Add textbook formalization pipeline (extract -> LLM formalize -> elaboration check -> library assembly)

- extract_section.py: slice a book section out of a pdftotext -layout dump and
  list its labeled Theorem/Proposition/Lemma/Corollary/Definition items.
- formalize.py: LLM-formalize a section into Lean 4 candidate statements
  (preferring Mathlib vocabulary) plus a definitions manifest.
- check_statements.py: elaboration-only sanity check against a real
  Mathlib-backed Lean project (must run outside the Cowork sandbox, which has
  no Lean toolchain and can't run macOS binaries anyway).
- build_library.py: assemble solved lean-bench results into a reusable .lean
  file, reusing each winning proof verbatim.
- llm.py: standalone OpenAI-compatible chat client + .env loader, kept
  independent of lean_agent so this pipeline works without it installed.
- Source PDFs and raw/layout text dumps are gitignored (copyrighted material);
  only code and the final short Lean statement datasets are tracked.

textbook/extract_section.py

@@ -0,0 +1,73 @@
+"""Slice one book section out of a `pdftotext -layout` dump and list its labeled
+Theorem/Proposition/Lemma/Corollary/Definition statements, as input for formalize.py.
+
+Produces two files: the section's raw text, and a JSON checklist of labeled items
+(kind, label, first line) in book order. The checklist exists so formalize.py's LLM
+step has an explicit inventory to cover and cannot silently skip or invent items.
+"""
+import argparse
+import json
+import re
+from pathlib import Path
+
+LABEL_RE = re.compile(r'^(Definition|Theorem|Proposition|Lemma|Corollary)\s+(\d+\.\d+(?:\.\d+)?)\.?\s*(.*)$')
+
+
+def find_heading_line(lines, heading):
+    for i, line in enumerate(lines):
+        if line.strip() == heading:
+            return i
+    raise ValueError(f'Heading not found: {heading!r}')
+
+
+def extract_section(full_text, start_heading, end_heading):
+    lines = full_text.split('\n')
+    start = find_heading_line(lines, start_heading)
+    end = find_heading_line(lines, end_heading) if end_heading else len(lines)
+    if end <= start:
+        raise ValueError('end_heading must come after start_heading')
+    return '\n'.join(lines[start:end])
+
+
+def labeled_statements(section_text, section_prefix):
+    """Unique labeled items in section_text whose label starts with section_prefix
+    (e.g. '1.6.'), keeping only the first occurrence of each label: later matches are
+    almost always proof continuations across a page break or cross-references, not new
+    statements. Returned sorted in book order (numeric, not lexical)."""
+    seen = {}
+    for line in section_text.split('\n'):
+        line = line.strip()
+        m = LABEL_RE.match(line)
+        if not m:
+            continue
+        kind, label, rest = m.group(1), m.group(2), m.group(3)
+        if not label.startswith(section_prefix) or label in seen:
+            continue
+        seen[label] = {"kind": kind, "label": label, "first_line": line[:120]}
+
+    def sort_key(item):
+        return tuple(int(p) for p in item['label'].split('.'))
+
+    return sorted(seen.values(), key=sort_key)
+
+
+def main():
+    parser = argparse.ArgumentParser(description='Slice one section out of a pdftotext -layout dump')
+    parser.add_argument('layout_txt', type=Path)
+    parser.add_argument('--start-heading', required=True, help="e.g. '1.6. Divisibility in the Integers'")
+    parser.add_argument('--end-heading', help="e.g. '1.7. Modular Arithmetic'; omit for end of file")
+    parser.add_argument('--section-prefix', required=True, help="e.g. '1.6.'")
+    parser.add_argument('--out-text', type=Path, required=True)
+    parser.add_argument('--out-index', type=Path, required=True)
+    args = parser.parse_args()
+
+    full_text = args.layout_txt.read_text(encoding='utf-8')
+    section_text = extract_section(full_text, args.start_heading, args.end_heading)
+    args.out_text.write_text(section_text, encoding='utf-8')
+    index = labeled_statements(section_text, args.section_prefix)
+    args.out_index.write_text(json.dumps(index, ensure_ascii=False, indent=2) + '\n', encoding='utf-8')
+    print(f'{len(index)} labeled statements -> {args.out_index}')
+
+
+if __name__ == '__main__':
+    main()