Research Explain Skill

Research Explain Skill

Description

Generates high-quality explanations of concepts using Gemini and Codex in parallel (Phase 1: MAGI strategy exploration), then synthesizes a single-voice explanation with Claude (Phase 2: convergent generation).

Usage

/research-explain "concept" [--domain physics|ai_ml|statistics|mathematics|paper] [--audience general-public|high-school|undergraduate|phd-student|researcher|expert|"free text"] [--weights '{"clarity":0.2,"accuracy":0.2}'] [--depth low|medium|high|max] [--personas N] [--claude-only] [--substitute "Gemini -> Opus"]

Arguments

• $ARGUMENTS — The concept to explain and optional flags:
  • --domain — Knowledge domain (physics, ai_ml, statistics, mathematics, paper). Auto-inferred if omitted.
  • --audience — Target audience (default: phd-student):
    • general-public — No assumed technical background
    • high-school — Basic math/science literacy
    • undergraduate — Introductory college-level knowledge in the domain
    • phd-student — Graduate-level domain knowledge (default)
    • researcher — Active researcher familiar with the field
    • expert — Deep specialist in the exact sub-field
    • "free text" — Any custom audience description (e.g., "medical doctors learning ML")
  • --weights — JSON object of scoring weights for explanation quality ranking. Keys: clarity, accuracy, depth, accessibility, completeness, engagement. Values must sum to 1.0. If omitted, Claude analyzes the prompt and audience to recommend adaptive weights for user confirmation (see Step 0a).
  • --depth — Controls explanation pipeline depth (default: medium):
    • low — Skip Phase 1 entirely; Claude generates explanation directly
    • medium — Full MAGI (parallel brainstorm + cross-review) → explanation
    • high — MAGI + adversarial debate → explanation with misconceptions section
    • max — Hierarchical MAGI-in-MAGI: N persona subagents → meta-review + debate → multi-perspective deep dive
  • --personas N|auto — Number of explanation-specialist subagents for --depth max (default: auto, range: 2-4). When auto, Claude analyzes the concept to determine the optimal persona count. Ignored for other depth levels.
  • --claude-only — Replace all Gemini/Codex MCP calls with Claude Agent subagents. Use when external model endpoints are unavailable or for a Claude-only workflow. Two subagents with distinct cognitive styles (Creative-Divergent and Analytical-Convergent) ensure perspective diversity.
  • --substitute "Agent -> Opus" — Replace a specific MAGI agent with Claude (Opus). Accepted: "Gemini -> Opus", "Codex -> Opus". Can be specified multiple times. If both substituted, equivalent to --claude-only.

Instructions

Shared rules: Read ${CLAUDE_PLUGIN_ROOT}/shared/rules.md before starting. §MCP, §Claude-Only, §LaTeX, §Substitute apply to this skill. Inline fallback (if shared rules unavailable): Gemini models: gemini-3.1-pro-preview → gemini-2.5-pro → Claude. Codex: gpt-5.4. All math in LaTeX only (no Unicode: σ₁→$\sigma_1$). Use @filepath for MCP file refs; subagents use Read tool.

MCP Tool Rules

See §MCP in shared rules. Additionally:

• Codex: Use mcp__codex-cli__ask-codex for analysis/review.
• Visualization (if plots are generated): See §Visualization.
• When to search: concept definitions, pedagogical resources, common misconceptions, recent breakthroughs, related concepts, fact-checking claims

Claude-Only Mode

See §Claude-Only and §Substitute in shared rules. This skill uses Teacher/Critic asymmetric roles (see Step 0b).

LaTeX Formatting Rules

See §LaTeX in shared rules.

Reusable Templates

ID	Name	Purpose
T1	Audience Weight Defaults	Per-audience baseline weights table
T2	Step 0a Procedure	Full adaptive weight recommendation logic (signal table, normalization, save format)
T3	explanation.md Template	Section structure, word count targets, quality checklist
T4	Output File Trees	Expected artifact layout per depth level

Read references/templates.md for full definitions.

