "context": {"method": "symbolic", "topic": "parabola"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vert-1-3-7-fad1118fcb00", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.45, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "parabola"}, "natural_language": "en", "observations": [], "plan": ["Read k from vertex form"], "prompt": "The parabola y = 1(x - (-3))^2 + (7) opens up. What is the y-coordinate of the vertex?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Vertex form y=a(x-h)^2+k has vertex (h,k)=(-3,7).", "strategy": ["Read k from vertex form"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "7"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "7", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "-5", "assumptions": [], "concept_id": "python.loops", "constraints": ["Vertex form", "Exact integer"], "context": {"method": "symbolic", "topic": "parabola"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-vert-3-0-5-a078d7d68627", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.25, "observations": 0.0, "plan": 0.4, "prompt_length": 0.45, "tests": 0.0, "total": 3.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "parabola"}, "natural_language": "en", "observations": [], "plan": ["Read k from vertex form"], "prompt": "The parabola y = 3(x - (0))^2 + (-5) opens up. What is the y-coordinate of the vertex?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Vertex form y=a(x-h)^2+k has vertex (h,k)=(0,-5).", "strategy": ["Read k from vertex form"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {"expected": "-5"}, "exit_code": null, "memory_mb": null, "method": "sympy", "passed": true, "result": "-5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "65", "assumptions": [], "concept_id": null, "constraints": ["Squared distance, not the root", "Exact integer"], "context": {"method": "symbolic", "topic": "analytic-geometry"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-d3-5-0-4-2-0-0-0292803c3237", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 1.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.3, "tests": 0.0, "total": 3.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "analytic-geometry"}, "natural_language": "en", "observations": [], "plan": ["Subtract coordinates", "Sum squares"], "prompt": "What is the squared Euclidean distance between (5,0,-4) and (-2,0,0) in R^3?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "d^2 = Δx^2+Δy^2+Δz^2 = 65.", "strategy": ["Subtract coordinates", "Sum squares"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "65", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "-8", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Trace is the diagonal sum"], "context": {"method": "symbolic", "topic": "trace"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tr-2-3-5-2-bd3a31b3e200", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.4, "prompt_length": 0.275, "tests": 0.0, "total": 2.25}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trace"}, "natural_language": "en", "observations": [], "plan": ["Add diagonal entries"], "prompt": "What is the trace of the matrix [[-3, -2], [-2, -5]]?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "tr(A)=sum of diagonal entries=-8.", "strategy": ["Add diagonal entries"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-4", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Trace is the diagonal sum"], "context": {"method": "symbolic", "topic": "trace"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tr-3-3-4-3-2-443776982180", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 1.0, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.5}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trace"}, "natural_language": "en", "observations": [], "plan": ["Add diagonal entries"], "prompt": "What is the trace of the matrix [[-3, -2, 0], [0, -4, -2], [-2, 0, 3]]?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "tr(A)=sum of diagonal entries=-4.", "strategy": ["Add diagonal entries"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Trace is the diagonal sum"], "context": {"method": "symbolic", "topic": "trace"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tr-2-4-6-3-dda613c1ce1b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.25, "observations": 0.0, "plan": 0.4, "prompt_length": 0.275, "tests": 0.0, "total": 1.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trace"}, "natural_language": "en", "observations": [], "plan": ["Add diagonal entries"], "prompt": "What is the trace of the matrix [[-4, 3], [3, 6]]?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "tr(A)=sum of diagonal entries=2.", "strategy": ["Add diagonal entries"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "2", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "15", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Trace is the diagonal sum"], "context": {"method": "symbolic", "topic": "trace"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tr-3-6-3-6-5-938c56a63062", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 1.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trace"}, "natural_language": "en", "observations": [], "plan": ["Add diagonal entries"], "prompt": "What is the trace of the matrix [[6, 5, 0], [0, 3, 5], [5, 0, 6]]?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "tr(A)=sum of diagonal entries=15.", "strategy": ["Add diagonal entries"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "15", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "11", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Trace is the diagonal sum"], "context": {"method": "symbolic", "topic": "trace"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tr-3-4-3-4-5-a958bde9bcac", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 1.625}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trace"}, "natural_language": "en", "observations": [], "plan": ["Add diagonal entries"], "prompt": "What is the trace of the matrix [[4, 5, 0], [0, 3, 5], [5, 0, 4]]?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "tr(A)=sum of diagonal entries=11.", "strategy": ["Add diagonal entries"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "11", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Trace is the diagonal sum"], "context": {"method": "symbolic", "topic": "trace"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tr-3-7-4-1-2-92d8cac73e92", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.125}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trace"}, "natural_language": "en", "observations": [], "plan": ["Add diagonal entries"], "prompt": "What is the trace of the matrix [[7, -2, 0], [0, 4, -2], [-2, 0, -1]]?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "tr(A)=sum of diagonal entries=10.", "strategy": ["Add diagonal entries"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "10", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-3", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Trace is the diagonal sum"], "context": {"method": "symbolic", "topic": "trace"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tr-3-5-1-1-0-a8697368509c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.0}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trace"}, "natural_language": "en", "observations": [], "plan": ["Add diagonal entries"], "prompt": "What is the trace of the matrix [[-5, 0, 0], [0, 1, 0], [0, 0, 1]]?