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candidate evidence library of concepts and formulas, and annotations identifying the evidence needed at each step along with complete evidence chains. It assesses whether retrieval-augmented generation systems retrieve knowledge that is both complete across the solution steps and applicable to the problem, rather than merely returning one related formula. It supports SAT math knowledge retrieval, evidence-chain evaluation, and the development of retrieval-augmented generation systems.\u003C\u002Fp>","2026-10-14 18:09:12","2026-10-19 17:19:16","0.00",0,5000,"SAT math dataset,multi-step math problems,evidence retrieval benchmark,RAG evaluation data,math formula retrieval,knowledge grounding,evidence chain annotations,SAT preparation data","An evidence retrieval benchmark for multi-step SAT math, with candidate concepts, formulas, and complete evidence chains to assess RAG retrieval completeness.","JSON","0.3GB","SAT math solution retrieval, mathematical evidence verification, multi-step problem solving","retrieval, evidence ranking, multi-step reasoning","V1.0","rivo\u002Fsample-packages\u002Fef290245-c5e4-40d5-8e4e-61d2438b802e\u002F20261014.zip",[583,588,594,599,605],{"id":572,"name":584,"field":585,"intro":586,"type":587},"File Name","file_name","File name","string",{"id":589,"name":590,"field":591,"intro":592,"type":593},8885,"Evidence Chain Summary","chain_summary","Calculated summary statistics for the multi-step evidence chain, including its size, dependency depth, and completeness.","object",{"id":595,"name":596,"field":597,"intro":598,"type":593},8886,"Original Problem and Annotation Record","source_record","The original record supplied during dataset creation, containing the problem, candidate evidence library, and complete step-by-step annotations.",{"id":600,"name":601,"field":602,"intro":603,"type":604},8887,"Normalized Evidence Chain","evidence_chain","An ordered evidence chain derived from the original step annotations, representing the complete and applicable knowledge required at each reasoning step.","array",{"id":606,"name":607,"field":608,"intro":609,"type":593},8888,"Retrieval Evaluation Target","retrieval_evaluation_target","A RAG retrieval evaluation target derived from the reference evidence chain, emphasizing evidence-set completeness and applicability.",[611,615,619,623],{"id":612,"question":613,"answer":614},6335,"What does the dataset contain?","It includes SAT math problems that require multi-step derivations, a candidate library of concepts and formulas, annotations for the evidence needed at each step, normalized evidence chains, and retrieval evaluation targets.",{"id":616,"question":617,"answer":618},6336,"What capability does it evaluate?","It focuses on whether a RAG system retrieves knowledge that is complete and applicable across the steps of a solution, rather than merely returning a superficially related formula or concept.",{"id":620,"question":621,"answer":622},6337,"Which use cases is it designed for?","It can support SAT math knowledge retrieval, evaluation of retrieval-augmented generation systems, multi-step math question-answering research, and analysis of evidence-chain completeness and knowledge grounding.",{"id":624,"question":625,"answer":626},6338,"How can I obtain the dataset and verify its license?","Check the dataset product page or contact the provider for access options, license scope, and usage restrictions. Confirm the applicable terms before commercial deployment, redistribution, or public release of evaluation results.",[628,640,649],{"id":629,"relate_table":630,"relate_id":631,"file_size":572,"file_name":632,"path":8,"duration":572,"cate":483,"file_format":633,"audio_rate":8,"audio_channel":522,"audio_bit_depth":522,"quality":8,"annotation":634,"cate_name":635,"chain_summary":636,"source_record":637,"evidence_chain":638,"retrieval_evaluation_target":639},15063,"union_cubo",233879107,"样例_3.json","json","{\"chain_summary\": \"{\\\"step_count\\\": 5, \\\"unique_required_evidence_count\\\": 5, \\\"dependency_depth\\\": 5, \\\"chain_complete\\\": true, \\\"evidence_sufficiency_rule\\\": \\\"It must cover five types of evidence: the exponential model, division of powers with the same base, square roots under positive constraints, solving for coefficients, and evaluating the target function; if only the exponential function definition or exponentiation formula is retrieved, it cannot support determining the parameters from two known function values and completing the final evaluation.\\\"}\", \"source_record\": \"{\\\"question_text\\\": \\\"The function f(x)=a·b^x, where a and b are both positive. Given f(1)=12 and f(3)=48, what is the value of f(5)?\\\", \\\"problem_category\\\": \\\"Exponential functions and exponent operations\\\", \\\"given_conditions\\\": [\\\"f(x)=a·b^x.\\\", \\\"a>0 and b>0.\\\", \\\"f(1)=12.\\\", \\\"f(3)=48.\\\"], \\\"answer_choices\\\": [\\\"A. 96\\\", \\\"B. 144\\\", \\\"C. 192\\\", \\\"D. 384\\\"], \\\"correct_answer\\\": \\\"C\\\", \\\"candidate_evidence_library\\\": [{\\\"evidence_key\\\": \\\"EXP-E1\\\", \\\"evidence_kind\\\": \\\"Function definition\\\", \\\"evidence_statement\\\": \\\"The exponential function model can be written as f(x)=a·b^x, where a is a positive initial coefficient and b is a positive growth or decay base.\\\", \\\"formula_text\\\": \\\"f(x)=a·b^x; a>0, b>0\\\", \\\"applicability_conditions\\\": [\\\"The problem explicitly gives an exponential function model.\\\", \\\"a and b are positive.\\\"], \\\"source_excerpt\\\": \\\"For an exponential function of the form f(x)=a·b^x, a determines the initial scale, and b determines the multiplicative rate of change for each one-unit increase in the input.\\\"}, {\\\"evidence_key\\\": \\\"EXP-E2\\\", \\\"evidence_kind\\\": \\\"Exponent operation rule\\\", \\\"evidence_statement\\\": \\\"When dividing powers with the same base, subtract the exponents; dividing the two function values can cancel the common coefficient a.\\\", \\\"formula_text\\\": \\\"(a·b^m)\u002F(a·b^n)=b^(m-n), a is not equal to 0\\\", \\\"applicability_conditions\\\": [\\\"The numerator and denominator use the same a and the same base b.\\\", \\\"The denominator is not zero.\\\"], \\\"source_excerpt\\\": \\\"When dividing powers with the same base, the base stays the same and the exponents are subtracted; common nonzero factors can be canceled.\\\"}, {\\\"evidence_key\\\": \\\"EXP-E3\\\", \\\"evidence_kind\\\": \\\"Calculation rule\\\", \\\"evidence_statement\\\": \\\"When b is positive and b^2=4, b can only be the positive square root 2.\\\", \\\"formula_text\\\": \\\"b^2=4 and b>0, so b=sqrt(4)=2\\\", \\\"applicability_conditions\\\": [\\\"b is positive.\\\", \\\"The square of b is known.\\\"], \\\"source_excerpt\\\": \\\"Under the positive number restriction, the only possible value whose square is 4 is 2, not the negative square root.\\\"}, {\\\"evidence_key\\\": \\\"EXP-E4\\\", \\\"evidence_kind\\\": \\\"Algebraic transformation rule\\\", \\\"evidence_statement\\\": \\\"After knowing f(1)=a·b, divide the function value by b to find the coefficient a.\\\", \\\"formula_text\\\": \\\"a=f(1)\u002Fb\\\", \\\"applicability_conditions\\\": [\\\"b is not equal to 0.\\\", \\\"f(1)=a·b holds.\\\"], \\\"source_excerpt\\\": \\\"Write the value of the exponential function at x=1 as a·b, then divide by the known base to obtain a.\\\"}, {\\\"evidence_key\\\": \\\"EXP-E5\\\", \\\"evidence_kind\\\": \\\"Exponential calculation rule\\\", \\\"evidence_statement\\\": \\\"When calculating the target function value, first compute the exponential power, then multiply by the coefficient.\\\", \\\"formula_text\\\": \\\"f(5)=a·b^5; 2^5=32\\\", \\\"applicability_conditions\\\": [\\\"The values of a and b have been determined.\\\", \\\"The target input is x=5.\\\"], \\\"source_excerpt\\\": \\\"Evaluating an exponential function follows the steps of first calculating b to the x-th power, then multiplying by coefficient a.\\\"}, {\\\"evidence_key\\\": \\\"EXP-D1\\\", \\\"evidence_kind\\\": \\\"Concept\\\", \\\"evidence_statement\\\": \\\"In an arithmetic sequence, adjacent terms maintain a fixed additive difference.\\\", \\\"formula_text\\\": \\\"u_n=u_1+(n-1)d\\\", \\\"applicability_conditions\\\": [\\\"The difference between adjacent terms remains constant.\\\"], \\\"source_excerpt\\\": \\\"The arithmetic model describes a sequence that changes by a fixed difference.\\\"}, {\\\"evidence_key\\\": \\\"EXP-D2\\\", \\\"evidence_kind\\\": \\\"Formula\\\", \\\"evidence_statement\\\": \\\"Logarithms can convert exponential relationships into power relationships.\\\", \\\"formula_text\\\": \\\"log_b(y)=x is equivalent to b^x=y\\\", \\\"applicability_conditions\\\": [\\\"b>0 and b is not equal to 1, y>0.\\\"], \\\"source_excerpt\\\": \\\"Logarithms are the inverse operation of exponentiation.\\\"}, {\\\"evidence_key\\\": \\\"EXP-D3\\\", \\\"evidence_kind\\\": \\\"Formula\\\", \\\"evidence_statement\\\": \\\"The roots of a quadratic equation can be determined by the discriminant and the quadratic formula.\\\", \\\"formula_text\\\": \\\"x=(-b±sqrt(b^2-4ac))\u002F(2a)\\\", \\\"applicability_conditions\\\": [\\\"The equation is quadratic.