When this skill is invoked, follow these steps exactly:

Step 0: Setup

1. Parse the concept to explain from $ARGUMENTS. If a --domain flag is provided, note the domain (physics, ai_ml, statistics, mathematics, paper). Otherwise, infer the domain from the concept.
2. Pipeline context detection: If an {output_dir} was provided by the calling context and .workspace.json already exists at the output root, skip directory creation and write to {output_dir}/explain/ instead of creating a new versioned directory.
3. Create the output directory: outputs/{sanitized_concept}_{YYYYMMDD}_v{N}/explain/
   • Sanitize the concept: lowercase, replace spaces with underscores, remove special characters, truncate to 50 chars.
   • Use today's date in YYYYMMDD format.
   • Version: Glob for outputs/{sanitized_concept}_{YYYYMMDD}_v*/ and set N = max existing + 1 (start at v1).
4. Write .workspace.json at the output directory root:

   {
     "output_dir": "{absolute_path}",
     "skill": "research-explain",
     "concept": "{original_concept}",
     "domain": "{domain}",
     "audience": "{audience}",
     "depth": "{depth}",
     "created_at": "{ISO-8601}"
   }
   

5. If a domain template exists at ${CLAUDE_PLUGIN_ROOT}/templates/domains/{domain}.md, read it for context.
6. Parse --audience: Accept general-public, high-school, undergraduate, phd-student, researcher, expert, or any quoted free-text string (default: phd-student). The audience propagates into every prompt, persona casting, weight defaults, and the final explanation.
7. Parse --weights:
   • If --weights is explicitly provided: Validate that keys are a subset of {clarity, accuracy, depth, accessibility, completeness, engagement} and values sum to 1.0. Save immediately to explain/weights.json with metadata:

     {
       "weights": { "<user-provided weights>" },
       "_meta": {
         "method": "explicit",
         "domain": "<detected domain>",
         "audience": "<detected audience>"
       }
     }
     

     Skip Step 0a entirely.
   • If --weights is not provided: Load the audience baseline from T1 in references/templates.md as a reference only (do not save yet — Step 0a handles saving after user confirmation).
8. Parse --depth: Accept low, medium, high, or max (default: medium).
   • low — Skip Phase 1 entirely; Claude generates explanation directly (jump to Step 2)
   • medium — Full MAGI + one-shot cross-review → strategy synthesis → explanation
   • high — Full MAGI + cross-review + adversarial debate → strategy synthesis → explanation with misconceptions
   • max — Hierarchical MAGI-in-MAGI pipeline (Steps 1-max-a through 1-max-d replace Steps 1a/1b/1b+/1c)
9. Parse --personas N|auto: Accept integer 2-4 or the string auto (default: auto). Only used when --depth max; ignored otherwise.
   • If auto: Defer persona count determination to Step 0b, where Claude analyzes the concept's complexity, number of distinct pedagogical angles, and audience needs to select the optimal N (2-4).
   • If an explicit integer is given: Use that value directly.
10. Parse --claude-only: Boolean flag (default: false). When present, all Gemini/Codex MCP calls are replaced with Claude Agent subagents. See the Claude-Only Mode section above for the replacement table and cognitive style definitions.

Step 0a: Adaptive Weight Recommendation

If --weights was explicitly provided: Skip this step entirely (weights already saved in Step 0). Full procedure: Read T2 in references/templates.md for the signal detection table, normalization rules, user confirmation flow, and weights.json save format.

When --weights is omitted: detect concept/audience signals → adjust baseline weights → present comparison table → ask user for confirmation (Accept recommended / Use audience defaults / Custom JSON) → save to explain/weights.json.

Step 0b: Dynamic Persona Casting

After setup, Claude analyzes the concept, domain, and audience to assign specialist personas:

For --depth low: Skip this step entirely.