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "tr(A)=sum of diagonal entries=-3.", "strategy": ["Add diagonal entries"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-3", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-4", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Trace is the diagonal sum"], "context": {"method": "symbolic", "topic": "trace"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tr-3-3-6-1-4-ac1aeace319e", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.4, "prompt_length": 0.4, "tests": 0.0, "total": 2.125}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trace"}, "natural_language": "en", "observations": [], "plan": ["Add diagonal entries"], "prompt": "What is the trace of the matrix [[3, 4, 0], [0, -6, 4], [4, 0, -1]]?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "tr(A)=sum of diagonal entries=-4.", "strategy": ["Add diagonal entries"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "-1", "assumptions": [], "concept_id": "go.concurrency", "constraints": ["Trace is the diagonal sum"], "context": {"method": "symbolic", "topic": "trace"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tr-2-2-1-3-0c465ffcf570", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.4, "prompt_length": 0.275, "tests": 0.0, "total": 1.875}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "trace"}, "natural_language": "en", "observations": [], "plan": ["Add diagonal entries"], "prompt": "What is the trace of the matrix [[-2, 3], [3, 1]]?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "tr(A)=sum of diagonal entries=-1.", "strategy": ["Add diagonal entries"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "-1", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "86", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-3-3-1-1-2-0-af75161ce588", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(-3,-3,1) and v=(1,-2,0). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(2,1,9); squared length=86.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "86", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "676", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-3-4-2-3-4-0-6a7f07a9f63a", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(3,4,2) and v=(-3,4,0). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(-8,-6,24); squared length=676.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "676", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "120", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-2-4-2-1-3-1-117ac0d9c64d", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.0500000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(2,4,2) and v=(-1,-3,1). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(10,-4,-2); squared length=120.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "120", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "56", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-2-2-2-2-1-0-1fdfa9b93e3b", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.0500000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(-2,2,2) and v=(-2,-1,0). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(2,-4,6); squared length=56.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "56", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "21", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-0-4-1-1-2-1-814589a1741d", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.8000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(0,4,1) and v=(-1,2,1). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(2,-1,4); squared length=21.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "21", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "118", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-1-3-1-2-3-1-3fef439591d6", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.8000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(1,3,1) and v=(2,-3,1). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(6,1,-9); squared length=118.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "118", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "72", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-2-2-0-3-1-1-60d789a5cd13", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.8000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(-2,2,0) and v=(3,1,1). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(2,2,-8); squared length=72.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "72", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "5", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-1-2-0-1-2-1-7b3b20bfc3a2", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.8000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(-1,2,0) and v=(-1,2,1). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(2,1,0); squared length=5.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "59", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-3-1-2-2-1-1-0538caff972f", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.0500000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(3,-1,2) and v=(-2,1,1). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(-3,-7,1); squared length=59.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "59", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "101", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-2-1-2-2-3-1-4e055e7b225c", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.0500000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(2,-1,2) and v=(-2,3,1). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(-7,-6,4); squared length=101.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "101", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-3-2-1-1-0-1-4496722e7b5e", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.8000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(-3,2,1) and v=(-1,0,1). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(2,2,2); squared length=12.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "12", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "16", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-4-0-0-1-1-0-8c0f39834c45", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.5, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 2.9250000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(4,0,0) and v=(-1,-1,0). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(0,0,-4); squared length=16.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "16", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "68", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-1-2-2-3-2-0-fef1e50138e2", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.75, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.1750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(1,-2,2) and v=(-3,2,0). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(-4,-6,-4); squared length=68.