241 lines
11 KiB
JSON
241 lines
11 KiB
JSON
{
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"goal": "Help me understand how Shannon entropy leads into channel capacity and thermodynamic entropy.",
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"study_plan": {
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"skill": "ocw-information-entropy-agent",
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"task": "Help me understand how Shannon entropy leads into channel capacity and thermodynamic entropy.",
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"steps": [
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{
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"concept_key": "mit-ocw-information-and-entropy::independent-reasoning-and-careful-comparison",
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"title": "Independent Reasoning and Careful Comparison",
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"status": "mastered",
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"prerequisites": [
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"mit-ocw-information-and-entropy::course-notes-and-reference-texts"
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],
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"prerequisite_titles": [
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"Course Notes and Reference Texts"
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],
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"supporting_lessons": [
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"Independent Reasoning and Careful Comparison"
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],
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"source_fragments": [
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{
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"lesson_title": "Independent Reasoning and Careful Comparison",
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"kind": "lesson_body",
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"text": "- Objective: Explain why the course requires precise comparison of related but non-identical concepts.\n- Exercise: Write a short note distinguishing Shannon entropy, channel capacity, and thermodynamic entropy.\nThe syllabus framing implies a style of work where analogy is useful but dangerous when used loosely. Learners must compare models carefully, state assumptions, and notice where similar mathematics does not imply identical interpretation."
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},
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{
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"lesson_title": "Independent Reasoning and Careful Comparison",
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"kind": "objective",
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"text": "Explain why the course requires precise comparison of related but non-identical concepts."
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}
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],
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"recommended_action": "Use Independent Reasoning and Careful Comparison as the primary teaching anchor."
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},
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{
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"concept_key": "mit-ocw-information-and-entropy::thermodynamics-and-entropy",
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"title": "Thermodynamics and Entropy",
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"status": "mastered",
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"prerequisites": [
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"mit-ocw-information-and-entropy::cryptography-and-information-hiding"
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],
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"prerequisite_titles": [
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"Cryptography and Information Hiding"
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],
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"supporting_lessons": [
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"Thermodynamics and Entropy"
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],
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"source_fragments": [
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{
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"lesson_title": "Thermodynamics and Entropy",
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"kind": "lesson_body",
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"text": "- Objective: Explain how thermodynamic entropy relates to, and differs from, Shannon entropy.\n- Exercise: Compare the two entropy notions and identify what is preserved across the analogy.\nThe course uses entropy as a bridge concept between communication theory and physics while insisting on careful interpretation."
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},
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{
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"lesson_title": "Thermodynamics and Entropy",
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"kind": "objective",
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"text": "Explain how thermodynamic entropy relates to, and differs from, Shannon entropy."
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}
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],
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"recommended_action": "Use Thermodynamics and Entropy as the primary teaching anchor."
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},
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{
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"concept_key": "mit-ocw-information-and-entropy::shannon-entropy",
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"title": "Shannon Entropy",
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"status": "mastered",
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"prerequisites": [
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"mit-ocw-information-and-entropy::counting-and-probability"
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],
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"prerequisite_titles": [
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"Counting and Probability"
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],
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"supporting_lessons": [
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"Shannon Entropy"
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],
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"source_fragments": [
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{
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"lesson_title": "Shannon Entropy",
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"kind": "lesson_body",
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"text": "- Objective: Explain Shannon entropy as a measure of uncertainty and compare high-entropy and low-entropy sources.\n- Exercise: Compute the entropy of a Bernoulli source and interpret the result.\nThe course then introduces entropy as a quantitative measure of uncertainty for a source model and uses it to reason about representation cost and surprise."
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},
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{
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"lesson_title": "Shannon Entropy",
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"kind": "objective",
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"text": "Explain Shannon entropy as a measure of uncertainty and compare high-entropy and low-entropy sources."
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}
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],
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"recommended_action": "Use Shannon Entropy as the primary teaching anchor."
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}
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],
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"guided_path_reference": [
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"mit-ocw-information-and-entropy::mit-ocw-6-050j-information-and-entropy-course-home",
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"mit-ocw-information-and-entropy::information-and-entropy",
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"mit-ocw-information-and-entropy::ultimate-limits-to-communication-and-computation",
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"mit-ocw-information-and-entropy::open-textbooks-problem-sets-and-programming-work",
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"mit-ocw-information-and-entropy::mit-ocw-6-050j-information-and-entropy-syllabus",
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"mit-ocw-information-and-entropy::prerequisites-and-mathematical-background",
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"mit-ocw-information-and-entropy::assessment-structure",
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"mit-ocw-information-and-entropy::course-notes-and-reference-texts",
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"mit-ocw-information-and-entropy::independent-reasoning-and-careful-comparison",
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"mit-ocw-information-and-entropy::mit-ocw-6-050j-information-and-entropy-unit-sequence",
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"mit-ocw-information-and-entropy::counting-and-probability",
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"mit-ocw-information-and-entropy::shannon-entropy",
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"mit-ocw-information-and-entropy::mutual-information",
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"mit-ocw-information-and-entropy::source-coding-and-compression",
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"mit-ocw-information-and-entropy::huffman-coding",
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"mit-ocw-information-and-entropy::channel-capacity",
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"mit-ocw-information-and-entropy::channel-coding",
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"mit-ocw-information-and-entropy::error-correcting-codes",
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"mit-ocw-information-and-entropy::cryptography-and-information-hiding",
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"mit-ocw-information-and-entropy::thermodynamics-and-entropy"
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]
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},
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"primary_concept": {
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"concept_key": "mit-ocw-information-and-entropy::independent-reasoning-and-careful-comparison",
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"title": "Independent Reasoning and Careful Comparison",
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"status": "mastered",
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"prerequisites": [
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"mit-ocw-information-and-entropy::course-notes-and-reference-texts"
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],
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"prerequisite_titles": [
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"Course Notes and Reference Texts"
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],
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"supporting_lessons": [
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"Independent Reasoning and Careful Comparison"
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],
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"source_fragments": [
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{
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"lesson_title": "Independent Reasoning and Careful Comparison",
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"kind": "lesson_body",
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"text": "- Objective: Explain why the course requires precise comparison of related but non-identical concepts.\n- Exercise: Write a short note distinguishing Shannon entropy, channel capacity, and thermodynamic entropy.\nThe syllabus framing implies a style of work where analogy is useful but dangerous when used loosely. Learners must compare models carefully, state assumptions, and notice where similar mathematics does not imply identical interpretation."