\\\"], \\\"source_excerpt\\\": \\\"The quadratic formula applies to quadratic equations in general form.\\\"}], \\\"gold_step_annotations\\\": [{\\\"step_key\\\": \\\"exp_s0\\\", \\\"step_order\\\": 0, \\\"reasoning_goal\\\": \\\"Write the two known function values as exponential expressions in terms of a and b.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E1\\\", \\\"evidence_role\\\": \\\"Exponential function model and parameter conditions\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"From the model, obtain a·b=12 and a·b^3=48, and a and b are both positive.\\\", \\\"prerequisite_step_keys\\\": []}, {\\\"step_key\\\": \\\"exp_s1\\\", \\\"step_order\\\": 1, \\\"reasoning_goal\\\": \\\"Divide the two function values to cancel a and find the square of b.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E2\\\", \\\"evidence_role\\\": \\\"Division of powers with the same base and cancellation of common factors\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"(a·b^3)\u002F(a·b)=48\u002F12, so b^2=4.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s0\\\"]}, {\\\"step_key\\\": \\\"exp_s2\\\", \\\"step_order\\\": 2, \\\"reasoning_goal\\\": \\\"Use the condition that b is positive to determine the exponential base b.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E3\\\", \\\"evidence_role\\\": \\\"Positive square root value\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"b=2.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s1\\\"]}, {\\\"step_key\\\": \\\"exp_s3\\\", \\\"step_order\\\": 3, \\\"reasoning_goal\\\": \\\"Use f(1)=12 to find the coefficient a of the exponential function.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E4\\\", \\\"evidence_role\\\": \\\"Solving for the coefficient from the function value\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"a·2=12, so a=6.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s2\\\"]}, {\\\"step_key\\\": \\\"exp_s4\\\", \\\"step_order\\\": 4, \\\"reasoning_goal\\\": \\\"Substitute a and b into the target input x=5 and calculate the function value.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E5\\\", \\\"evidence_role\\\": \\\"Exponential function evaluation and exponentiation\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"f(5)=6·2^5=6·32=192, so choose C.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s3\\\"]}]}\", \"evidence_chain\": \"[{\\\"step_key\\\": \\\"exp_s0\\\", \\\"step_order\\\": 0, \\\"step_goal\\\": \\\"Expand the two known function values according to the exponential function model.\\\", \\\"prerequisite_step_keys\\\": [], \\\"required_evidence_keys\\\": [\\\"EXP-E1\\\"], \\\"required_evidence_roles\\\": [\\\"Exponential function model and parameter conditions\\\"], \\\"expected_conclusion\\\": \\\"Obtain a·b=12 and a·b^3=48.\\\"}, {\\\"step_key\\\": \\\"exp_s1\\\", \\\"step_order\\\": 1, \\\"step_goal\\\": \\\"Cancel a by division and obtain b^2.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s0\\\"], \\\"required_evidence_keys\\\": [\\\"EXP-E2\\\"], \\\"required_evidence_roles\\\": [\\\"Division of powers with the same base and cancellation of common factors\\\"], \\\"expected_conclusion\\\": \\\"Obtain b^2=4.\\\"}, {\\\"step_key\\\": \\\"exp_s2\\\", \\\"step_order\\\": 2, \\\"step_goal\\\": \\\"Use the positive number constraint to find b.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s1\\\"], \\\"required_evidence_keys\\\": [\\\"EXP-E3\\\"], \\\"required_evidence_roles\\\": [\\\"Positive square root value\\\"], \\\"expected_conclusion\\\": \\\"Obtain b=2.\\\"}, {\\\"step_key\\\": \\\"exp_s3\\\", \\\"step_order\\\": 3, \\\"step_goal\\\": \\\"Find coefficient a from f(1).\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s2\\\"], \\\"required_evidence_keys\\\": [\\\"EXP-E4\\\"], \\\"required_evidence_roles\\\": [\\\"Solving for the coefficient from the function value\\\"], \\\"expected_conclusion\\\": \\\"Obtain a=6.\\\"}, {\\\"step_key\\\": \\\"exp_s4\\\", \\\"step_order\\\": 4, \\\"step_goal\\\": \\\"Calculate the exponential function value at x=5 and match the choices.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s3\\\"], \\\"required_evidence_keys\\\": [\\\"EXP-E5\\\"], \\\"required_evidence_roles\\\": [\\\"Exponential function evaluation and exponentiation\\\"], \\\"expected_conclusion\\\": \\\"f(5)=192, the correct choice is C.\\\"}]\", \"retrieval_evaluation_target\": \"{\\\"must_retrieve_all_required\\\": true, \\\"relevant_evidence_keys\\\": [\\\"EXP-E1\\\", \\\"EXP-E2\\\", \\\"EXP-E3\\\", \\\"EXP-E4\\\", \\\"EXP-E5\\\"], \\\"distractor_evidence_keys\\\": [\\\"EXP-D1\\\", \\\"EXP-D2\\\", \\\"EXP-D3\\\"], \\\"coverage_unit\\\": \\\"Evaluate necessary evidence coverage by reasoning step, and require the entire evidence chain from parameter identification to target evaluation to be complete\\\"}\"}","文本","{\"step_count\": 5, \"unique_required_evidence_count\": 5, \"dependency_depth\": 5, \"chain_complete\": true, \"evidence_sufficiency_rule\": \"It must cover five types of evidence: the exponential model, division of powers with the same base, square roots under positive constraints, solving for coefficients, and evaluating the target function; if only the exponential function definition or exponentiation formula is retrieved, it cannot support determining the parameters from two known function values and completing the final evaluation.\"}","{\"question_text\": \"The function f(x)=a·b^x, where a and b are both positive. Given f(1)=12 and f(3)=48, what is the value of f(5)?\", \"problem_category\": \"Exponential functions and exponent operations\", \"given_conditions\": [\"f(x)=a·b^x.\", \"a>0 and b>0.\", \"f(1)=12.\", \"f(3)=48.\"], \"answer_choices\": [\"A. 96\", \"B. 144\", \"C. 192\", \"D. 384\"], \"correct_answer\": \"C\", \"candidate_evidence_library\": [{\"evidence_key\": \"EXP-E1\", \"evidence_kind\": \"Function definition\", \"evidence_statement\": \"The exponential function model can be written as f(x)=a·b^x, where a is a positive initial coefficient and b is a positive growth or decay base.\", \"formula_text\": \"f(x)=a·b^x; a>0, b>0\", \"applicability_conditions\": [\"The problem explicitly gives an exponential function model.\", \"a and b are positive.\"], \"source_excerpt\": \"For an exponential function of the form f(x)=a·b^x, a determines the initial scale, and b determines the multiplicative rate of change for each one-unit increase in the input.\"}, {\"evidence_key\": \"EXP-E2\", \"evidence_kind\": \"Exponent operation rule\", \"evidence_statement\": \"When dividing powers with the same base, subtract the exponents; dividing the two function values can cancel the common coefficient a.\", \"formula_text\": \"(a·b^m)\u002F(a·b^n)=b^(m-n), a is not equal to 0\", \"applicability_conditions\": [\"The numerator and denominator use the same a and the same base b.\", \"The denominator is not zero.\"], \"source_excerpt\": \"When dividing powers with the same base, the base stays the same and the exponents are subtracted; common nonzero factors can be canceled.\"}, {\"evidence_key\": \"EXP-E3\", \"evidence_kind\": \"Calculation rule\", \"evidence_statement\": \"When b is positive and b^2=4, b can only be the positive square root 2.\", \"formula_text\": \"b^2=4 and b>0, so b=sqrt(4)=2\", \"applicability_conditions\": [\"b is positive.\", \"The square of b is known.\"], \"source_excerpt\": \"Under the positive number restriction, the only possible value whose square is 4 is 2, not the negative square root.\"}, {\"evidence_key\": \"EXP-E4\", \"evidence_kind\": \"Algebraic transformation rule\", \"evidence_statement\": \"After knowing f(1)=a·b, divide the function value by b to find the coefficient a.\", \"formula_text\": \"a=f(1)\u002Fb\", \"applicability_conditions\": [\"b is not equal to 0.\", \"f(1)=a·b holds.\"], \"source_excerpt\": \"Write the value of the exponential function at x=1 as a·b, then divide by the known base to obtain a.\"}, {\"evidence_key\": \"EXP-E5\", \"evidence_kind\": \"Exponential calculation rule\", \"evidence_statement\": \"When calculating the target function value, first compute the exponential power, then multiply by the coefficient.\", \"formula_text\": \"f(5)=a·b^5; 2^5=32\", \"applicability_conditions\": [\"The values of a and b have been determined.\", \"The target input is x=5.\"], \"source_excerpt\": \"Evaluating an exponential function follows the steps of first calculating b to the x-th power, then multiplying by coefficient a.\"}, {\"evidence_key\": \"EXP-D1\", \"evidence_kind\": \"Concept\", \"evidence_statement\": \"In an arithmetic sequence, adjacent terms maintain a fixed additive difference.\", \"formula_text\": \"u_n=u_1+(n-1)d\", \"applicability_conditions\": [\"The difference between adjacent terms remains constant.\"], \"source_excerpt\": \"The arithmetic model describes a sequence that changes by a fixed difference.\"}, {\"evidence_key\": \"EXP-D2\", \"evidence_kind\": \"Formula\", \"evidence_statement\": \"Logarithms can convert exponential relationships into power relationships.\", \"formula_text\": \"log_b(y)=x is equivalent to b^x=y\", \"applicability_conditions\": [\"b>0 and b is not equal to 1, y>0.\"], \"source_excerpt\": \"Logarithms are the inverse operation of exponentiation.