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "68", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "26", "assumptions": [], "concept_id": null, "constraints": ["3D cross product", "Squared Euclidean norm"], "context": {"method": "symbolic", "topic": "cross-product"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-cross-3-1-0-1-1-1-e61ae44291c4", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.875, "observations": 0.0, "plan": 0.8, "prompt_length": 0.225, "tests": 0.0, "total": 3.3000000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "cross-product"}, "natural_language": "en", "observations": [], "plan": ["Compute cross product", "Sum squares"], "prompt": "Let u=(3,-1,0) and v=(-1,-1,1). What is ||u × v||^2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "u×v=(-1,-3,-4); squared length=26.", "strategy": ["Compute cross product", "Sum squares"], "task_type": "linear_algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "26", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "165", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Smaller of the two clock angles", "Degrees"], "context": {"method": "symbolic", "topic": "clock-angle"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-clock-0-30-75114f5571a2", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.075}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "clock-angle"}, "natural_language": "en", "observations": [], "plan": ["Place both hands", "Take min(d, 360-d)"], "prompt": "On a 12-hour analog clock, what is the smaller angle in degrees between the hour and minute hands at 00:30?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Hour hand at 0.5*(60h+m)=15.0°, minute at 6m=180°, smaller difference=165.", "strategy": ["Place both hands", "Take min(d, 360-d)"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "165", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "102.5", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Smaller of the two clock angles", "Degrees"], "context": {"method": "symbolic", "topic": "clock-angle"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-clock-8-25-7b4434f80f6b", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.075}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "clock-angle"}, "natural_language": "en", "observations": [], "plan": ["Place both hands", "Take min(d, 360-d)"], "prompt": "On a 12-hour analog clock, what is the smaller angle in degrees between the hour and minute hands at 08:25?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Hour hand at 0.5*(60h+m)=252.5°, minute at 6m=150°, smaller difference=102.5.", "strategy": ["Place both hands", "Take min(d, 360-d)"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "102.5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "75", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Smaller of the two clock angles", "Degrees"], "context": {"method": "symbolic", "topic": "clock-angle"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-clock-3-30-ecbab872ba73", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.075}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "clock-angle"}, "natural_language": "en", "observations": [], "plan": ["Place both hands", "Take min(d, 360-d)"], "prompt": "On a 12-hour analog clock, what is the smaller angle in degrees between the hour and minute hands at 03:30?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Hour hand at 0.5*(60h+m)=105.0°, minute at 6m=180°, smaller difference=75.", "strategy": ["Place both hands", "Take min(d, 360-d)"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "75", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "107.5", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Smaller of the two clock angles", "Degrees"], "context": {"method": "symbolic", "topic": "clock-angle"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-clock-1-25-d74cda1adfbf", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.075}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "clock-angle"}, "natural_language": "en", "observations": [], "plan": ["Place both hands", "Take min(d, 360-d)"], "prompt": "On a 12-hour analog clock, what is the smaller angle in degrees between the hour and minute hands at 01:25?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Hour hand at 0.5*(60h+m)=42.5°, minute at 6m=150°, smaller difference=107.5.", "strategy": ["Place both hands", "Take min(d, 360-d)"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "107.5", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "90", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["Smaller of the two clock angles", "Degrees"], "context": {"method": "symbolic", "topic": "clock-angle"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-clock-3-0-55995c37f862", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.8, "prompt_length": 0.5, "tests": 0.0, "total": 3.075}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "clock-angle"}, "natural_language": "en", "observations": [], "plan": ["Place both hands", "Take min(d, 360-d)"], "prompt": "On a 12-hour analog clock, what is the smaller angle in degrees between the hour and minute hands at 03:00?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "Hour hand at 0.5*(60h+m)=90.0°, minute at 6m=0°, smaller difference=90.", "strategy": ["Place both hands", "Take min(d, 360-d)"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "90", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "91", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "triangular"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tri-13-3597a67e987b", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.225, "tests": 0.0, "total": 1.7000000000000002}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "triangular"}, "natural_language": "en", "observations": [], "plan": ["Apply the triangular formula"], "prompt": "What is the 13th triangular number T_n = n(n+1)/2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "T_13=13·14/2=91.", "strategy": ["Apply the triangular formula"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "91", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "496", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "triangular"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tri-31-d42c595a4392", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.225, "tests": 0.0, "total": 1.7000000000000002}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "triangular"}, "natural_language": "en", "observations": [], "plan": ["Apply the triangular formula"], "prompt": "What is the 31th triangular number T_n = n(n+1)/2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "T_31=31·32/2=496.", "strategy": ["Apply the triangular formula"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "496", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "78", "assumptions": [], "concept_id": null, "constraints": ["Exact integer"], "context": {"method": "symbolic", "topic": "triangular"}, "difficulty": "introductory", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-tri-12-fa675a9c8465", "metadata": {"difficulty_score": {"constraints": 0.7, "keywords": 0.0, "math_ops": 0.375, "observations": 0.0, "plan": 0.4, "prompt_length": 0.225, "tests": 0.0, "total": 1.7000000000000002}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "triangular"}, "natural_language": "en", "observations": [], "plan": ["Apply the triangular formula"], "prompt": "What is the 12th triangular number T_n = n(n+1)/2?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "T_12=12·13/2=78.", "strategy": ["Apply the triangular formula"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "78", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "163", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-115-8-e46e84cf2dbd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 115 in base 8 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "115 in base 8 is 163 (check: int('163', 8)=115).