For --depth medium|high (2 personas — asymmetric Teacher/Critic roles):

1. Analyze the concept's sub-topics, prerequisite structure, common misconceptions, and audience needs.
2. Assign a Teacher persona (Agent A / Gemini) — an expert communicator profile suited for explaining this concept to the target audience (e.g., "Richard Feynman — Intuitive Physics Explainer" or "3Blue1Brown-style Visual Mathematics Educator"). The Teacher's job is to draft the best possible explanation.
3. Assign a Critic persona (Agent B / Codex) — a pedagogical analyst profile suited for finding flaws in explanations (e.g., "George Pólya — Mathematical Problem-Solving Analyst" or "Cognitive Science Assessment Specialist"). The Critic's job is to identify prerequisites, misconceptions, confusion neighbors, and calibration questions.
4. Each persona definition should include: name/title, expertise areas (3-5 bullet points), and a guiding question that shapes their perspective. Name the persona after a real historical figure (위인) whose work is closely related to the persona's domain. This immediately signals the persona's intellectual lineage and communication style.
5. Personas are complementary: the Teacher builds understanding, the Critic stress-tests it.
6. If --claude-only: Relabel the personas in explain/personas.md:
   • "Teacher persona (Gemini)" → "Subagent A (Creative-Divergent, Teacher)"
   • "Critic persona (Codex)" → "Subagent B (Analytical-Convergent, Critic)"
   • Include the cognitive style directive in each persona definition so subagents receive it directly.
7. Save to explain/personas.md.

For --depth max (N personas):

Read references/depth_max.md — "Step 0b (depth max)" section for the full N-persona casting procedure (N selection heuristic, persona archetypes N=2/3/4, definition requirements, claude-only relabeling).

Step 1a: Parallel Asymmetric Analysis (--depth medium|high|max)

If --depth low: Skip this step entirely and proceed to Step 2. If --depth max: Skip this step — use Steps 1-max-a through 1-max-d instead (read references/depth_max.md).

Execute these two calls simultaneously (in the same message). Prepend the assigned persona from explain/personas.md to each prompt.

Agent A — Teacher Draft (Gemini):

mcp__gemini-cli__ask-gemini(
  prompt: "[Persona: {teacher_persona_name} — {teacher_persona_expertise}]
Guiding question: {teacher_guiding_question}
Target audience: {audience}

Domain context: @{domain_template_path}

Concept to explain: {concept}

You are a master explainer. Generate a comprehensive draft explanation of this concept for the specified audience. Your explanation should:

1. **Core Explanation**: Build understanding from first principles appropriate to the audience level. Use analogies, examples, and progressive complexity.
2. **Key Intuitions**: What are the 2-3 most important intuitions the audience must grasp?
3. **Mathematical Formalism** (if applicable): Include relevant equations with clear notation explanations. Follow LaTeX formatting rules: inline math with $...$ and display equations with $$ on separate lines.
4. **Concrete Examples**: Provide 2-3 worked examples or real-world applications.
5. **Connections**: How does this concept relate to concepts the audience likely already knows?

Write for maximum clarity and understanding. Use the persona's communication style.",
  model: "gemini-3.1-pro-preview"  // fallback: "gemini-2.5-pro" → Claude
)

Note: Omit the Domain context: @{domain_template_path} line from the prompt when no domain template exists.

Agent B — Critic Analysis (Codex):

mcp__codex-cli__ask-codex(
  prompt: "[Persona: {critic_persona_name} — {critic_persona_expertise}]
Guiding question: {critic_guiding_question}
Target audience: {audience}

Domain context: @{domain_template_path}

Concept to explain: {concept}

You are a pedagogical analyst and explanation critic. Generate a comprehensive critical analysis covering:

1. **Prerequisites Map**: What concepts must the audience understand before this one? List in dependency order. For each, note whether the audience level likely already has it.
2. **Common Misconceptions** (at least 5): For each misconception:
   - State the misconception clearly
   - Explain why it is plausible (what leads people to believe it)
   - Explain precisely why it is wrong
   - Provide a corrective reframing
3. **Confusion Neighbors**: Concepts that are commonly confused with this one. For each pair:
   - This concept IS NOT [confused concept]
   - Key distinguishing feature
4. **Precision-Accessibility Tradeoffs**: Where must an explanation sacrifice precision for accessibility at this audience level? What simplifications are acceptable vs. dangerous?
5. **Calibration Questions** (5-10): Questions that test genuine understanding (not just recall). Include expected correct answers and common wrong answers with explanations of what each wrong answer reveals about the student's misunderstanding.",
  model: "gpt-5.4"
)

Note: Omit the Domain context: @{domain_template_path} line from the prompt when no domain template exists.

