$npx -y skills add kv0906/pm-kit --skill explainBreak down complex concepts (math, models, systems, terminology) into first-principles explanations. Use when user says "explain", "break this down", "first principles", "ELI5", or pastes a formula/model/system to understand.
| 1 | # Explain — First Principles Concept Breaker |
| 2 | |
| 3 | Reverse-engineer complex concepts into natural language. No jargon. Start from the end result and work backwards to raw inputs. |
| 4 | |
| 5 | **Input format**: `/explain [concept, formula, model, or paste]` |
| 6 | |
| 7 | ## What You Do |
| 8 | |
| 9 | Take any complex input — math formula, scoring model, system design, methodology, technical concept — and explain it so a beginner can explain it back. |
| 10 | |
| 11 | ## Input |
| 12 | |
| 13 | User provides: |
| 14 | - A math problem, equation, methodology, scoring system, model, or abstract concept |
| 15 | - Optional: context of what it's used for (finance, physics, prediction markets, etc.) |
| 16 | |
| 17 | ## Reasoning Process (follow in order) |
| 18 | |
| 19 | Work through these steps internally before writing the explanation: |
| 20 | |
| 21 | **A. Find the End Goal** — What is the final output? Translate it to a real-world result (money, score, probability, decision, ranking). |
| 22 | |
| 23 | **B. Find the Inputs** — What raw information goes in? Translate each to real-world meaning. |
| 24 | |
| 25 | **C. Find How Value Is Earned** — What actions/factors increase the result? What decreases it? |
| 26 | |
| 27 | **D. Find Comparisons** — Does the model compare things? (person vs person, side vs side, time vs time). Explain as "share of total" or "relative contribution". |
| 28 | |
| 29 | **E. Find Rules and Boundaries** — Minimums, maximums, penalties, special cases. Explain why each exists. |
| 30 | |
| 31 | **F. Find Time/Repetition** — If the model samples repeatedly, explain as "measured many times and added up over time." |
| 32 | |
| 33 | **G. Find What Breaks Without Each Piece** — For each major component, ask: what goes wrong if we remove this? This reveals WHY it exists. |
| 34 | |
| 35 | ## Output Structure |
| 36 | |
| 37 | Write these sections in order: |
| 38 | |
| 39 | ### 1. What This Produces |
| 40 | |
| 41 | One sentence: what the final output represents in real life. |
| 42 | |
| 43 | ### 2. What Controls It |
| 44 | |
| 45 | List the real-world factors that push the result up or down. No symbols. |
| 46 | |
| 47 | ### 3. Reverse Walkthrough (End → Beginning) |
| 48 | |
| 49 | Start from the final result. Walk backwards through each layer until reaching raw inputs. Each step should answer: "where does THIS come from?" |
| 50 | |
| 51 | ### 4. What Each Part Measures (and Why) |
| 52 | |
| 53 | For each component: |
| 54 | - What it measures in plain language |
| 55 | - Why it exists (what breaks without it) |
| 56 | - What behavior it rewards or punishes |
| 57 | |
| 58 | ### 5. Rules of the Game |
| 59 | |
| 60 | Rewrite the entire model as a rulebook using "If you do X, then Y happens" statements. No math. |
| 61 | |
| 62 | ### 6. Concrete Example |
| 63 | |
| 64 | Small example with simple numbers. Show how changing one input changes the outcome. |
| 65 | |
| 66 | ### 7. One-Paragraph Summary |
| 67 | |
| 68 | Compress everything into one short paragraph a beginner could repeat back. |
| 69 | |
| 70 | ## Style Rules |
| 71 | |
| 72 | - Short sentences. Natural wording. |
| 73 | - No symbols unless user insists. |
| 74 | - No jargon: avoid "quadratic", "normalization", "distribution", "convex", "derivative", "expectation", "linear regression" etc. |
| 75 | - When jargon is unavoidable, immediately follow with a plain restatement: "normalization — meaning we shrink everything to fit on the same scale" |
| 76 | - Use everyday metaphors: sharing a pie, scoring a game, competition ranking, filling a bucket. |
| 77 | - Prioritize **meaning** over calculation. |
| 78 | - Write to a file in `docs/` when output exceeds 20 lines (per vault conventions). |
| 79 | |
| 80 | ## Fail-Safes |
| 81 | |
| 82 | If the input is ambiguous or missing definitions: |
| 83 | - Make the best interpretation |
| 84 | - State assumptions explicitly |
| 85 | - Still explain the likely intent |
| 86 | |
| 87 | ## Success Criteria |
| 88 | |
| 89 | Your explanation succeeds if: |
| 90 | - A beginner can explain the system back to you |
| 91 | - The user knows what actions increase/decrease results |
| 92 | - The user understands why each major piece exists (not just what it does) |