\"}, {\"evidence_key\": \"EXP-D3\", \"evidence_kind\": \"Formula\", \"evidence_statement\": \"The roots of a quadratic equation can be determined by the discriminant and the quadratic formula.\", \"formula_text\": \"x=(-b±sqrt(b^2-4ac))\u002F(2a)\", \"applicability_conditions\": [\"The equation is quadratic.\"], \"source_excerpt\": \"The quadratic formula applies to quadratic equations in general form.\"}], \"gold_step_annotations\": [{\"step_key\": \"exp_s0\", \"step_order\": 0, \"reasoning_goal\": \"Write the two known function values as exponential expressions in terms of a and b.\", \"evidence_links\": [{\"evidence_key\": \"EXP-E1\", \"evidence_role\": \"Exponential function model and parameter conditions\", \"is_necessary\": true}], \"expected_conclusion\": \"From the model, obtain a·b=12 and a·b^3=48, and a and b are both positive.\", \"prerequisite_step_keys\": []}, {\"step_key\": \"exp_s1\", \"step_order\": 1, \"reasoning_goal\": \"Divide the two function values to cancel a and find the square of b.\", \"evidence_links\": [{\"evidence_key\": \"EXP-E2\", \"evidence_role\": \"Division of powers with the same base and cancellation of common factors\", \"is_necessary\": true}], \"expected_conclusion\": \"(a·b^3)\u002F(a·b)=48\u002F12, so b^2=4.\", \"prerequisite_step_keys\": [\"exp_s0\"]}, {\"step_key\": \"exp_s2\", \"step_order\": 2, \"reasoning_goal\": \"Use the condition that b is positive to determine the exponential base b.\", \"evidence_links\": [{\"evidence_key\": \"EXP-E3\", \"evidence_role\": \"Positive square root value\", \"is_necessary\": true}], \"expected_conclusion\": \"b=2.\", \"prerequisite_step_keys\": [\"exp_s1\"]}, {\"step_key\": \"exp_s3\", \"step_order\": 3, \"reasoning_goal\": \"Use f(1)=12 to find the coefficient a of the exponential function.\", \"evidence_links\": [{\"evidence_key\": \"EXP-E4\", \"evidence_role\": \"Solving for the coefficient from the function value\", \"is_necessary\": true}], \"expected_conclusion\": \"a·2=12, so a=6.\", \"prerequisite_step_keys\": [\"exp_s2\"]}, {\"step_key\": \"exp_s4\", \"step_order\": 4, \"reasoning_goal\": \"Substitute a and b into the target input x=5 and calculate the function value.\", \"evidence_links\": [{\"evidence_key\": \"EXP-E5\", \"evidence_role\": \"Exponential function evaluation and exponentiation\", \"is_necessary\": true}], \"expected_conclusion\": \"f(5)=6·2^5=6·32=192, so choose C.\", \"prerequisite_step_keys\": [\"exp_s3\"]}]}","[{\"step_key\": \"exp_s0\", \"step_order\": 0, \"step_goal\": \"Expand the two known function values according to the exponential function model.\", \"prerequisite_step_keys\": [], \"required_evidence_keys\": [\"EXP-E1\"], \"required_evidence_roles\": [\"Exponential function model and parameter conditions\"], \"expected_conclusion\": \"Obtain a·b=12 and a·b^3=48.\"}, {\"step_key\": \"exp_s1\", \"step_order\": 1, \"step_goal\": \"Cancel a by division and obtain b^2.\", \"prerequisite_step_keys\": [\"exp_s0\"], \"required_evidence_keys\": [\"EXP-E2\"], \"required_evidence_roles\": [\"Division of powers with the same base and cancellation of common factors\"], \"expected_conclusion\": \"Obtain b^2=4.\"}, {\"step_key\": \"exp_s2\", \"step_order\": 2, \"step_goal\": \"Use the positive number constraint to find b.\", \"prerequisite_step_keys\": [\"exp_s1\"], \"required_evidence_keys\": [\"EXP-E3\"], \"required_evidence_roles\": [\"Positive square root value\"], \"expected_conclusion\": \"Obtain b=2.\"}, {\"step_key\": \"exp_s3\", \"step_order\": 3, \"step_goal\": \"Find coefficient a from f(1).\", \"prerequisite_step_keys\": [\"exp_s2\"], \"required_evidence_keys\": [\"EXP-E4\"], \"required_evidence_roles\": [\"Solving for the coefficient from the function value\"], \"expected_conclusion\": \"Obtain a=6.\"}, {\"step_key\": \"exp_s4\", \"step_order\": 4, \"step_goal\": \"Calculate the exponential function value at x=5 and match the choices.\", \"prerequisite_step_keys\": [\"exp_s3\"], \"required_evidence_keys\": [\"EXP-E5\"], \"required_evidence_roles\": [\"Exponential function evaluation and exponentiation\"], \"expected_conclusion\": \"f(5)=192, the correct choice is C.\"}]","{\"must_retrieve_all_required\": true, \"relevant_evidence_keys\": [\"EXP-E1\", \"EXP-E2\", \"EXP-E3\", \"EXP-E4\", \"EXP-E5\"], \"distractor_evidence_keys\": [\"EXP-D1\", \"EXP-D2\", \"EXP-D3\"], \"coverage_unit\": \"Evaluate necessary evidence coverage by reasoning step, and require the entire evidence chain from parameter identification to target evaluation to be complete\"}",{"id":641,"relate_table":630,"relate_id":642,"file_size":572,"file_name":643,"path":8,"duration":572,"cate":483,"file_format":633,"audio_rate":8,"audio_channel":522,"audio_bit_depth":522,"quality":8,"annotation":644,"cate_name":635,"chain_summary":645,"source_record":646,"evidence_chain":647,"retrieval_evaluation_target":648},15062,1040496672,"样例_2.json","{\"chain_summary\": \"{\\\"step_count\\\": 4, \\\"unique_required_evidence_count\\\": 5, \\\"dependency_depth\\\": 4, \\\"chain_complete\\\": true, \\\"evidence_sufficiency_rule\\\": \\\"It must cover segment addition, the two leg relationships corresponding to the hypotenuse altitude, positive square root values, and the triangle perimeter formula; if only the hypotenuse altitude theorem is retrieved but segment partition or perimeter formula is missing, the complete solution chain cannot be supported.\\\"}\", \"source_record\": \"{\\\"question_text\\\": \\\"In right triangle ABC, ∠C=90°. The altitude CD is drawn from C to the hypotenuse AB, and D lies on segment AB. Given AD=9 and DB=16, what is the perimeter of triangle ABC?\\\", \\\"problem_category\\\": \\\"Right triangles, hypotenuse altitude, and segment relationships\\\", \\\"given_conditions\\\": [\\\"Triangle ABC is a right triangle, ∠C=90°.\\\", \\\"CD is perpendicular to AB, and D lies on segment AB.\\\", \\\"AD=9.\\\", \\\"DB=16.\\\", \\\"AC and BC are both positive lengths.\\\"], \\\"answer_choices\\\": [\\\"A. 54\\\", \\\"B. 60\\\", \\\"C. 64\\\", \\\"D. 70\\\"], \\\"correct_answer\\\": \\\"B\\\", \\\"candidate_evidence_library\\\": [{\\\"evidence_key\\\": \\\"GEO-E1\\\", \\\"evidence_kind\\\": \\\"Segment relationship\\\", \\\"evidence_statement\\\": \\\"When point D lies inside segment AB, the entire hypotenuse equals the sum of the two adjacent segments.\\\", \\\"formula_text\\\": \\\"AB=AD+DB\\\", \\\"applicability_conditions\\\": [\\\"D lies on segment AB.\\\", \\\"AD and DB are two adjacent parts of AB.\\\"], \\\"source_excerpt\\\": \\\"If point D lies on segment AB, then the length of AB equals the sum of the lengths of AD and DB.\\\"}, {\\\"evidence_key\\\": \\\"GEO-E2\\\", \\\"evidence_kind\\\": \\\"Theorem\\\", \\\"evidence_statement\\\": \\\"In a right triangle, after drawing the altitude from the right-angle vertex to the hypotenuse, the square of one leg equals the product of the hypotenuse and the projection segment of that leg on the hypotenuse.\\\", \\\"formula_text\\\": \\\"AC^2=AB×AD\\\", \\\"applicability_conditions\\\": [\\\"ABC has a right angle at C.\\\", \\\"CD is perpendicular to AB.\\\", \\\"D lies on AB.\\\"], \\\"source_excerpt\\\": \\\"The altitude to the hypotenuse divides the right triangle into two similar triangles, so AC^2=AB×AD.\\\"}, {\\\"evidence_key\\\": \\\"GEO-E3\\\", \\\"evidence_kind\\\": \\\"Theorem\\\", \\\"evidence_statement\\\": \\\"Similarly, from the altitude to the hypotenuse and similar triangle relationships, the square of the other leg equals the product of the hypotenuse and its projection segment.\\\", \\\"formula_text\\\": \\\"BC^2=AB×DB\\\", \\\"applicability_conditions\\\": [\\\"ABC has a right angle at C.\\\", \\\"CD is perpendicular to AB.\\\", \\\"D lies on AB.\\\"], \\\"source_excerpt\\\": \\\"In a right triangle, the hypotenuse projection corresponding to leg BC is DB, so BC^2=AB×DB.\\\"}, {\\\"evidence_key\\\": \\\"GEO-E4\\\", \\\"evidence_kind\\\": \\\"Calculation rule\\\", \\\"evidence_statement\\\": \\\"Lengths are positive, so from the square of a positive length, take the positive square root to obtain the corresponding segment length.\\\", \\\"formula_text\\\": \\\"If x>0 and x^2=k, then x=sqrt(k)\\\", \\\"applicability_conditions\\\": [\\\"x represents a segment length or another positive quantity.\\\", \\\"k is a nonnegative number.\\\"], \\\"source_excerpt\\\": \\\"Geometric lengths cannot be negative, so the positive square root should be used when finding segment lengths.\\\"}, {\\\"evidence_key\\\": \\\"GEO-E5\\\", \\\"evidence_kind\\\": \\\"Formula\\\", \\\"evidence_statement\\\": \\\"The perimeter of a triangle equals the sum of the lengths of its three sides.\\\", \\\"formula_text\\\": \\\"P=AB+AC+BC\\\", \\\"applicability_conditions\\\": [\\\"AB, AC, and BC are the three sides of the same triangle.\\\", \\\"All lengths use the same unit.\\\"], \\\"source_excerpt\\\": \\\"The perimeter of any triangle is the sum of the lengths of its three sides.\\\"}, {\\\"evidence_key\\\": \\\"GEO-D1\\\", \\\"evidence_kind\\\": \\\"Formula\\\", \\\"evidence_statement\\\": \\\"The area of a triangle can be calculated as base times height divided by 2.\\\", \\\"formula_text\\\": \\\"K=base×height\u002F2\\\", \\\"applicability_conditions\\\": [\\\"A base and its corresponding height are known.