Chapter Digest

Purpose

Reference books are long and readers have little time. They need a summary they can trust to cover everything that matters, in a fraction of the length. Concise means cutting padding and repetition, never cutting a definition, theorem, formula, algorithm, condition, or exam-worthy point. When in doubt about an item, keep it and make it shorter.

Step 1: Get the actual text

• Work from the text the user provides. If a file is uploaded and its content is not already visible, read it fully with the file-reading or pdf-reading skill (if available) before writing anything.
• Note the page range and the section headings you can see. Check for unreadable pages, bad scans, or missing figures, and tell the user which parts you could not read instead of guessing.
• If they only name a chapter without providing it, say that you have not been given the text. Offer either to work from an upload, or a general overview from your own knowledge, clearly labeled as such, since it may not match their edition.
• Never present anything as coming from the book unless it is in the text provided.

Step 2: Inventory before summarizing

Read through once and list, in order:

• Every heading and subheading.
• Every definition, theorem, lemma, property, rule, and law.
• Every formula and equation that is used later.
• Every algorithm, procedure, or method.
• Every worked example and its type.
• Every warning, note, or "common mistake" the author points out.
• Summary or key-terms boxes and chapter-end exercises, if present.

This inventory is the coverage checklist. Nothing on it may silently disappear from the digest.

For long sections (more than about 15 to 20 pages), process in chunks of that size: inventory and digest each chunk, then merge into one document with a single outline. Do not stretch one pass over a whole long chapter, because details get lost.

Step 3: Choose the depth

• 1-page: the core ideas, the key formulas and algorithms, and the top mistakes. For a quick pre-class or pre-exam glance.
• Standard (default): about 10 to 15 percent of the original length. Complete outline, every inventory item, shortened examples.
• Detailed: about 25 to 30 percent. Adds proof ideas, more examples, and derivation sketches.

If the user does not say which, use standard and mention the option to shrink or expand.

Step 4: Write the digest

Follow references/digest-template.md for the exact layout. In short:

1. Big picture (about 5 lines).
2. Outline following the book's own headings, in order.
3. A "nothing dropped" table of definitions, theorems, formulas, and algorithms, each with a one-line "use it when".
4. Worked examples reduced to method (steps, key trick, result).
5. Traps and must-remember box.
6. Self-check questions with answers.
7. Coverage check.

Adapt the content to the subject using references/formats-by-subject.md (algorithms, math, numerical methods, digital design, programming).

Step 5: Verify before delivering

• Every inventory item appears in the digest. Fix gaps, or list them in the coverage check with the reason.
• Every formula, constant, bound, and condition matches the source exactly. Recheck signs, exponents, indices, and inequality directions.
• Every algorithm keeps its steps and its complexity or convergence claim.
• Nothing has been added from outside the text. If extra help is useful, put it in a separate box labeled "Extra (not from the text)".
• If the book seems to contain an error or a confusing statement, do not quietly change it. Flag it to the user.

Fidelity and wording

• Paraphrase in your own words and keep quotations to short formal definitions or statements. State theorems and definitions accurately, with all their conditions.
• Keep the book's notation so the reader's notes and the book line up. Note when you introduce a shorthand.
• Keep the author's order of ideas, because it is easier to review against the book.

Style

• Friendly and direct in the chat message around the digest; match the user's tone.
• The digest itself should be clean and scannable: short lines, tables, and numbered steps instead of long paragraphs.
• Plain-text math in chat (x^2, sqrt(x), O(n log n)) so nothing breaks if LaTeX fails to render. LaTeX or proper typesetting is fine inside a PDF.
• Do not over-explain things the user has said they already know.

Delivering

• A 1-page digest can go in the chat.
• A standard or detailed digest works best as a document to keep (PDF, or Word if requested), made with the matching document skill if available.
• After delivering, offer follow-ups that build on the digest: a quiz from the self-check questions, flashcards, or feeding it into an exam study plan or cram pack.

Example

User uploads: a 16-page section of CLRS on heapsort and says "summarize this, I have no time".

You: Got it, 16 pages 💪 I'll do a standard digest (about 2 pages) and keep every definition, procedure, and complexity result.

Digest includes: the heap property and array index formulas, MAX-HEAPIFY, BUILD-MAX-HEAP, HEAPSORT each in short pseudocode with its running time, the reason building a heap is O(n) and not O(n log n) in two lines, a comparison table with other sorts, common mistakes (off-by-one indexing), five self-check questions, and a coverage list of every heading in those pages.