| name | math-explainer |
| description | Use when drafting a mathematical concept explanation for the "Proving Nothing" book — produces book-ready, dependency-aware, multimodal (Sage + manim), fact-checked material executing the Sanderson + Tao teaching method via a six-stage pipeline. Triggers include "explain <concept>", "draft the math for <concept>", "build the explanation for <concept>". Not for systems/applications prose, source ingestion, or interactive tutoring. |
math-explainer
Turn "explain " into book-ready material that executes the Sanderson + Tao method. Run the six stages in order; do not skip the Stage 6 gate.
Load first: references/sanderson-moves.md and references/tao-staging.md (the method rubric), then references/pipeline.md and references/draft-quality.md (the reader-experience rules the editorial panel enforces).
The pipeline
- Stage 1 — Scope & dependency resolution. Follow
references/dependency-protocol.md. Run scripts/resolve_deps.py master-graph/.outline/MATH_FOUNDATIONS.md "<concept>". Output: concept_brief.
- Stage 2 — Stuck-point prediction. From the prerequisites + Tao's "dumb questions", list misconceptions and the bad intuitions the rigorous phase must destroy.
- Stage 3 — Multimodal explanation. Tao's three phases with Sanderson moves inside (
references/pipeline.md). Produce figures with scripts/run_sage.py <recipe.sage>; validate any animation values with scripts/manim_render.py.
- Stage 4 — Factual-accuracy verification. Follow
references/accuracy-protocol.md; reach verified == true.
- Stage 5 — Comprehension checks. Recall (pre), apply (rigorous), transfer (post), and a "re-derive it" task; each with an answer key and on-miss route to a prerequisite.
- Stage 6 — Assembly & gate. Assemble the bundle (embedding the Stage-4
accuracy_report and Stage-5 comprehension_set), write bundle.json, run scripts/scorecard.py bundle.json. The scorecard binds its accuracy/comprehension checks to those embedded artifacts (validated by scripts/schemas.py), so a self-asserted flag cannot pass. Also write draft.md per references/draft-quality.md and run scripts/draft_lint.py draft.md (must report CLEAN — no pipeline/QA vocabulary in reader prose). Ship only when the scorecard PASSes and the draft lints CLEAN.
Method rubric (enforced by the Stage 6 scorecard)
Led with a visual; concrete before abstract; motivated before defined; notation earned; staged pre→rigorous→post; every heuristic paired with its rigorous counterpart; every predicted stuck-point addressed; accuracy verified; comprehension covers all three Tao levels + rediscovery; a "you could have invented this" prompt present.
Dependencies
SageMath (sage on PATH) for figures; manim (optional) for animation — driven by a manim MCP server or a local manim install via scripts/manim_render.py (render_scene); fall back to Sage figures if unavailable. Run scripts/check_env.py to verify the tools (sage, manim, graphify) and the pipeline MODE (full-multimodal / figure-only). The master graph, MATH_FOUNDATIONS.md, the book-knowledge ledger, and CHAPTER_BIBLE.md are read-only inputs.