\\\"], \\\"source_excerpt\\\": \\\"The area of a triangle equals half the product of a base and its corresponding height.\\\"}, {\\\"evidence_key\\\": \\\"GEO-D2\\\", \\\"evidence_kind\\\": \\\"Concept\\\", \\\"evidence_statement\\\": \\\"Similar triangles have equal corresponding angles and proportional corresponding sides.\\\", \\\"formula_text\\\": \\\"AB\u002FAC=ratio of corresponding sides\\\", \\\"applicability_conditions\\\": [\\\"The two triangles have equal corresponding angles.\\\"], \\\"source_excerpt\\\": \\\"The ratios of corresponding sides of similar triangles are equal.\\\"}, {\\\"evidence_key\\\": \\\"GEO-D3\\\", \\\"evidence_kind\\\": \\\"Formula\\\", \\\"evidence_statement\\\": \\\"The circumference of a circle equals the diameter times pi.\\\", \\\"formula_text\\\": \\\"C=πd\\\", \\\"applicability_conditions\\\": [\\\"The figure is a circle and d is the diameter.\\\"], \\\"source_excerpt\\\": \\\"The circumference formula of a circle is pi times the diameter.\\\"}], \\\"gold_step_annotations\\\": [{\\\"step_key\\\": \\\"geo_s0\\\", \\\"step_order\\\": 0, \\\"reasoning_goal\\\": \\\"Use the fact that D divides the hypotenuse into two segments to find the hypotenuse AB.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"GEO-E1\\\", \\\"evidence_role\\\": \\\"Segment partition addition rule\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"AB=AD+DB=9+16=25.\\\", \\\"prerequisite_step_keys\\\": []}, {\\\"step_key\\\": \\\"geo_s1\\\", \\\"step_order\\\": 1, \\\"reasoning_goal\\\": \\\"Use the hypotenuse altitude theorem and the positive length condition to find leg AC.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"GEO-E2\\\", \\\"evidence_role\\\": \\\"Relationship between a leg and its projected segment\\\", \\\"is_necessary\\\": true}, {\\\"evidence_key\\\": \\\"GEO-E4\\\", \\\"evidence_role\\\": \\\"Positive square root value rule\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"AC^2=25×9=225; since AC is positive, AC=15.\\\", \\\"prerequisite_step_keys\\\": [\\\"geo_s0\\\"]}, {\\\"step_key\\\": \\\"geo_s2\\\", \\\"step_order\\\": 2, \\\"reasoning_goal\\\": \\\"Use the projection relationship of the other leg to find BC.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"GEO-E3\\\", \\\"evidence_role\\\": \\\"Relationship between the other leg and its projected segment\\\", \\\"is_necessary\\\": true}, {\\\"evidence_key\\\": \\\"GEO-E4\\\", \\\"evidence_role\\\": \\\"Positive square root value rule\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"BC^2=25×16=400; since BC is positive, BC=20.\\\", \\\"prerequisite_step_keys\\\": [\\\"geo_s0\\\"]}, {\\\"step_key\\\": \\\"geo_s3\\\", \\\"step_order\\\": 3, \\\"reasoning_goal\\\": \\\"Add the three sides to get the perimeter of triangle ABC.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"GEO-E5\\\", \\\"evidence_role\\\": \\\"Triangle perimeter formula\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"P=25+15+20=60, so choose B.\\\", \\\"prerequisite_step_keys\\\": [\\\"geo_s1\\\", \\\"geo_s2\\\"]}]}\", \"evidence_chain\": \"[{\\\"step_key\\\": \\\"geo_s0\\\", \\\"step_order\\\": 0, \\\"step_goal\\\": \\\"Find the hypotenuse AB from AD and DB.\\\", \\\"prerequisite_step_keys\\\": [], \\\"required_evidence_keys\\\": [\\\"GEO-E1\\\"], \\\"required_evidence_roles\\\": [\\\"Segment partition addition rule\\\"], \\\"expected_conclusion\\\": \\\"AB=25.\\\"}, {\\\"step_key\\\": \\\"geo_s1\\\", \\\"step_order\\\": 1, \\\"step_goal\\\": \\\"Find leg AC using the hypotenuse altitude theorem.\\\", \\\"prerequisite_step_keys\\\": [\\\"geo_s0\\\"], \\\"required_evidence_keys\\\": [\\\"GEO-E2\\\", \\\"GEO-E4\\\"], \\\"required_evidence_roles\\\": [\\\"Relationship between a leg and its projected segment\\\", \\\"Positive square root value rule\\\"], \\\"expected_conclusion\\\": \\\"AC=15.\\\"}, {\\\"step_key\\\": \\\"geo_s2\\\", \\\"step_order\\\": 2, \\\"step_goal\\\": \\\"Find leg BC from the other projection relationship.\\\", \\\"prerequisite_step_keys\\\": [\\\"geo_s0\\\"], \\\"required_evidence_keys\\\": [\\\"GEO-E3\\\", \\\"GEO-E4\\\"], \\\"required_evidence_roles\\\": [\\\"Relationship between the other leg and its projected segment\\\", \\\"Positive square root value rule\\\"], \\\"expected_conclusion\\\": \\\"BC=20.\\\"}, {\\\"step_key\\\": \\\"geo_s3\\\", \\\"step_order\\\": 3, \\\"step_goal\\\": \\\"Add the three sides to get the perimeter.\\\", \\\"prerequisite_step_keys\\\": [\\\"geo_s1\\\", \\\"geo_s2\\\"], \\\"required_evidence_keys\\\": [\\\"GEO-E5\\\"], \\\"required_evidence_roles\\\": [\\\"Triangle perimeter formula\\\"], \\\"expected_conclusion\\\": \\\"The perimeter is 60, so the correct choice is B.\\\"}]\", \"retrieval_evaluation_target\": \"{\\\"must_retrieve_all_required\\\": true, \\\"relevant_evidence_keys\\\": [\\\"GEO-E1\\\", \\\"GEO-E2\\\", \\\"GEO-E3\\\", \\\"GEO-E4\\\", \\\"GEO-E5\\\"], \\\"distractor_evidence_keys\\\": [\\\"GEO-D1\\\", \\\"GEO-D2\\\", \\\"GEO-D3\\\"], \\\"coverage_unit\\\": \\\"Step-level necessary evidence and complete evidence-chain coverage of dependency branches\\\"}\"}","{\"step_count\": 4, \"unique_required_evidence_count\": 5, \"dependency_depth\": 4, \"chain_complete\": true, \"evidence_sufficiency_rule\": \"It must cover segment addition, the two leg relationships corresponding to the hypotenuse altitude, positive square root values, and the triangle perimeter formula; if only the hypotenuse altitude theorem is retrieved but segment partition or perimeter formula is missing, the complete solution chain cannot be supported.\"}","{\"question_text\": \"In right triangle ABC, ∠C=90°. The altitude CD is drawn from C to the hypotenuse AB, and D lies on segment AB. Given AD=9 and DB=16, what is the perimeter of triangle ABC?\", \"problem_category\": \"Right triangles, hypotenuse altitude, and segment relationships\", \"given_conditions\": [\"Triangle ABC is a right triangle, ∠C=90°.\", \"CD is perpendicular to AB, and D lies on segment AB.\", \"AD=9.\", \"DB=16.\", \"AC and BC are both positive lengths.\"], \"answer_choices\": [\"A. 54\", \"B. 60\", \"C. 64\", \"D. 70\"], \"correct_answer\": \"B\", \"candidate_evidence_library\": [{\"evidence_key\": \"GEO-E1\", \"evidence_kind\": \"Segment relationship\", \"evidence_statement\": \"When point D lies inside segment AB, the entire hypotenuse equals the sum of the two adjacent segments.\", \"formula_text\": \"AB=AD+DB\", \"applicability_conditions\": [\"D lies on segment AB.\", \"AD and DB are two adjacent parts of AB.\"], \"source_excerpt\": \"If point D lies on segment AB, then the length of AB equals the sum of the lengths of AD and DB.\"}, {\"evidence_key\": \"GEO-E2\", \"evidence_kind\": \"Theorem\", \"evidence_statement\": \"In a right triangle, after drawing the altitude from the right-angle vertex to the hypotenuse, the square of one leg equals the product of the hypotenuse and the projection segment of that leg on the hypotenuse.\", \"formula_text\": \"AC^2=AB×AD\", \"applicability_conditions\": [\"ABC has a right angle at C.\", \"CD is perpendicular to AB.\", \"D lies on AB.\"], \"source_excerpt\": \"The altitude to the hypotenuse divides the right triangle into two similar triangles, so AC^2=AB×AD.\"}, {\"evidence_key\": \"GEO-E3\", \"evidence_kind\": \"Theorem\", \"evidence_statement\": \"Similarly, from the altitude to the hypotenuse and similar triangle relationships, the square of the other leg equals the product of the hypotenuse and its projection segment.\", \"formula_text\": \"BC^2=AB×DB\", \"applicability_conditions\": [\"ABC has a right angle at C.\", \"CD is perpendicular to AB.\", \"D lies on AB.\"], \"source_excerpt\": \"In a right triangle, the hypotenuse projection corresponding to leg BC is DB, so BC^2=AB×DB.\"}, {\"evidence_key\": \"GEO-E4\", \"evidence_kind\": \"Calculation rule\", \"evidence_statement\": \"Lengths are positive, so from the square of a positive length, take the positive square root to obtain the corresponding segment length.\", \"formula_text\": \"If x>0 and x^2=k, then x=sqrt(k)\", \"applicability_conditions\": [\"x represents a segment length or another positive quantity.\", \"k is a nonnegative number.\"], \"source_excerpt\": \"Geometric lengths cannot be negative, so the positive square root should be used when finding segment lengths.\"}, {\"evidence_key\": \"GEO-E5\", \"evidence_kind\": \"Formula\", \"evidence_statement\": \"The perimeter of a triangle equals the sum of the lengths of its three sides.\", \"formula_text\": \"P=AB+AC+BC\", \"applicability_conditions\": [\"AB, AC, and BC are the three sides of the same triangle.\", \"All lengths use the same unit.\"], \"source_excerpt\": \"The perimeter of any triangle is the sum of the lengths of its three sides.\"}, {\"evidence_key\": \"GEO-D1\", \"evidence_kind\": \"Formula\", \"evidence_statement\": \"The area of a triangle can be calculated as base times height divided by 2.\", \"formula_text\": \"K=base×height\u002F2\", \"applicability_conditions\": [\"A base and its corresponding height are known.\"], \"source_excerpt\": \"The area of a triangle equals half the product of a base and its corresponding height.\"}, {\"evidence_key\": \"GEO-D2\", \"evidence_kind\": \"Concept\", \"evidence_statement\": \"Similar triangles have equal corresponding angles and proportional corresponding sides.