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},
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{
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"lesson_title": "Independent Reasoning and Careful Comparison",
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"kind": "objective",
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"text": "Explain why the course requires precise comparison of related but non-identical concepts."
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}
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],
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"recommended_action": "Use Independent Reasoning and Careful Comparison as the primary teaching anchor."
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},
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"secondary_concept": {
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"concept_key": "mit-ocw-information-and-entropy::thermodynamics-and-entropy",
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"title": "Thermodynamics and Entropy",
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"status": "mastered",
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"prerequisites": [
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"mit-ocw-information-and-entropy::cryptography-and-information-hiding"
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],
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"prerequisite_titles": [
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"Cryptography and Information Hiding"
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],
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"supporting_lessons": [
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"Thermodynamics and Entropy"
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],
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"source_fragments": [
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|
{
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"lesson_title": "Thermodynamics and Entropy",
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"kind": "lesson_body",
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"text": "- Objective: Explain how thermodynamic entropy relates to, and differs from, Shannon entropy.\n- Exercise: Compare the two entropy notions and identify what is preserved across the analogy.\nThe course uses entropy as a bridge concept between communication theory and physics while insisting on careful interpretation."
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},
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{
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"lesson_title": "Thermodynamics and Entropy",
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"kind": "objective",
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"text": "Explain how thermodynamic entropy relates to, and differs from, Shannon entropy."
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}
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],
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"recommended_action": "Use Thermodynamics and Entropy as the primary teaching anchor."
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},
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"practice_task": "[stubbed-response] [practice] Concept: Independent Reasoning and Careful Comparison Prerequisites: Course Notes and Reference Texts Supporting lessons",
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"evaluation": {
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"concept_key": "mit-ocw-information-and-entropy::independent-reasoning-and-careful-comparison",
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"submission": "Entropy measures uncertainty because more possible outcomes require more information to describe, but one limitation is that thermodynamic entropy is not identical to Shannon entropy.",
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"verdict": "needs_revision",
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"aggregated": {
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"correctness": 0.6000000000000001,
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"explanation": 0.85,
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"critique": 0.6499999999999999
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},
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"evaluators": [
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{
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"name": "rubric",
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"dimensions": {
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"correctness": 0.8,
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"explanation": 0.85
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},
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"notes": "Heuristic scaffold rubric score."
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},
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{
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"name": "symbolic_rule",
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"dimensions": {
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"correctness": 0.4
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},
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"notes": "Stub symbolic evaluator."
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},
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{
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"name": "critique",
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"dimensions": {
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"critique": 0.6499999999999999
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},
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"notes": "Stub critique evaluator."
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}
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],
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"skill_reference": {
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"skill_name": "ocw-information-entropy-agent",
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"mastered_by_demo_agent": true,
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"supporting_lessons": [
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"Independent Reasoning and Careful Comparison"
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]
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},
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"follow_up": "Rework the answer so it states the equality/relationship explicitly and explains why it matters."
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},
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"turns": [
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{
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"role": "user",
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"label": "Learner Goal",
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"content": "Help me understand how Shannon entropy leads into channel capacity and thermodynamic entropy."
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},
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{
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"role": "assistant",
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"label": "Didactopus Mentor",
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"content": "[stubbed-response] [mentor] Concept: Independent Reasoning and Careful Comparison Prerequisites: Course Notes and Reference Texts Supporting lessons"
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},
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{
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"role": "assistant",
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"label": "Didactopus Practice Designer",
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"content": "[stubbed-response] [practice] Concept: Independent Reasoning and Careful Comparison Prerequisites: Course Notes and Reference Texts Supporting lessons"
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},
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{
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"role": "user",
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"label": "Learner Submission",
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"content": "Entropy measures uncertainty because more possible outcomes require more information to describe, but one limitation is that thermodynamic entropy is not identical to Shannon entropy."
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},
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{
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"role": "assistant",
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"label": "Didactopus Evaluator",
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"content": "[stubbed-response] [evaluator] Concept: Independent Reasoning and Careful Comparison Prerequisites: Course Notes and Reference Texts Supporting lessons"
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},
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{
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"role": "assistant",
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"label": "Didactopus Mentor",
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"content": "[stubbed-response] [mentor] Concept: Independent Reasoning and Careful Comparison Prerequisites: Course Notes and Reference Texts Supporting lessons"
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}
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]
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} |