Note: If Codex MCP is unavailable, fall back to mcp__gemini-cli__ask-gemini with the Gemini fallback chain and critic-focused framing.

If --claude-only: Per §SubagentExec, spawn simultaneously:

• A (CD, Teacher): Draft explanation of {concept} for {audience} using persona. Read domain template. Deliverables: 1.Core Explanation (first principles, analogies, progressive complexity), 2.Key Intuitions (2-3), 3.Mathematical Formalism (LaTeX), 4.Concrete Examples (2-3 worked), 5.Connections to audience's existing knowledge. Use persona's communication style. Save to explain/gemini_ideas.md.
• B (AC, Critic): Critical analysis for {concept}/{audience} using persona. Deliverables: 1.Prerequisites Map (dependency order; note which audience likely has), 2.Common Misconceptions (≥5; each: statement → why plausible → why wrong → corrective reframing), 3.Confusion Neighbors (per pair: "IS NOT" + key distinguishing feature), 4.Precision-Accessibility Tradeoffs, 5.Calibration Questions (5-10; each: question + correct answer + common wrong answers + what each wrong answer reveals). Save to explain/codex_ideas.md.

Save results to:

• explain/gemini_ideas.md — Teacher's (or Subagent A's) draft explanation with header noting source, persona, and timestamp
• explain/codex_ideas.md — Critic's (or Subagent B's) analysis with header noting source, persona, and timestamp

Step 1b: Cross-Check (--depth medium or --depth high only)

If --depth low: Skip this step entirely and proceed to Step 2.

Pre-check: Verify gemini_ideas.md and codex_ideas.md both exist and are non-empty before proceeding. If either is missing, re-run only the failed agent from Step 1a.

After both Phase 1a results are saved, execute these two calls simultaneously. Prepend the assigned persona to each review prompt:

Teacher reviews Critic's analysis (Round 1):

mcp__gemini-cli__ask-gemini(
  prompt: "[Persona: {teacher_persona_name} — {teacher_persona_expertise}]
Target audience: {audience}

Review the following critical analysis of an explanation for: {concept}

@{output_dir}/explain/codex_ideas.md

For each item in the Critic's analysis:
1. **Misconceptions**: Are these real misconceptions at this audience level? Are any missing? Would your explanation actually trigger any of these?
2. **Prerequisites**: Agree/disagree with the prerequisite ordering? Are any prerequisites overestimated or underestimated for this audience?
3. **Confusion Neighbors**: Are these the right confusion neighbors? Suggest additions or removals.
4. **Precision-Accessibility Tradeoffs**: Are the identified tradeoffs fair? Where would you push back?
5. **Calibration Questions**: Would your explanation enable the audience to answer these correctly? Flag any questions that are unfair for the audience level.

Also note: What aspects of the Critic's analysis should change your draft explanation?",
  model: "gemini-3.1-pro-preview"  // fallback: "gemini-2.5-pro" → Claude
)

Critic reviews Teacher's draft (Round 1):

mcp__codex-cli__ask-codex(
  prompt: "[Persona: {critic_persona_name} — {critic_persona_expertise}]
Target audience: {audience}

Review the following draft explanation of: {concept}

@{output_dir}/explain/gemini_ideas.md

Evaluate the Teacher's explanation on these dimensions:
1. **Accuracy**: Are there any incorrect statements, oversimplifications that cross into inaccuracy, or misleading analogies?
2. **Completeness**: Does it cover all essential aspects? What critical gaps exist?
3. **Audience Calibration**: Is the language, depth, and assumed knowledge appropriate for {audience}?
4. **Misconception Risk**: Does any part of the explanation inadvertently reinforce common misconceptions?
5. **Analogy Fidelity**: Do the analogies accurately map to the concept? Where do they break down, and are those breakdown points acknowledged?
6. **Progressive Structure**: Does the explanation build understanding in the right order? Are there logical jumps?

For each issue found, provide:
- The specific problematic passage
- Why it's problematic
- A suggested fix",
  model: "gpt-5.4"
)

Note: If Codex MCP is unavailable, fall back to mcp__gemini-cli__ask-gemini with the Gemini fallback chain.