\", \"formula_text\": \"AB\u002FAC=ratio of corresponding sides\", \"applicability_conditions\": [\"The two triangles have equal corresponding angles.\"], \"source_excerpt\": \"The ratios of corresponding sides of similar triangles are equal.\"}, {\"evidence_key\": \"GEO-D3\", \"evidence_kind\": \"Formula\", \"evidence_statement\": \"The circumference of a circle equals the diameter times pi.\", \"formula_text\": \"C=πd\", \"applicability_conditions\": [\"The figure is a circle and d is the diameter.\"], \"source_excerpt\": \"The circumference formula of a circle is pi times the diameter.\"}], \"gold_step_annotations\": [{\"step_key\": \"geo_s0\", \"step_order\": 0, \"reasoning_goal\": \"Use the fact that D divides the hypotenuse into two segments to find the hypotenuse AB.\", \"evidence_links\": [{\"evidence_key\": \"GEO-E1\", \"evidence_role\": \"Segment partition addition rule\", \"is_necessary\": true}], \"expected_conclusion\": \"AB=AD+DB=9+16=25.\", \"prerequisite_step_keys\": []}, {\"step_key\": \"geo_s1\", \"step_order\": 1, \"reasoning_goal\": \"Use the hypotenuse altitude theorem and the positive length condition to find leg AC.\", \"evidence_links\": [{\"evidence_key\": \"GEO-E2\", \"evidence_role\": \"Relationship between a leg and its projected segment\", \"is_necessary\": true}, {\"evidence_key\": \"GEO-E4\", \"evidence_role\": \"Positive square root value rule\", \"is_necessary\": true}], \"expected_conclusion\": \"AC^2=25×9=225; since AC is positive, AC=15.\", \"prerequisite_step_keys\": [\"geo_s0\"]}, {\"step_key\": \"geo_s2\", \"step_order\": 2, \"reasoning_goal\": \"Use the projection relationship of the other leg to find BC.\", \"evidence_links\": [{\"evidence_key\": \"GEO-E3\", \"evidence_role\": \"Relationship between the other leg and its projected segment\", \"is_necessary\": true}, {\"evidence_key\": \"GEO-E4\", \"evidence_role\": \"Positive square root value rule\", \"is_necessary\": true}], \"expected_conclusion\": \"BC^2=25×16=400; since BC is positive, BC=20.\", \"prerequisite_step_keys\": [\"geo_s0\"]}, {\"step_key\": \"geo_s3\", \"step_order\": 3, \"reasoning_goal\": \"Add the three sides to get the perimeter of triangle ABC.\", \"evidence_links\": [{\"evidence_key\": \"GEO-E5\", \"evidence_role\": \"Triangle perimeter formula\", \"is_necessary\": true}], \"expected_conclusion\": \"P=25+15+20=60, so choose B.\", \"prerequisite_step_keys\": [\"geo_s1\", \"geo_s2\"]}]}","[{\"step_key\": \"geo_s0\", \"step_order\": 0, \"step_goal\": \"Find the hypotenuse AB from AD and DB.\", \"prerequisite_step_keys\": [], \"required_evidence_keys\": [\"GEO-E1\"], \"required_evidence_roles\": [\"Segment partition addition rule\"], \"expected_conclusion\": \"AB=25.\"}, {\"step_key\": \"geo_s1\", \"step_order\": 1, \"step_goal\": \"Find leg AC using the hypotenuse altitude theorem.\", \"prerequisite_step_keys\": [\"geo_s0\"], \"required_evidence_keys\": [\"GEO-E2\", \"GEO-E4\"], \"required_evidence_roles\": [\"Relationship between a leg and its projected segment\", \"Positive square root value rule\"], \"expected_conclusion\": \"AC=15.\"}, {\"step_key\": \"geo_s2\", \"step_order\": 2, \"step_goal\": \"Find leg BC from the other projection relationship.\", \"prerequisite_step_keys\": [\"geo_s0\"], \"required_evidence_keys\": [\"GEO-E3\", \"GEO-E4\"], \"required_evidence_roles\": [\"Relationship between the other leg and its projected segment\", \"Positive square root value rule\"], \"expected_conclusion\": \"BC=20.\"}, {\"step_key\": \"geo_s3\", \"step_order\": 3, \"step_goal\": \"Add the three sides to get the perimeter.\", \"prerequisite_step_keys\": [\"geo_s1\", \"geo_s2\"], \"required_evidence_keys\": [\"GEO-E5\"], \"required_evidence_roles\": [\"Triangle perimeter formula\"], \"expected_conclusion\": \"The perimeter is 60, so the correct choice is B.\"}]","{\"must_retrieve_all_required\": true, \"relevant_evidence_keys\": [\"GEO-E1\", \"GEO-E2\", \"GEO-E3\", \"GEO-E4\", \"GEO-E5\"], \"distractor_evidence_keys\": [\"GEO-D1\", \"GEO-D2\", \"GEO-D3\"], \"coverage_unit\": \"Step-level necessary evidence and complete evidence-chain coverage of dependency branches\"}",{"id":650,"relate_table":630,"relate_id":651,"file_size":572,"file_name":652,"path":8,"duration":572,"cate":483,"file_format":633,"audio_rate":8,"audio_channel":522,"audio_bit_depth":522,"quality":8,"annotation":653,"cate_name":635,"chain_summary":654,"source_record":655,"evidence_chain":656,"retrieval_evaluation_target":657},15061,193875682,"样例_1.json","{\"chain_summary\": \"{\\\"step_count\\\": 4, \\\"unique_required_evidence_count\\\": 6, \\\"dependency_depth\\\": 4, \\\"chain_complete\\\": true, \\\"evidence_sufficiency_rule\\\": \\\"Only when LIN-E1 through LIN-E6 are all covered and the evidence is applicable to the corresponding steps can modeling, substitution, solving, and verification be completed; if only linear equation formulas are retrieved and variable definitions, substitution rules, or verification rules are missing, the evidence chain is incomplete.\\\"}\", \"source_record\": \"{\\\"question_text\\\": \\\"A school sold adult tickets and student tickets. Buying 2 adult tickets and 3 student tickets costs $33 total, and buying 4 adult tickets and 1 student ticket costs $31 total. If the price of an adult ticket is a dollars and the price of a student ticket is s dollars, what is the price of an adult ticket?\\\", \\\"problem_category\\\": \\\"Systems of linear equations and modeling real-world situations\\\", \\\"given_conditions\\\": [\\\"The adult ticket price is a dollars and the student ticket price is s dollars.\\\", \\\"The total price of 2 adult tickets and 3 student tickets is $33.\\\", \\\"The total price of 4 adult tickets and 1 student ticket is $31.\\\", \\\"a and s are both positive.\\\"], \\\"answer_choices\\\": [\\\"A. $6\\\", \\\"B. $7\\\", \\\"C. $8\\\", \\\"D. $9\\\"], \\\"correct_answer\\\": \\\"A\\\", \\\"candidate_evidence_library\\\": [{\\\"evidence_key\\\": \\\"LIN-E1\\\", \\\"evidence_kind\\\": \\\"Conceptual definition\\\", \\\"evidence_statement\\\": \\\"Set the unknown prices in the real-world situation as variables, and keep the variables consistent with the units in the problem.\\\", \\\"formula_text\\\": \\\"a = adult ticket price, s = student ticket price\\\", \\\"applicability_conditions\\\": [\\\"The problem contains unknown quantities to be found.\\\", \\\"The variables can represent the unit price or value of the same type of quantity.\\\"], \\\"source_excerpt\\\": \\\"When modeling, first define variables for the unknown quantities, then set up equations based on the quantitative relationships.\\\"}, {\\\"evidence_key\\\": \\\"LIN-E2\\\", \\\"evidence_kind\\\": \\\"Modeling rule\\\", \\\"evidence_statement\\\": \\\"The total price equals the sum of the unit price times quantity for each type of item, so the two ticket purchase conditions respectively form two linear equations.\\\", \\\"formula_text\\\": \\\"2a+3s=33; 4a+s=31\\\", \\\"applicability_conditions\\\": [\\\"The unit price of each ticket type is fixed in the problem.\\\", \\\"The total price is obtained by multiplying quantity by unit price and then adding.\\\"], \\\"source_excerpt\\\": \\\"If there are two types of items with quantities m and n and unit prices x and y, then the total price relationship is mx+ny=total price.\\\"}, {\\\"evidence_key\\\": \\\"LIN-E3\\\", \\\"evidence_kind\\\": \\\"Problem-solving rule\\\", \\\"evidence_statement\\\": \\\"By rearranging a linear equation and simplifying coefficients, one unknown can be expressed as an expression in terms of the other unknown.\\\", \\\"formula_text\\\": \\\"4a+s=31 can be transformed into s=31-4a\\\", \\\"applicability_conditions\\\": [\\\"The coefficient of the variable in the equation is nonzero.\\\", \\\"Perform the same operation on both sides of the equation.\\\"], \\\"source_excerpt\\\": \\\"When solving a linear equation, keep the term containing the target variable on one side, move the remaining terms to the other side, and simplify.\\\"}, {\\\"evidence_key\\\": \\\"LIN-E4\\\", \\\"evidence_kind\\\": \\\"Problem-solving rule\\\", \\\"evidence_statement\\\": \\\"The substitution method substitutes the variable expression obtained from one equation into the other equation to reduce the number of unknowns.\\\", \\\"formula_text\\\": \\\"If s=31-4a, then 2a+3s=33 can be transformed into 2a+3(31-4a)=33\\\", \\\"applicability_conditions\\\": [\\\"The substituted expression is equivalent to the original variable.\\\", \\\"After substitution, the same system of equations is used.\\\"], \\\"source_excerpt\\\": \\\"In a system of linear equations, first solve for one variable, then substitute its expression into the other equation to obtain a single-variable equation.\\\"}, {\\\"evidence_key\\\": \\\"LIN-E5\\\", \\\"evidence_kind\\\": \\\"Calculation rule\\\", \\\"evidence_statement\\\": \\\"Linear equations can be solved by combining like terms and performing the same addition, subtraction, multiplication, or division operations on both sides of the equation.\\\", \\\"formula_text\\\": \\\"2a+93-12a=33; -10a=-60; a=6\\\", \\\"applicability_conditions\\\": [\\\"The operations on both sides of the equation remain equivalent.