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_formalize.py

@@ -0,0 +1,90 @@
+from __future__ import annotations
+
+from leanbench.detect import KIND_PROBLEM, KIND_STATEMENT, Detection
+from leanbench.formalize import formalize, formalize_all, verification_mode
+from leanbench.llm import ScriptedClient
+from leanbench.verify import MODE_FULL, MODE_STATEMENT
+
+from .conftest import formalize_reply
+
+
+def make_detection(kind: str = KIND_STATEMENT) -> Detection:
+    return Detection(
+        kind=kind,
+        label="Theorem 1.6.2",
+        summary="divisibility is additive",
+        start_page=12,
+        start_index=100,
+        end_page=12,
+        end_index=260,
+        text="Theorem 1.6.2. If a divides b and a divides c then a divides b + c.",
+    )
+
+
+def test_open_problems_are_only_checked_as_statements() -> None:
+    assert verification_mode(make_detection(KIND_PROBLEM)) == MODE_STATEMENT
+    assert verification_mode(make_detection(KIND_STATEMENT)) == MODE_FULL
+
+
+def test_formalize_produces_verified_code_and_types(fake_checker) -> None:
+    client = ScriptedClient([formalize_reply()])
+    result = formalize(client, make_detection(), checker=fake_checker)
+    assert result.lean_code.startswith("theorem test_decl")
+    assert result.verified
+    assert not result.proved, "a sorry in the code means it is not proved"
+    assert ("Int", "input") in result.index_types
+
+
+def test_a_real_proof_counts_as_proved(fake_checker) -> None:
+    client = ScriptedClient(
+        [formalize_reply(lean_code="theorem t (n : Nat) : n = n := rfl", has_proof=True)]
+    )
+    result = formalize(client, make_detection(), checker=fake_checker)
+    assert result.has_proof and result.proved
+
+
+def test_lean_diagnostics_drive_a_repair_attempt(fake_checker) -> None:
+    client = ScriptedClient(
+        [
+            formalize_reply(lean_code="theorem t : BAD := by sorry"),
+            formalize_reply(lean_code="theorem t (n : Nat) : n = n := rfl", has_proof=True),
+        ]
+    )
+    result = formalize(client, make_detection(), checker=fake_checker, repair_attempts=1)
+    assert result.attempts == 2
+    assert result.verified
+    assert len(client.calls) == 2
+    repair_prompt = client.calls[1][-1]["content"]
+    assert "error: bad" in repair_prompt, "the compiler's own words go back to the model"
+
+
+def test_repair_gives_up_after_the_budget(fake_checker) -> None:
+    client = ScriptedClient([formalize_reply(lean_code="theorem t : BAD := by sorry")] * 3)
+    result = formalize(client, make_detection(), checker=fake_checker, repair_attempts=1)
+    assert result.attempts == 2
+    assert not result.verified
+
+
+def test_model_may_decline_an_unformalizable_passage(fake_checker) -> None:
+    client = ScriptedClient(['{"skip": true, "reason": "prose only"}'])
+    result = formalize(client, make_detection(), checker=fake_checker)
+    assert result.skipped and result.skip_reason == "prose only"
+    assert fake_checker.calls == []
+
+
+def test_imports_inside_the_body_are_stripped(fake_checker) -> None:
+    client = ScriptedClient(
+        [formalize_reply(lean_code="import Mathlib\ntheorem t (n : Nat) : n = n := rfl")]
+    )
+    result = formalize(client, make_detection(), checker=fake_checker)
+    assert "import" not in result.lean_code
+
+
+def test_one_bad_item_does_not_stop_the_batch(fake_checker) -> None:
+    client = ScriptedClient(["garbage, not json", formalize_reply()])
+    results = formalize_all(
+        client, [make_detection(), make_detection(KIND_PROBLEM)], checker=fake_checker
+    )
+    assert len(results) == 2
+    assert results[0].skipped and "formalizer failed" in results[0].skip_reason
+    assert results[1].verified