If --claude-only: Per §SubagentExec, spawn simultaneously:

• A (CD, Teacher reviewing Critic): Read codex_ideas.md. Review all 5 sections: misconceptions (real at this level? missing?), prerequisites (ordering? over/underestimated?), confusion neighbors (additions/removals?), precision-accessibility tradeoffs (fair?), calibration questions (answerable from your explanation?). Also: what should change in your draft? Save to explain/gemini_review_of_codex.md.
• B (AC, Critic reviewing Teacher): Read gemini_ideas.md. Evaluate 6 dimensions: accuracy, completeness, audience calibration, misconception risk, analogy fidelity (where do analogies break?), progressive structure (logical jumps?). Per issue: specific passage + why problematic + suggested fix. Save to explain/codex_review_of_gemini.md.

Save results to:

• explain/gemini_review_of_codex.md
• explain/codex_review_of_gemini.md

Step 1b+: Adversarial Debate (--depth high only)

If --depth low or --depth medium: Skip this step entirely.

After Round 1 cross-review, Claude identifies the top 3 points of disagreement between the Teacher and Critic, focusing on:

• Misconception risk: Disagreement on whether an explanation approach reinforces misconceptions
• Analogy fidelity: Disagreement on whether an analogy is accurate enough or dangerously misleading
• Precision-accessibility tradeoff: Disagreement on where the acceptable simplification boundary lies for this audience

Save the disagreement summary to explain/disagreements.md before the debate calls.

Execute Round 2 simultaneously:

Teacher Round 2 — Defend/Concede/Revise:

mcp__gemini-cli__ask-gemini(
  prompt: "[Persona: {teacher_persona_name}]
Target audience: {audience}

You (Teacher) and the Critic reviewed each other's work on explaining: {concept}

Here are the top 3 points of disagreement:

@{output_dir}/explain/disagreements.md

For each disagreement:
1. **Defend** your pedagogical choice if you believe it best serves understanding for this audience, providing evidence from learning science or teaching experience
2. **Concede** if the Critic's objection reveals a genuine accuracy or misconception risk, explaining why
3. **Revise** your approach to a new position that balances clarity and accuracy if appropriate

Your original review:
@{output_dir}/explain/gemini_review_of_codex.md

Critic's review of your draft:
@{output_dir}/explain/codex_review_of_gemini.md",
  model: "gemini-3.1-pro-preview"  // fallback chain applies
)

Critic Round 2 — Defend/Concede/Revise:

mcp__codex-cli__ask-codex(
  prompt: "[Persona: {critic_persona_name}]
Target audience: {audience}

You (Critic) and the Teacher reviewed each other's work on explaining: {concept}

Here are the top 3 points of disagreement:

@{output_dir}/explain/disagreements.md

For each disagreement:
1. **Defend** your objection if you believe the accuracy/misconception risk is genuine, providing specific examples of how learners are misled
2. **Concede** if the Teacher's pedagogical choice genuinely aids understanding without significant accuracy cost, explaining why
3. **Revise** your assessment to a new position that respects both rigor and accessibility if appropriate

Your original review:
@{output_dir}/explain/codex_review_of_gemini.md

Teacher's review of your analysis:
@{output_dir}/explain/gemini_review_of_codex.md",
  model: "gpt-5.4"
)

If --claude-only: Per §SubagentExec, spawn simultaneously:

• A (CD, Teacher Round 2): Read disagreements.md + gemini_review_of_codex.md + codex_review_of_gemini.md. Per disagreement: Defend (with learning science evidence) / Concede (if genuine accuracy or misconception risk) / Revise (balance clarity + accuracy). Save to explain/debate_round2_gemini.md.
• B (AC, Critic Round 2): Read same 3 files. Per disagreement: Defend (with specific examples of how learners are misled) / Concede (if pedagogical choice genuinely aids understanding without accuracy cost) / Revise (balance rigor + accessibility). Save to explain/debate_round2_codex.md.

Save results to:

• explain/debate_round2_gemini.md
• explain/debate_round2_codex.md

Steps 1-max-a through 1-max-d: Hierarchical MAGI-in-MAGI (--depth max only)

Skip unless --depth max. Read references/depth_max.md for all four steps. These steps replace Steps 1a/1b/1b+/1c entirely when --depth max is active.