\\\", \\\"Only combine like terms; do not change the exponents of variables.\\\"], \\\"source_excerpt\\\": \\\"After simplifying the single-variable linear equation, inverse operations can be used to find the unique value of the variable.\\\"}, {\\\"evidence_key\\\": \\\"LIN-E6\\\", \\\"evidence_kind\\\": \\\"Verification rule\\\", \\\"evidence_statement\\\": \\\"Substitute the obtained variable values back into the original equations. If all original equations hold, then the solution satisfies all quantitative conditions of the problem.\\\", \\\"formula_text\\\": \\\"2(6)+3(7)=33; 4(6)+7=31\\\", \\\"applicability_conditions\\\": [\\\"The original equations must be used for checking.\\\", \\\"Each equation should yield a correct equality.\\\"], \\\"source_excerpt\\\": \\\"After solving the system of equations, substitute the result back into the original equations to check and rule out calculation errors.\\\"}, {\\\"evidence_key\\\": \\\"LIN-D1\\\", \\\"evidence_kind\\\": \\\"Concept\\\", \\\"evidence_statement\\\": \\\"Slope represents the ratio of the change in the vertical coordinate to the change in the horizontal coordinate of a line.\\\", \\\"formula_text\\\": \\\"m=(y2-y1)\u002F(x2-x1)\\\", \\\"applicability_conditions\\\": [\\\"The problem involves a line in the coordinate plane.\\\"], \\\"source_excerpt\\\": \\\"Slope is used to describe the steepness of a line.\\\"}, {\\\"evidence_key\\\": \\\"LIN-D2\\\", \\\"evidence_kind\\\": \\\"Formula\\\", \\\"evidence_statement\\\": \\\"Quadratic equations can be solved using the quadratic formula.\\\", \\\"formula_text\\\": \\\"x=(-b±sqrt(b^2-4ac))\u002F(2a)\\\", \\\"applicability_conditions\\\": [\\\"The equation is ax^2+bx+c=0 and a is not equal to 0.\\\"], \\\"source_excerpt\\\": \\\"The roots of a quadratic equation can be determined by the discriminant and the quadratic formula.\\\"}, {\\\"evidence_key\\\": \\\"LIN-D3\\\", \\\"evidence_kind\\\": \\\"Concept\\\", \\\"evidence_statement\\\": \\\"Unit rate represents the quantity corresponding to each unit.\\\", \\\"formula_text\\\": \\\"Unit rate = total amount \u002F number of units\\\", \\\"applicability_conditions\\\": [\\\"The problem requires comparing unit quantities or unit prices.\\\"], \\\"source_excerpt\\\": \\\"Unit rate problems usually require dividing the total amount by the corresponding quantity.\\\"}], \\\"gold_step_annotations\\\": [{\\\"step_key\\\": \\\"lin_s0\\\", \\\"step_order\\\": 0, \\\"reasoning_goal\\\": \\\"Define unknown prices and translate the two ticket purchase conditions into a system of linear equations.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"LIN-E1\\\", \\\"evidence_role\\\": \\\"Definition of unknown quantities\\\", \\\"is_necessary\\\": true}, {\\\"evidence_key\\\": \\\"LIN-E2\\\", \\\"evidence_role\\\": \\\"Modeling of quantitative relationships\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"Obtain the system of equations 2a+3s=33 and 4a+s=31.\\\", \\\"prerequisite_step_keys\\\": []}, {\\\"step_key\\\": \\\"lin_s1\\\", \\\"step_order\\\": 1, \\\"reasoning_goal\\\": \\\"Isolate the student ticket price s from the second equation.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"LIN-E3\\\", \\\"evidence_role\\\": \\\"Rearranging and transforming linear equations\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"From 4a+s=31, obtain s=31-4a.\\\", \\\"prerequisite_step_keys\\\": [\\\"lin_s0\\\"]}, {\\\"step_key\\\": \\\"lin_s2\\\", \\\"step_order\\\": 2, \\\"reasoning_goal\\\": \\\"Substitute the expression for s into the first equation and find the adult ticket price a.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"LIN-E4\\\", \\\"evidence_role\\\": \\\"Substitution method\\\", \\\"is_necessary\\\": true}, {\\\"evidence_key\\\": \\\"LIN-E5\\\", \\\"evidence_role\\\": \\\"Combining like terms and inverse operations\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"2a+3(31-4a)=33, simplifying gives -10a=-60, so a=6.\\\", \\\"prerequisite_step_keys\\\": [\\\"lin_s1\\\"]}, {\\\"step_key\\\": \\\"lin_s3\\\", \\\"step_order\\\": 3, \\\"reasoning_goal\\\": \\\"Find the other variable and verify whether the solution satisfies the original ticket purchase conditions, thereby choosing the answer.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"LIN-E6\\\", \\\"evidence_role\\\": \\\"Verification by substituting back into original equations\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"s=31-4(6)=7, and both original equations hold, so the adult ticket price is $6, choose A.\\\", \\\"prerequisite_step_keys\\\": [\\\"lin_s2\\\"]}]}\", \"evidence_chain\": \"[{\\\"step_key\\\": \\\"lin_s0\\\", \\\"step_order\\\": 0, \\\"step_goal\\\": \\\"Define unknown prices and set up a system of two linear equations in two variables.\\\", \\\"prerequisite_step_keys\\\": [], \\\"required_evidence_keys\\\": [\\\"LIN-E1\\\", \\\"LIN-E2\\\"], \\\"required_evidence_roles\\\": [\\\"Definition of unknown quantities\\\", \\\"Modeling of quantitative relationships\\\"], \\\"expected_conclusion\\\": \\\"Obtain 2a+3s=33 and 4a+s=31.\\\"}, {\\\"step_key\\\": \\\"lin_s1\\\", \\\"step_order\\\": 1, \\\"step_goal\\\": \\\"Isolate s from the second linear equation.\\\", \\\"prerequisite_step_keys\\\": [\\\"lin_s0\\\"], \\\"required_evidence_keys\\\": [\\\"LIN-E3\\\"], \\\"required_evidence_roles\\\": [\\\"Rearranging and transforming linear equations\\\"], \\\"expected_conclusion\\\": \\\"Obtain s=31-4a.\\\"}, {\\\"step_key\\\": \\\"lin_s2\\\", \\\"step_order\\\": 2, \\\"step_goal\\\": \\\"Substitute and simplify the single-variable equation to solve for a.\\\", \\\"prerequisite_step_keys\\\": [\\\"lin_s1\\\"], \\\"required_evidence_keys\\\": [\\\"LIN-E4\\\", \\\"LIN-E5\\\"], \\\"required_evidence_roles\\\": [\\\"Substitution method\\\", \\\"Combining like terms and inverse operations\\\"], \\\"expected_conclusion\\\": \\\"Obtain a=6.\\\"}, {\\\"step_key\\\": \\\"lin_s3\\\", \\\"step_order\\\": 3, \\\"step_goal\\\": \\\"Find s and substitute the result back into the original equations to verify.\\\", \\\"prerequisite_step_keys\\\": [\\\"lin_s2\\\"], \\\"required_evidence_keys\\\": [\\\"LIN-E6\\\"], \\\"required_evidence_roles\\\": [\\\"Verification by substituting back into original equations\\\"], \\\"expected_conclusion\\\": \\\"s=7 and both equations hold, so the correct choice is A.\\\"}]\", \"retrieval_evaluation_target\": \"{\\\"must_retrieve_all_required\\\": true, \\\"relevant_evidence_keys\\\": [\\\"LIN-E1\\\", \\\"LIN-E2\\\", \\\"LIN-E3\\\", \\\"LIN-E4\\\", \\\"LIN-E5\\\", \\\"LIN-E6\\\"], \\\"distractor_evidence_keys\\\": [\\\"LIN-D1\\\", \\\"LIN-D2\\\", \\\"LIN-D3\\\"], \\\"coverage_unit\\\": \\\"Step-level necessary evidence and complete coverage of the entire evidence chain\\\"}\"}","{\"step_count\": 4, \"unique_required_evidence_count\": 6, \"dependency_depth\": 4, \"chain_complete\": true, \"evidence_sufficiency_rule\": \"Only when LIN-E1 through LIN-E6 are all covered and the evidence is applicable to the corresponding steps can modeling, substitution, solving, and verification be completed; if only linear equation formulas are retrieved and variable definitions, substitution rules, or verification rules are missing, the evidence chain is incomplete.\"}","{\"question_text\": \"A school sold adult tickets and student tickets. Buying 2 adult tickets and 3 student tickets costs $33 total, and buying 4 adult tickets and 1 student ticket costs $31 total. If the price of an adult ticket is a dollars and the price of a student ticket is s dollars, what is the price of an adult ticket?\", \"problem_category\": \"Systems of linear equations and modeling real-world situations\", \"given_conditions\": [\"The adult ticket price is a dollars and the student ticket price is s dollars.\", \"The total price of 2 adult tickets and 3 student tickets is $33.\", \"The total price of 4 adult tickets and 1 student ticket is $31.\", \"a and s are both positive.\"], \"answer_choices\": [\"A. $6\", \"B. $7\", \"C. $8\", \"D. $9\"], \"correct_answer\": \"A\", \"candidate_evidence_library\": [{\"evidence_key\": \"LIN-E1\", \"evidence_kind\": \"Conceptual definition\", \"evidence_statement\": \"Set the unknown prices in the real-world situation as variables, and keep the variables consistent with the units in the problem.\", \"formula_text\": \"a = adult ticket price, s = student ticket price\", \"applicability_conditions\": [\"The problem contains unknown quantities to be found.\", \"The variables can represent the unit price or value of the same type of quantity.\"], \"source_excerpt\": \"When modeling, first define variables for the unknown quantities, then set up equations based on the quantitative relationships.\"}, {\"evidence_key\": \"LIN-E2\", \"evidence_kind\": \"Modeling rule\", \"evidence_statement\": \"The total price equals the sum of the unit price times quantity for each type of item, so the two ticket purchase conditions respectively form two linear equations.\", \"formula_text\": \"2a+3s=33; 4a+s=31\", \"applicability_conditions\": [\"The unit price of each ticket type is fixed in the problem.\", \"The total price is obtained by multiplying quantity by unit price and then adding.