5f: Phase 1b.2 — Formulate runner wires to arborist.qa.parse_claims (live)

First sub-battery to bridge from synthetic gold output to actual
organism behavior. run_formulate now supports two fixture modes
selected per-task:

- Embedded (Phase 1a): produced_lattice in the fixture. 10 seed
  fixtures continue to pass via this path.
- Live (Phase 1b.2): only input_text in the fixture; runner calls
  arborist.qa.parse_claims.parse_pointer_claims(input_text) and
  matches the live output against expected_lattice.

Embedded takes precedence if both fields are present. Per-task
detail.source ("embedded" | "live") surfaces in bench output so
synthetic vs live signal is distinguishable.

Surface:

- bench/batteries/b_5f.py — _live_produced_lattice helper +
  two-mode dispatch in run_formulate
- bench/fixtures/5f/formulate-live-v1.jsonl — 15 live-mode fixtures
  with input_text + expected_lattice (no produced_lattice)
- Makefile: bench-5f-formulate-live target
- Tests: 4 new in tests/test_bench_batteries.py
  - live path routes through real parser, all 15 pass
  - embedded path still works (10 Phase-1a fixtures)
  - _live_produced_lattice helper directly verifies parse output
  - fixture missing both fields fails cleanly with explanatory reason

Phase 1a fixture digests unchanged. _DEFAULT_FIXTURES still points
at formulate-v1.jsonl so `runner --all` behavior is identical;
live-mode fixtures invoked via explicit --fixtures path.

Full suite: 1196 passed, 36 skipped.

Pattern set. Function/Finetuning/Falsification/Feedback Loop
follow in subsequent commits.

tests/test_bench_batteries.py

@@ -413,6 +413,61 @@ def test_capital_cost_delta_handles_missing_budget():
     }) == 5.0
 
 
+# --- 5F Phase 1b.2 — Formulate live wire-up ---------------------
+
+
+def test_5f_formulate_live_path_routes_through_parse_claims():
+    """The new formulate-live-v1.jsonl fixtures use input_text only;
+    runner derives produced_lattice via parse_pointer_claims and
+    matches against expected_lattice."""
+    res = b_5f.run_formulate(F5F / "formulate-live-v1.jsonl")
+    assert res.pass_count == 15
+    assert res.metrics["structural_match_rate"] == 1.0
+    # Every task ran through the live path.
+    for t in res.per_task:
+        assert t.detail["source"] == "live"
+
+
+def test_5f_formulate_embedded_path_still_works():
+    """Phase 1a fixtures (embedded produced_lattice) keep working
+    after the Phase 1b.2 wire-up. Backward compat invariant."""
+    res = b_5f.run_formulate(F5F / "formulate-v1.jsonl")
+    assert res.pass_count == 10
+    for t in res.per_task:
+        assert t.detail["source"] == "embedded"
+
+
+def test_5f_formulate_live_helper_uses_real_arborist_parser(tmp_path):
+    """The live path actually calls
+    arborist.qa.parse_claims.parse_pointer_claims — not a stub."""
+    from bench.batteries.b_5f import _live_produced_lattice
+
+    out = _live_produced_lattice("- Hello world. [E1]\n- Second one. [E2]")
+    assert out["claims"][0]["claim_text"] == "Hello world."
+    assert out["claims"][0]["pointer_ids"] == ["E1"]
+    assert out["claims"][1]["claim_text"] == "Second one."
+    assert out["claims"][1]["pointer_ids"] == ["E2"]
+
+
+def test_5f_formulate_rejects_fixture_with_neither_field(tmp_path):
+    """Task without produced_lattice OR input_text → fails cleanly."""
+    p = tmp_path / "bad.jsonl"
+    p.write_text(
+        json.dumps({"_meta": {"battery": "5f", "sub_battery": "formulate", "version": "v1"}}) + "\n" +
+        json.dumps({
+            "id": "test",
+            "carrier": "text",
+            "domain": "claim_lattice",
+            "pi_star_ref": "claim-lattice@v1",
+            "expected_lattice": {"claim_count": 0, "claims": []},
+        }) + "\n",
+        encoding="utf-8",
+    )
+    res = b_5f.run_formulate(p)
+    assert res.fail_count == 1
+    assert "produced_lattice" in res.per_task[0].detail["reason"]
+
+
 # --- 5R Phase 2 (#000021) ----------------------------------------