Rebuild lean-bench: pages in, verified indexed Lean out

Replaces the previous tree entirely. The pipeline is four separable pieces, each
testable on its own:

1. leanbench/llm.py      provider-neutral OpenAI-compatible connector, stdlib only,
                        with retries, JSON coercion and a scripted client so the
                        rest of the code is testable without a network.
2. leanbench/detect.py   per-page detection of formalizable mathematics. Case 1 is
                        mathematics asserted as fact (definition/theorem/lemma/...,
                        deliberately not sub-classified); case 2 is a problem left
                        open to the reader. Hits come back as spans -- start page
                        and index, end page and index -- so several per page is
                        normal. A hit cut off by the page end makes the detector
                        re-read that page together with the next, repeatedly, so an
                        item spread over three pages is found whole.
                        Offsets come from verbatim quotes resolved by
                        leanbench/anchors.py (exact -> whitespace-insensitive ->
                        fuzzy), because models quote well and count badly.
3. leanbench/formalize.py + leanbench/verify.py
                        each span becomes one Lean 4 declaration, judged by the real
                        compiler: full elaboration for case 1, statement legality
                        only for case 2, which has no proof to check. Lean's own
                        diagnostics feed back for a repair attempt. "verified" (Lean
                        accepted it) and "proved" (accepted with no sorry) are kept
                        strictly apart.
4. leanbench/db.py       indexed SQLite plus JSONL export. Every item is indexed by
                        the types of its inputs, or by its own type when it is not a
                        proof, and records the source book (sha256) and the page it
                        starts on -- so `drop --source H --pages A-B` followed by a
                        re-ingest redoes exactly those pages and nothing else.

Infrastructure:

- lean/            Lake project pinned to Mathlib.
- docker/          image carrying Lean 4 and a prebuilt Mathlib. The Mathlib
                   revision and the toolchain are resolved against each other at
                   build time rather than both hardcoded, so the build does not rot.
                   docker/smoke.py runs the whole pipeline inside the image against
                   the real compiler, with the LLM scripted.
- .gitea/workflows ci (lint + tests in a venv, since the runner image's Python is
                   Debian-managed and refuses installs into itself), docker (build,
                   verify, optionally push), ingest (submit a book by hand).

The docker workflow is not a throwaway build: it leaves the image, the layer cache,
an idle `lean-bench` container and the `lean-bench-data` / `lean-bench-books`
volumes in place on the runner, and never prunes, so the environment is there to be
used afterwards. Pushing to the registry is optional and cannot fail the build --
Gitea's container registry does not accept the built-in Actions token, so that needs
a REGISTRY_TOKEN secret with write:package.

58 tests; they need neither network nor Lean.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Ci5T3gWDhhmqDec3e1XtYZ

tests/test_typeindex.py

@@ -0,0 +1,81 @@
+from __future__ import annotations
+
+from leanbench.typeindex import ROLE_GOAL, ROLE_INPUT, ROLE_OWN, index_types, parse_signature
+
+
+def test_theorem_is_indexed_by_the_types_of_its_inputs() -> None:
+    code = "theorem add_dvd (a b c : Int) (h : a ∣ b) (k : a ∣ c) : a ∣ b + c := by\n  sorry"
+    signature = parse_signature(code)
+    assert signature is not None
+    assert signature.is_proof
+    assert signature.name == "add_dvd"
+    assert "Int" in signature.inputs
+    pairs = index_types(code)
+    assert ("Int", ROLE_INPUT) in pairs
+
+
+def test_definition_is_indexed_by_its_own_type() -> None:
+    code = "def divides (a b : Int) : Prop := ∃ k : Int, b = a * k"
+    signature = parse_signature(code)
+    assert signature is not None
+    assert not signature.is_proof
+    pairs = index_types(code)
+    assert ("Int", ROLE_INPUT) in pairs
+    assert ("Prop", ROLE_OWN) in pairs, "a predicate's own type is the point of it"
+    assert all(role != ROLE_GOAL for _, role in pairs)
+
+
+def test_a_proof_is_not_indexed_by_Prop() -> None:
+    pairs = index_types("theorem t (n : Nat) : n = n := rfl")
+    assert all(name != "Prop" for name, _ in pairs)
+
+
+def test_definition_of_a_concrete_type_records_it() -> None:
+    pairs = index_types("def double (n : Nat) : Nat := 2 * n")
+    assert ("Nat", ROLE_OWN) in pairs
+
+
+def test_instance_binders_count_as_inputs() -> None:
+    code = "theorem foo {G : Type*} [Group G] (x : G) : x * 1 = x := by simp"
+    signature = parse_signature(code)
+    assert signature is not None
+    assert "Group" in signature.inputs
+
+
+def test_unicode_number_types_are_normalised() -> None:
+    code = "theorem sq_nonneg' (n : ℤ) : 0 ≤ n ^ 2 := by positivity"
+    pairs = dict(index_types(code))
+    assert pairs.get("Int") == ROLE_INPUT
+
+
+def test_structure_records_its_own_type() -> None:
+    code = "structure Monoid' (M : Type) : Type where\n  one : M"
+    signature = parse_signature(code)
+    assert signature is not None
+    assert signature.keyword == "structure"
+    assert signature.own or signature.inputs
+
+
+def test_model_supplied_types_are_merged_without_duplicates() -> None:
+    code = "theorem t (n : Nat) : n = n := rfl"
+    pairs = index_types(code, ["Nat", "Polynomial", "  "])
+    names = [name for name, _ in pairs]
+    assert names.count("Nat") == 1
+    assert "Polynomial" in names
+
+
+def test_comments_do_not_leak_into_the_index() -> None:
+    code = "-- about Matrix stuff\n/- Group -/\ntheorem t (n : Nat) : n = n := rfl"
+    names = [name for name, _ in index_types(code)]
+    assert "Matrix" not in names and "Group" not in names
+
+
+def test_declaration_keyword_detected_after_attributes() -> None:
+    code = "@[simp]\nprivate theorem t (n : Nat) : n = n := rfl"
+    signature = parse_signature(code)
+    assert signature is not None and signature.keyword == "theorem"
+
+
+def test_unparsable_code_yields_nothing_rather_than_nonsense() -> None:
+    assert parse_signature("this is not lean") is None
+    assert index_types("this is not lean") == []