\"], \"source_excerpt\": \"If there are two types of items with quantities m and n and unit prices x and y, then the total price relationship is mx+ny=total price.\"}, {\"evidence_key\": \"LIN-E3\", \"evidence_kind\": \"Problem-solving rule\", \"evidence_statement\": \"By rearranging a linear equation and simplifying coefficients, one unknown can be expressed as an expression in terms of the other unknown.\", \"formula_text\": \"4a+s=31 can be transformed into s=31-4a\", \"applicability_conditions\": [\"The coefficient of the variable in the equation is nonzero.\", \"Perform the same operation on both sides of the equation.\"], \"source_excerpt\": \"When solving a linear equation, keep the term containing the target variable on one side, move the remaining terms to the other side, and simplify.\"}, {\"evidence_key\": \"LIN-E4\", \"evidence_kind\": \"Problem-solving rule\", \"evidence_statement\": \"The substitution method substitutes the variable expression obtained from one equation into the other equation to reduce the number of unknowns.\", \"formula_text\": \"If s=31-4a, then 2a+3s=33 can be transformed into 2a+3(31-4a)=33\", \"applicability_conditions\": [\"The substituted expression is equivalent to the original variable.\", \"After substitution, the same system of equations is used.\"], \"source_excerpt\": \"In a system of linear equations, first solve for one variable, then substitute its expression into the other equation to obtain a single-variable equation.\"}, {\"evidence_key\": \"LIN-E5\", \"evidence_kind\": \"Calculation rule\", \"evidence_statement\": \"Linear equations can be solved by combining like terms and performing the same addition, subtraction, multiplication, or division operations on both sides of the equation.\", \"formula_text\": \"2a+93-12a=33; -10a=-60; a=6\", \"applicability_conditions\": [\"The operations on both sides of the equation remain equivalent.\", \"Only combine like terms; do not change the exponents of variables.\"], \"source_excerpt\": \"After simplifying the single-variable linear equation, inverse operations can be used to find the unique value of the variable.\"}, {\"evidence_key\": \"LIN-E6\", \"evidence_kind\": \"Verification rule\", \"evidence_statement\": \"Substitute the obtained variable values back into the original equations. If all original equations hold, then the solution satisfies all quantitative conditions of the problem.\", \"formula_text\": \"2(6)+3(7)=33; 4(6)+7=31\", \"applicability_conditions\": [\"The original equations must be used for checking.\", \"Each equation should yield a correct equality.\"], \"source_excerpt\": \"After solving the system of equations, substitute the result back into the original equations to check and rule out calculation errors.\"}, {\"evidence_key\": \"LIN-D1\", \"evidence_kind\": \"Concept\", \"evidence_statement\": \"Slope represents the ratio of the change in the vertical coordinate to the change in the horizontal coordinate of a line.\", \"formula_text\": \"m=(y2-y1)\u002F(x2-x1)\", \"applicability_conditions\": [\"The problem involves a line in the coordinate plane.\"], \"source_excerpt\": \"Slope is used to describe the steepness of a line.\"}, {\"evidence_key\": \"LIN-D2\", \"evidence_kind\": \"Formula\", \"evidence_statement\": \"Quadratic equations can be solved using the quadratic formula.\", \"formula_text\": \"x=(-b±sqrt(b^2-4ac))\u002F(2a)\", \"applicability_conditions\": [\"The equation is ax^2+bx+c=0 and a is not equal to 0.\"], \"source_excerpt\": \"The roots of a quadratic equation can be determined by the discriminant and the quadratic formula.\"}, {\"evidence_key\": \"LIN-D3\", \"evidence_kind\": \"Concept\", \"evidence_statement\": \"Unit rate represents the quantity corresponding to each unit.\", \"formula_text\": \"Unit rate = total amount \u002F number of units\", \"applicability_conditions\": [\"The problem requires comparing unit quantities or unit prices.\"], \"source_excerpt\": \"Unit rate problems usually require dividing the total amount by the corresponding quantity.\"}], \"gold_step_annotations\": [{\"step_key\": \"lin_s0\", \"step_order\": 0, \"reasoning_goal\": \"Define unknown prices and translate the two ticket purchase conditions into a system of linear equations.\", \"evidence_links\": [{\"evidence_key\": \"LIN-E1\", \"evidence_role\": \"Definition of unknown quantities\", \"is_necessary\": true}, {\"evidence_key\": \"LIN-E2\", \"evidence_role\": \"Modeling of quantitative relationships\", \"is_necessary\": true}], \"expected_conclusion\": \"Obtain the system of equations 2a+3s=33 and 4a+s=31.\", \"prerequisite_step_keys\": []}, {\"step_key\": \"lin_s1\", \"step_order\": 1, \"reasoning_goal\": \"Isolate the student ticket price s from the second equation.\", \"evidence_links\": [{\"evidence_key\": \"LIN-E3\", \"evidence_role\": \"Rearranging and transforming linear equations\", \"is_necessary\": true}], \"expected_conclusion\": \"From 4a+s=31, obtain s=31-4a.\", \"prerequisite_step_keys\": [\"lin_s0\"]}, {\"step_key\": \"lin_s2\", \"step_order\": 2, \"reasoning_goal\": \"Substitute the expression for s into the first equation and find the adult ticket price a.\", \"evidence_links\": [{\"evidence_key\": \"LIN-E4\", \"evidence_role\": \"Substitution method\", \"is_necessary\": true}, {\"evidence_key\": \"LIN-E5\", \"evidence_role\": \"Combining like terms and inverse operations\", \"is_necessary\": true}], \"expected_conclusion\": \"2a+3(31-4a)=33, simplifying gives -10a=-60, so a=6.\", \"prerequisite_step_keys\": [\"lin_s1\"]}, {\"step_key\": \"lin_s3\", \"step_order\": 3, \"reasoning_goal\": \"Find the other variable and verify whether the solution satisfies the original ticket purchase conditions, thereby choosing the answer.\", \"evidence_links\": [{\"evidence_key\": \"LIN-E6\", \"evidence_role\": \"Verification by substituting back into original equations\", \"is_necessary\": true}], \"expected_conclusion\": \"s=31-4(6)=7, and both original equations hold, so the adult ticket price is $6, choose A.\", \"prerequisite_step_keys\": [\"lin_s2\"]}]}","[{\"step_key\": \"lin_s0\", \"step_order\": 0, \"step_goal\": \"Define unknown prices and set up a system of two linear equations in two variables.\", \"prerequisite_step_keys\": [], \"required_evidence_keys\": [\"LIN-E1\", \"LIN-E2\"], \"required_evidence_roles\": [\"Definition of unknown quantities\", \"Modeling of quantitative relationships\"], \"expected_conclusion\": \"Obtain 2a+3s=33 and 4a+s=31.\"}, {\"step_key\": \"lin_s1\", \"step_order\": 1, \"step_goal\": \"Isolate s from the second linear equation.\", \"prerequisite_step_keys\": [\"lin_s0\"], \"required_evidence_keys\": [\"LIN-E3\"], \"required_evidence_roles\": [\"Rearranging and transforming linear equations\"], \"expected_conclusion\": \"Obtain s=31-4a.\"}, {\"step_key\": \"lin_s2\", \"step_order\": 2, \"step_goal\": \"Substitute and simplify the single-variable equation to solve for a.\", \"prerequisite_step_keys\": [\"lin_s1\"], \"required_evidence_keys\": [\"LIN-E4\", \"LIN-E5\"], \"required_evidence_roles\": [\"Substitution method\", \"Combining like terms and inverse operations\"], \"expected_conclusion\": \"Obtain a=6.\"}, {\"step_key\": \"lin_s3\", \"step_order\": 3, \"step_goal\": \"Find s and substitute the result back into the original equations to verify.\", \"prerequisite_step_keys\": [\"lin_s2\"], \"required_evidence_keys\": [\"LIN-E6\"], \"required_evidence_roles\": [\"Verification by substituting back into original equations\"], \"expected_conclusion\": \"s=7 and both equations hold, so the correct choice is A.\"}]","{\"must_retrieve_all_required\": true, \"relevant_evidence_keys\": [\"LIN-E1\", \"LIN-E2\", \"LIN-E3\", \"LIN-E4\", \"LIN-E5\", \"LIN-E6\"], \"distractor_evidence_keys\": [\"LIN-D1\", \"LIN-D2\", \"LIN-D3\"], \"coverage_unit\": \"Step-level necessary evidence and complete coverage of the entire evidence chain\"}","{\"chain_summary\":\"{\\\"step_count\\\": 5, \\\"unique_required_evidence_count\\\": 5, \\\"dependency_depth\\\": 5, \\\"chain_complete\\\": true, \\\"evidence_sufficiency_rule\\\": \\\"It must cover five types of evidence: the exponential model, division of powers with the same base, square roots under positive constraints, solving for coefficients, and evaluating the target function; if only the exponential function definition or exponentiation formula is retrieved, it cannot support determining the parameters from two known function values and completing the final evaluation.\\\"}\",\"source_record\":\"{\\\"question_text\\\": \\\"The function f(x)=a·b^x, where a and b are both positive. Given f(1)=12 and f(3)=48, what is the value of f(5)?\\\", \\\"problem_category\\\": \\\"Exponential functions and exponent operations\\\", \\\"given_conditions\\\": [\\\"f(x)=a·b^x.\\\", \\\"a>0 and b>0.\\\", \\\"f(1)=12.\\\", \\\"f(3)=48.\\\"], \\\"answer_choices\\\": [\\\"A. 96\\\", \\\"B. 144\\\", \\\"C. 192\\\", \\\"D. 384\\\"], \\\"correct_answer\\\": \\\"C\\\", \\\"candidate_evidence_library\\\": [{\\\"evidence_key\\\": \\\"EXP-E1\\\", \\\"evidence_kind\\\": \\\"Function definition\\\", \\\"evidence_statement\\\": \\\"The exponential function model can be written as f(x)=a·b^x, where a is a positive initial coefficient and b is a positive growth or decay base.