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "163", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1b", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-27-16-f6139860f990", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 27 in base 16 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "27 in base 16 is 1b (check: int('1b', 16)=27).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "1b", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "50", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-80-16-ba633d879629", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 80 in base 16 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "80 in base 16 is 50 (check: int('50', 16)=80).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "50", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "24", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-20-8-f767662a2451", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 20 in base 8 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "20 in base 8 is 24 (check: int('24', 8)=20).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "24", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "41", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-33-8-032920c7636f", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 33 in base 8 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "33 in base 8 is 41 (check: int('41', 8)=33).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "41", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4d", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-77-16-39025a365371", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 77 in base 16 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "77 in base 16 is 4d (check: int('4d', 16)=77).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "4d", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "b8", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-184-16-21d8d5d3ce24", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 184 in base 16 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "184 in base 16 is b8 (check: int('b8', 16)=184).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "b8", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "2a", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-42-16-30c2feeb62ed", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 42 in base 16 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "42 in base 16 is 2a (check: int('2a', 16)=42).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "2a", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1100101", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-101-2-434180efc208", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 101 in base 2 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "101 in base 2 is 1100101 (check: int('1100101', 2)=101).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "1100101", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "33", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-27-8-20d1ba920f85", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 27 in base 8 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "27 in base 8 is 33 (check: int('33', 8)=27).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "33", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "233", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-155-8-ec543bee26bf", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 155 in base 8 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "155 in base 8 is 233 (check: int('233', 8)=155).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "233", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10110100", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-180-2-a7a12d1e1efd", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 180 in base 2 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "180 in base 2 is 10110100 (check: int('10110100', 2)=180).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "10110100", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "277", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-191-8-b3cb907fb1c6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 191 in base 8 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "191 in base 8 is 277 (check: int('277', 8)=191).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "277", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "302", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-194-8-5dbb080f3c6f", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 194 in base 8 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "194 in base 8 is 302 (check: int('302', 8)=194).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "302", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10110001", "assumptions": [], "concept_id": "python.conditionals", "constraints": ["No 0b/0o/0x prefix", "Lowercase hex"], "context": {"method": "symbolic", "topic": "base-conversion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-base-177-2-d05a98fc6c64", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.0, "observations": 0.0, "plan": 0.8, "prompt_length": 0.325, "tests": 0.0, "total": 2.5250000000000004}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "base-conversion"}, "natural_language": "en", "observations": [], "plan": ["Repeated division", "Collect remainders"], "prompt": "Write the positive integer 177 in base 2 (no prefix, lowercase if hex).", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "177 in base 2 is 10110001 (check: int('10110001', 2)=177).", "strategy": ["Repeated division", "Collect remainders"], "task_type": "number_theory", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "10110001", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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{"answer": "42", "assumptions": [], "concept_id": null, "constraints": ["Inverse proportion", "Exact integer y"], "context": {"method": "symbolic", "topic": "inverse-proportion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-invp-7-18-3-88a78bb15c80", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 2.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "inverse-proportion"}, "natural_language": "en", "observations": [], "plan": ["Compute xy", "Divide by the new x"], "prompt": "y is inversely proportional to x. When x=7, y=18. What is y when x=3?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "xy constant=126; y=126/3=42.", "strategy": ["Compute xy", "Divide by the new x"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "42", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "10", "assumptions": [], "concept_id": null, "constraints": ["Inverse proportion", "Exact integer y"], "context": {"method": "symbolic", "topic": "inverse-proportion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-invp-4-20-8-ffb821945bf0", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 2.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "inverse-proportion"}, "natural_language": "en", "observations": [], "plan": ["Compute xy", "Divide by the new x"], "prompt": "y is inversely proportional to x. When x=4, y=20. What is y when x=8?