Lambda Map

λambda map builder (schema: 1)

The map is what separates λambda from a generic AI tutor: every MCQ a session asks traces to a real assessed problem and the marks it carries. This skill builds that map from the learner's own course materials — the map derives from their institution's copyrighted content, so it lives in their private vault and is never redistributed.

Usage

/lambda-map <course-name> <path> [more paths...]

Paths may be folders or files: lecture PDFs, tutorial/problem-set PDFs, past exam papers, quiz exports, notebooks, lecture transcripts (.txt/.md/.vtt dumps of what was actually said).

Transcripts are an emphasis signal, not a question source: past papers show what an earlier offering examined, but the transcript shows what this offering's lecturer stressed, skipped, or hinted at ("this will be on the exam", "we won't cover the proof"). When transcripts are present, weight the map's marks-bound routing toward the current offering's emphasis and note explicit verbal exam hints in the relevant map rows. File transcripts in the ## Sources ledger like any other input.

Sparse sources (school-shaped courses)

Not every course arrives university-shaped. A school student may have only a scope & sequence, a textbook, and a couple of practice tests — no outline, no tutorial sets, no marks schedule. The map builds anyway, by substitution:

• Scope & sequence / syllabus → units. Its rows become the map's ## sections; the textbook's chapter structure is the fallback when even that is missing.
• Textbook exercises → drills. Chapter exercise sets fill the Drill column (Ch 11 Ex 11C Q4–9 is a perfectly good drill pointer).
• Practice tests / past papers → assessed targets. However few; a single practice test still anchors marks-bound ordering.
• No marks data at all? Leave the marks empty and order sections by the scope & sequence — routing degrades to curriculum order, and the map upgrades in place the day a practice paper arrives (weekly-update path below).

Never fabricate marks or assessment weights. A sparse map that says less is better than a confident map that lies.

Procedure

1. Inventory and classify. List candidate files; classify each as questions or solutions (*solution*, *answers*, *marking*, keys). The learner's own submitted work (assignments, graded quizzes, past answers) may be indexed for ROUTING — what the course asks, where the marks sit — but is NEVER mastery evidence: it may be AI-assisted or otherwise not the learner's own, and the map must not seed or imply any mastery state from it. Beliefs about the learner update only on what λ observes in its own sessions. Solutions are grounding, not content: read them to confirm marks, intended method, and concept labels — never copy solution text, steps, or final answers into the map. The map must read cleanly as if built from questions alone.

2. Index per assessment surface. For each question file, extract a per-question index: question number, marks (if stated), one line on what it asks (the task, not the topic label), and the concept(s) it exercises. For large collections, fan out subagents per file/folder and merge. 2b. Extract the notation register. While indexing, record the course's own symbol conventions: what each recurring symbol denotes in this course's materials (e.g. which letter the course uses for a parameter, an ordering, a message, a mean), and any known clash with common textbook conventions. The map gains a ## Notation section:

   ## Notation (course register — teach and quiz in THIS)
   
   | Symbol | Course meaning | Clash warning |
   |---|---|---|
   | $\mu$ | Poisson mean (this course) | many texts write $\lambda$ |
   

   Only record symbols actually observed in the materials — never infer a convention from a textbook. Weekly updates extend this table as new sheets introduce symbols.

3. Reverse-index by concept. For each lecture/chapter-level concept, list every drill (tutorial/problem-set question) and every assessed target (exam/quiz question with marks) that exercises it.

4. Weight it. Open the map with a > [!important] Marks at stake callout: which concepts carry the most assessed marks, which appear in the most recent / most format-relevant papers, and any concept that appears in exactly one exemplar (flag it — thin coverage means the drills are precious).

5. Write courses/<course-name>/map.md in the vault. Open it with a skills: frontmatter block declaring the skills a /lambda session on this course must load — this is the course's composition manifest, read in the session protocol's Step 0. Every course gets lambda-core (default) and, if quantitative, lambda-notation (the $/LaTeX rules) and lambda-draw (figures); add lambda-math for arithmetic-heavy courses (simplest-form discipline), and the field skill for the subject as it arrives (lambda-science, lambda-english, lambda-humanities):

---
skills: [lambda-core, lambda-notation, lambda-draw, lambda-math]
---

# <course> routing map (schema: 1)

Built <date> from question files only; no solutions opened.
Source roots: <paths>

> [!important] Marks at stake
> <the weighting summary>

## <Unit / lecture / chapter>

| Concept | Drill | Assessed target |
|---|---|---|
| <concept> | <Tut X Qy — one-line task> | <Exam year Qz [marks]> |

End the map with a ## Sources ledger: one line per indexed file with the date it was indexed. This is what makes weekly updates cheap.

If the syllabus states prerequisites, open the map with an assumes: <slug>, <slug> line naming substrate atoms (SPEC "The substrate") — declared dependencies, NOT map rows: they carry no drills or marks, and sessions re-verify them by fast lane at need. Never probe them at map-build time; the register also grows lazily from descent events, so an empty or absent line is fine.

6. Report: units mapped, questions indexed, the top-3 marks concentrations, and any blind spots (concepts with no drill or no assessed exemplar).

Weekly updates — courses arrive incrementally

A real student does not hold the full term's corpus on day one; tutorial sheets and solutions land week by week. Design for that:

• Re-running the command is the update mechanism. If courses/<name>/map.md already exists, read it and its ## Sources ledger first; index only files not in the ledger; append the new questions to the right unit tables; recompute the marks-at-stake callout; add the new files to the ledger. Never rebuild from scratch — existing rows and their wording stay put.
• Thin early-term coverage degrades gracefully. When few or no assessed surfaces exist yet, weight rows by lecture emphasis instead of marks and tag them no assessed exemplar yet — sessions then anchor to drills alone, and the tags disappear as past papers and quizzes enter the ledger.
• In the update report, call out which previous blind spots the new week's material just covered.

Conventions

• Marks in brackets everywhere: Q3 [5].
• One-line descriptions state the task ("derive the conditional of a bivariate Gaussian given evidence"), not a topic label.
• Callout hygiene: every callout line, including the [!type] line, starts with > .
• If the vault is a git repo, commit: λ-map: <course> — <n> questions.