textbook-index

Build / extend the index

python3 skills/textbook-index/scripts/extract_toc.py <book-or-dir> ... \
        --out-dir references/textbooks/toc --summary /tmp/toc.json [--max-level 2]
python3 skills/textbook-index/scripts/extract_toc.py --selftest

• PDF with bookmarks → bm (pages = physical PDF pages).
• No usable bookmarks → parses the printed "Contents" pages (txt, printed page numbers); rejects OCR garbage using a dictionary hit-rate check (needs /usr/share/dict/words; otherwise accepts with a warning).
• Scanned (no text layer), DjVu without djvused, or noisy OCR → stub; fill a chapter-level TOC from the publisher's public page and label it TOC from public source.
• Output contains only bibliographic data + TOC; never commit PDFs or body text. Then add a row to references/textbooks/CATALOG.md and, if it fills a gap, to TOPIC-MAP.md.

Query ("which book/chapter proves X?")

1. TOPIC-MAP.md row for the topic → first look / second opinion.
2. grep -ril "<term>" references/textbooks/toc/ for terms the map lacks; beware homonyms (Frobenius norm vs Frobenius automorphism vs Frobenius group; "character" of a group vs of a field; "lattice" of subgroups vs Euclidean lattice; "trace" of a matrix vs field trace).
3. Open your own copy at the section; copy the exact statement, and check each hypothesis against your setting (characteristic, ring vs field, finite vs infinite group, prime vs prime power modulus, Galois vs non-Galois extension). Most mis-citations fail here, not at the conclusion.
4. Record in MATH-REFS.md: | id | statement we use | source (book, section, printed page) | hypotheses checked? | used in |.
5. If the statement is load-bearing, hand it to theorist for a Sage/Lean check.

Ignition pattern for idea mining

"Book B chapter C + concrete bottleneck step S": ask what structure in C acts on the objects of S (a group action, a grading, a decomposition, a norm, an extremal bound). This pairing, not "give me ideas", is what produces candidate free parameters for idea-mining-loop.