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "xy constant=80; y=80/8=10.", "strategy": ["Compute xy", "Divide by the new x"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "10", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "6", "assumptions": [], "concept_id": null, "constraints": ["Inverse proportion", "Exact integer y"], "context": {"method": "symbolic", "topic": "inverse-proportion"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-invp-3-8-4-e9861c11d291", "metadata": {"difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.125, "observations": 0.0, "plan": 0.8, "prompt_length": 0.35, "tests": 0.0, "total": 2.6750000000000003}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "inverse-proportion"}, "natural_language": "en", "observations": [], "plan": ["Compute xy", "Divide by the new x"], "prompt": "y is inversely proportional to x. When x=3, y=8. What is y when x=4?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "xy constant=24; y=24/4=6.", "strategy": ["Compute xy", "Divide by the new x"], "task_type": "algebra", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "integer-check", "passed": true, "result": "6", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "3.125", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-5-45-8bf43e48d757", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 5 and central angle 45 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (45/360)·5^2 = 3.125.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "3.125", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "8.333333333", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-10-30-caccb4cebf0a", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 10 and central angle 30 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (30/360)·10^2 = 8.333333333333334.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "8.333333333", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "21.33333333", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-8-120-00867c74ffe9", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 8 and central angle 120 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (120/360)·8^2 = 21.333333333333332.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "21.33333333", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "24", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-12-60-9ffaa1698db6", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 12 and central angle 60 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (60/360)·12^2 = 24.0.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "24", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "33.33333333", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-10-120-943f5946ad71", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 10 and central angle 120 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (120/360)·10^2 = 33.333333333333336.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "33.33333333", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "8.333333333", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-5-120-1655e5f80f03", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 5 and central angle 120 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (120/360)·5^2 = 8.333333333333334.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "8.333333333", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "1.333333333", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-4-30-dd70d400a0d5", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 4 and central angle 30 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (30/360)·4^2 = 1.3333333333333333.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "1.333333333", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12.25", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-7-90-385ddcde0a18", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 7 and central angle 90 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (90/360)·7^2 = 12.25.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "12.25", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "20.25", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-9-90-b29226cbbef3", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 9 and central angle 90 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (90/360)·9^2 = 20.25.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "20.25", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "12", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-12-30-97eb2556e163", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 12 and central angle 30 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (30/360)·12^2 = 12.0.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "12", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4.166666667", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-5-60-ada5626cc0ce", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 5 and central angle 60 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (60/360)·5^2 = 4.166666666666667.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "4.166666667", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "4", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-4-90-98ef1c1bb7f4", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 4 and central angle 90 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (90/360)·4^2 = 4.0.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "4", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
{"answer": "50", "assumptions": [], "concept_id": "math.geometry", "constraints": ["Report A/π, not A", "Degrees not radians"], "context": {"method": "symbolic", "topic": "sector"}, "difficulty": "beginner", "domain": "mathematics", "education_level": null, "evidence": null, "id": "or-mathematics-math-sec-10-180-9c4aa90a153c", "metadata": {"concept_id_inferred": true, "difficulty_score": {"constraints": 1.4, "keywords": 0.0, "math_ops": 0.625, "observations": 0.0, "plan": 0.8, "prompt_length": 0.55, "tests": 0.0, "total": 3.375}, "pipeline_version": "1.3.8", "schema_version": "1.3.8", "topic": "sector"}, "natural_language": "en", "observations": [], "plan": ["Use (θ/360)πr^2", "Divide by π"], "prompt": "A circular sector has radius 10 and central angle 180 degrees. What is its area divided by π (exact decimal or integer)?", "provenance": {"commit": null, "derived": false, "derived_from": null, "generated_at": "2026-08-19T01:35:16Z", "generator": "open_reason.generation.mathematics", "generator_version": "1.3.8", "license": "Apache License 2.0", "license_spdx": "Apache-2.0", "retrieved_at": null, "source": "open_reason.generation.mathematics", "source_id": null, "source_type": "synthetic", "source_url": null, "source_version": null, "transformation": null, "trust_tier": "tier7_synthetic", "unknown_reason": null}, "quality": {"evidence_confidence": 0.617, "notes": [], "score_components": {"authority_score": 0.55, "community_score": 0.0, "cross_source_score": 0.0, "provenance_score": 1.0, "recency_score": 0.7, "verification_score": 1.0}, "tier": "S", "verification_method": "sympy", "verified": true}, "runtime": null, "solution": "A/π = (θ/360)r^2 = (180/360)·10^2 = 50.0.", "strategy": ["Use (θ/360)πr^2", "Divide by π"], "task_type": "geometry", "temporal": null, "transformation": ["task_generation", "difficulty_assignment", "verification", "knowledge_normalization"], "translation_status": "original", "verification": {"command": null, "compiler_version": null, "details": {}, "exit_code": null, "memory_mb": null, "method": "numeric", "passed": true, "result": "50", "runtime_s": null, "runtime_version": null, "stderr": null, "stdout": null, "tests_failed": null, "tests_passed": null}}
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