Summary of what runs:

• 1-max-a: Spawn N persona subagents in parallel; each runs a self-contained mini-MAGI pipeline (Gemini draft + Codex analysis + cross-review + conclusion).
• 1-max-b: Collect and verify all N conclusions; build all_conclusions.md consolidated file.
• 1-max-c: Layer 2 meta-reviews (Gemini + Codex simultaneously) → extract top 3 cross-persona disagreements → adversarial debate.
• 1-max-d: Layer 3 enriched synthesis: weighted scoring across all strategies → explain/synthesis.md with 9-section structure including traceability table.

Step 1c: Strategy Synthesis

If --depth max: Skip — synthesis is produced by Step 1-max-d (read references/depth_max.md). If --depth low: Skip — proceed directly to Step 2.

1. Read all available documents:
   • Always: gemini_ideas.md, codex_ideas.md
   • If --depth medium or high: gemini_review_of_codex.md, codex_review_of_gemini.md
   • If --depth high: debate_round2_gemini.md, debate_round2_codex.md
   • Always: weights.json, personas.md
2. Load weights.json and extract the "weights" object. Use the weights to compute a weighted score for each explanation strategy:
   • For each candidate strategy, rate it on each weight dimension (0-10 scale): clarity, accuracy, depth, accessibility, completeness, engagement
   • Compute the weighted sum: score = Σ(weight_i × rating_i)
   • Rank strategies by weighted score
3. Synthesize into an explanation strategy document that includes:
   • Personas Used — brief summary of assigned Teacher and Critic personas
   • Scoring Weights — the weights used for ranking (from weights.json), including _meta.method
   • Recommended Explanation Strategy (ranked by weighted score, showing score breakdown):
     • Best analogies and examples to use
     • Optimal explanation structure/ordering
     • Key intuitions to emphasize
   • Prerequisites Summary — consolidated prerequisite chain for the target audience
   • Misconception Inventory — merged and deduplicated misconceptions from both agents
   • Confusion Neighbors — consolidated confusion neighbor list
   • Consensus Points — pedagogical choices both agents agreed on
   • Divergence Points — areas of disagreement and how to resolve them
   • Debate Resolution (--depth high only) — for each of the 3 debated disagreements, document the final resolution: who conceded, what was revised, and the synthesized position
   • Calibration Questions — best questions from the Critic's analysis, selected for the target audience
4. Save to explain/synthesis.md.

Step 2: Explanation Generation

Claude reads all Phase 1 artifacts and generates the final explanation. This step is always executed by Claude directly (never delegated to MCP tools) to ensure a single authoritative voice.

For --depth low (no Phase 1 artifacts):

1. Read explain/weights.json (if available).
2. If a domain template exists, read it for context.
3. Generate explain/explanation.md directly based on the concept, audience, and domain.

For --depth medium|high|max (Phase 1 artifacts available):

1. Read explain/synthesis.md and all referenced artifacts.
2. Read explain/weights.json to understand the quality priorities.

Generate explain/explanation.md: Read T3 in references/templates.md for the full section structure, word count targets per depth, and quality checklist.

Save to explain/explanation.md.

Step 3: User Feedback

Present the explanation to the user with:

• A concise summary of what was generated (concept, audience, depth, word count)
• The location of all output files
• Clear options for refinement:
  • Adjust audience level: Re-generate for a different audience
  • Adjust depth: Add/remove sections
  • Refine specific section: Focus on improving one part
  • Expand a topic: Deep-dive into a specific aspect mentioned in the explanation

Wait for user input before proceeding.

Output Files

See T4 in references/templates.md for full artifact trees per depth level (low, medium, high, max).

Quick summary:

• --depth low: weights.json + explanation.md
• --depth medium: adds personas.md, gemini_ideas.md, codex_ideas.md, cross-reviews, synthesis.md
• --depth high: adds disagreements.md, debate_round2_*.md
• --depth max: adds persona_N/ subdirs, all_conclusions.md, meta-reviews, meta-debate files