\\\", \\\"formula_text\\\": \\\"f(x)=a·b^x; a>0, b>0\\\", \\\"applicability_conditions\\\": [\\\"The problem explicitly gives an exponential function model.\\\", \\\"a and b are positive.\\\"], \\\"source_excerpt\\\": \\\"For an exponential function of the form f(x)=a·b^x, a determines the initial scale, and b determines the multiplicative rate of change for each one-unit increase in the input.\\\"}, {\\\"evidence_key\\\": \\\"EXP-E2\\\", \\\"evidence_kind\\\": \\\"Exponent operation rule\\\", \\\"evidence_statement\\\": \\\"When dividing powers with the same base, subtract the exponents; dividing the two function values can cancel the common coefficient a.\\\", \\\"formula_text\\\": \\\"(a·b^m)\\\u002F(a·b^n)=b^(m-n), a is not equal to 0\\\", \\\"applicability_conditions\\\": [\\\"The numerator and denominator use the same a and the same base b.\\\", \\\"The denominator is not zero.\\\"], \\\"source_excerpt\\\": \\\"When dividing powers with the same base, the base stays the same and the exponents are subtracted; common nonzero factors can be canceled.\\\"}, {\\\"evidence_key\\\": \\\"EXP-E3\\\", \\\"evidence_kind\\\": \\\"Calculation rule\\\", \\\"evidence_statement\\\": \\\"When b is positive and b^2=4, b can only be the positive square root 2.\\\", \\\"formula_text\\\": \\\"b^2=4 and b>0, so b=sqrt(4)=2\\\", \\\"applicability_conditions\\\": [\\\"b is positive.\\\", \\\"The square of b is known.\\\"], \\\"source_excerpt\\\": \\\"Under the positive number restriction, the only possible value whose square is 4 is 2, not the negative square root.\\\"}, {\\\"evidence_key\\\": \\\"EXP-E4\\\", \\\"evidence_kind\\\": \\\"Algebraic transformation rule\\\", \\\"evidence_statement\\\": \\\"After knowing f(1)=a·b, divide the function value by b to find the coefficient a.\\\", \\\"formula_text\\\": \\\"a=f(1)\\\u002Fb\\\", \\\"applicability_conditions\\\": [\\\"b is not equal to 0.\\\", \\\"f(1)=a·b holds.\\\"], \\\"source_excerpt\\\": \\\"Write the value of the exponential function at x=1 as a·b, then divide by the known base to obtain a.\\\"}, {\\\"evidence_key\\\": \\\"EXP-E5\\\", \\\"evidence_kind\\\": \\\"Exponential calculation rule\\\", \\\"evidence_statement\\\": \\\"When calculating the target function value, first compute the exponential power, then multiply by the coefficient.\\\", \\\"formula_text\\\": \\\"f(5)=a·b^5; 2^5=32\\\", \\\"applicability_conditions\\\": [\\\"The values of a and b have been determined.\\\", \\\"The target input is x=5.\\\"], \\\"source_excerpt\\\": \\\"Evaluating an exponential function follows the steps of first calculating b to the x-th power, then multiplying by coefficient a.\\\"}, {\\\"evidence_key\\\": \\\"EXP-D1\\\", \\\"evidence_kind\\\": \\\"Concept\\\", \\\"evidence_statement\\\": \\\"In an arithmetic sequence, adjacent terms maintain a fixed additive difference.\\\", \\\"formula_text\\\": \\\"u_n=u_1+(n-1)d\\\", \\\"applicability_conditions\\\": [\\\"The difference between adjacent terms remains constant.\\\"], \\\"source_excerpt\\\": \\\"The arithmetic model describes a sequence that changes by a fixed difference.\\\"}, {\\\"evidence_key\\\": \\\"EXP-D2\\\", \\\"evidence_kind\\\": \\\"Formula\\\", \\\"evidence_statement\\\": \\\"Logarithms can convert exponential relationships into power relationships.\\\", \\\"formula_text\\\": \\\"log_b(y)=x is equivalent to b^x=y\\\", \\\"applicability_conditions\\\": [\\\"b>0 and b is not equal to 1, y>0.\\\"], \\\"source_excerpt\\\": \\\"Logarithms are the inverse operation of exponentiation.\\\"}, {\\\"evidence_key\\\": \\\"EXP-D3\\\", \\\"evidence_kind\\\": \\\"Formula\\\", \\\"evidence_statement\\\": \\\"The roots of a quadratic equation can be determined by the discriminant and the quadratic formula.\\\", \\\"formula_text\\\": \\\"x=(-b±sqrt(b^2-4ac))\\\u002F(2a)\\\", \\\"applicability_conditions\\\": [\\\"The equation is quadratic.\\\"], \\\"source_excerpt\\\": \\\"The quadratic formula applies to quadratic equations in general form.\\\"}], \\\"gold_step_annotations\\\": [{\\\"step_key\\\": \\\"exp_s0\\\", \\\"step_order\\\": 0, \\\"reasoning_goal\\\": \\\"Write the two known function values as exponential expressions in terms of a and b.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E1\\\", \\\"evidence_role\\\": \\\"Exponential function model and parameter conditions\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"From the model, obtain a·b=12 and a·b^3=48, and a and b are both positive.\\\", \\\"prerequisite_step_keys\\\": []}, {\\\"step_key\\\": \\\"exp_s1\\\", \\\"step_order\\\": 1, \\\"reasoning_goal\\\": \\\"Divide the two function values to cancel a and find the square of b.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E2\\\", \\\"evidence_role\\\": \\\"Division of powers with the same base and cancellation of common factors\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"(a·b^3)\\\u002F(a·b)=48\\\u002F12, so b^2=4.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s0\\\"]}, {\\\"step_key\\\": \\\"exp_s2\\\", \\\"step_order\\\": 2, \\\"reasoning_goal\\\": \\\"Use the condition that b is positive to determine the exponential base b.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E3\\\", \\\"evidence_role\\\": \\\"Positive square root value\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"b=2.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s1\\\"]}, {\\\"step_key\\\": \\\"exp_s3\\\", \\\"step_order\\\": 3, \\\"reasoning_goal\\\": \\\"Use f(1)=12 to find the coefficient a of the exponential function.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E4\\\", \\\"evidence_role\\\": \\\"Solving for the coefficient from the function value\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"a·2=12, so a=6.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s2\\\"]}, {\\\"step_key\\\": \\\"exp_s4\\\", \\\"step_order\\\": 4, \\\"reasoning_goal\\\": \\\"Substitute a and b into the target input x=5 and calculate the function value.\\\", \\\"evidence_links\\\": [{\\\"evidence_key\\\": \\\"EXP-E5\\\", \\\"evidence_role\\\": \\\"Exponential function evaluation and exponentiation\\\", \\\"is_necessary\\\": true}], \\\"expected_conclusion\\\": \\\"f(5)=6·2^5=6·32=192, so choose C.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s3\\\"]}]}\",\"evidence_chain\":\"[{\\\"step_key\\\": \\\"exp_s0\\\", \\\"step_order\\\": 0, \\\"step_goal\\\": \\\"Expand the two known function values according to the exponential function model.\\\", \\\"prerequisite_step_keys\\\": [], \\\"required_evidence_keys\\\": [\\\"EXP-E1\\\"], \\\"required_evidence_roles\\\": [\\\"Exponential function model and parameter conditions\\\"], \\\"expected_conclusion\\\": \\\"Obtain a·b=12 and a·b^3=48.\\\"}, {\\\"step_key\\\": \\\"exp_s1\\\", \\\"step_order\\\": 1, \\\"step_goal\\\": \\\"Cancel a by division and obtain b^2.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s0\\\"], \\\"required_evidence_keys\\\": [\\\"EXP-E2\\\"], \\\"required_evidence_roles\\\": [\\\"Division of powers with the same base and cancellation of common factors\\\"], \\\"expected_conclusion\\\": \\\"Obtain b^2=4.\\\"}, {\\\"step_key\\\": \\\"exp_s2\\\", \\\"step_order\\\": 2, \\\"step_goal\\\": \\\"Use the positive number constraint to find b.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s1\\\"], \\\"required_evidence_keys\\\": [\\\"EXP-E3\\\"], \\\"required_evidence_roles\\\": [\\\"Positive square root value\\\"], \\\"expected_conclusion\\\": \\\"Obtain b=2.\\\"}, {\\\"step_key\\\": \\\"exp_s3\\\", \\\"step_order\\\": 3, \\\"step_goal\\\": \\\"Find coefficient a from f(1).\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s2\\\"], \\\"required_evidence_keys\\\": [\\\"EXP-E4\\\"], \\\"required_evidence_roles\\\": [\\\"Solving for the coefficient from the function value\\\"], \\\"expected_conclusion\\\": \\\"Obtain a=6.\\\"}, {\\\"step_key\\\": \\\"exp_s4\\\", \\\"step_order\\\": 4, \\\"step_goal\\\": \\\"Calculate the exponential function value at x=5 and match the choices.\\\", \\\"prerequisite_step_keys\\\": [\\\"exp_s3\\\"], \\\"required_evidence_keys\\\": [\\\"EXP-E5\\\"], \\\"required_evidence_roles\\\": [\\\"Exponential function evaluation and exponentiation\\\"], \\\"expected_conclusion\\\": \\\"f(5)=192, the correct choice is C.\\\"}]\",\"retrieval_evaluation_target\":\"{\\\"must_retrieve_all_required\\\": true, \\\"relevant_evidence_keys\\\": [\\\"EXP-E1\\\", \\\"EXP-E2\\\", \\\"EXP-E3\\\", \\\"EXP-E4\\\", \\\"EXP-E5\\\"], \\\"distractor_evidence_keys\\\": [\\\"EXP-D1\\\", \\\"EXP-D2\\\", \\\"EXP-D3\\\"], \\\"coverage_unit\\\": \\\"Evaluate necessary evidence coverage by reasoning step, and require the entire evidence chain from parameter identification to target evaluation to be complete\\\"}\"}","MOBIUSI INC","https:\u002F\u002Fstatic.mobiusi.com\u002Fmobiwusi\u002F20250829\u002F7bf4ac62b4533e2b809998a6f1c5491e.png?Expires=1792463130&OSSAccessKeyId=LTAI5tH8MQqhgeiAtrzCHrxM&Signature=v6Tr8jBrdm4s5wU1SnnyGsYg%2Bhw%3D&x-oss-process=image%2Fresize%2Cm_fill%2Cw_35%2Ch_35",[662,668],{"type":663,"title":664,"count_data":665},"bar","Length distribution",[666],{"name":667,"value":483},"1k lower",{"type":669,"title":670,"count_data":671},"pie","Language 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