CCL allreduce: rename to lrab_hierarchical_allreduce + descriptive plots

Rename the intercube all-reduce identity to lrab_hierarchical_allreduce
(module, config key, distributed test) so the name reflects both levels
it implements: LRAB intra-SIP (local reduce to center root + broadcast)
and the hierarchical inter-SIP topology exchange (ring/torus/mesh).
ADR-0032 slug kept as the stable decision id; pure rename, no logic change.

Also in this batch:
- ADR-0032 (EN+KO): document the shipped center-root bidirectional reduce
  (doc was stale corner-root); annotate ccl.yaml root_cube as a placeholder.
- Rename allreduce + pe2pe latency plots to descriptive, title-matching
  filenames and retitle the in-plot headings; drop overview/overview_log.
- Point the PPTX image refs at the new plot names.

Doc + derived-artifact + rename only; no simulation behavior changed.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

tests/test_distributed_lrab_hierarchical_allreduce.py

@@ -0,0 +1,119 @@
+"""End-to-end distributed test for intercube allreduce.
+
+Exercises the full process-group path:
+    dist.init_process_group(backend="ahbm")
+    → mp.spawn(nprocs=n_sips)
+    → each worker: set_device → allocate → fill → dist.all_reduce → verify
+
+This is the same flow a real DDP training script would use.
+"""
+from __future__ import annotations
+
+import os
+import textwrap
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+TOPOLOGY_PATH = Path(__file__).parent.parent / "topology.yaml"
+
+N_CUBES = 16
+N_ELEM = 8
+
+
+def _write_ccl_yaml(tmp_path) -> str:
+    body = textwrap.dedent("""\
+        defaults:
+          algorithm: lrab_hierarchical_allreduce
+          buffer_kind: tcm
+          backpressure: sleep
+          n_slots: 4
+          slot_size: 4096
+          vc_chunk_size: 256
+          ipcq_credit_size_bytes: 16
+
+        algorithms:
+          lrab_hierarchical_allreduce:
+            module: kernbench.ccl.algorithms.lrab_hierarchical_allreduce
+            topology: none
+            buffer_kind: tcm
+            n_elem: 8
+            root_cube: 15
+    """)
+    (tmp_path / "ccl.yaml").write_text(body)
+    return str(tmp_path)
+
+
+def _worker(rank: int, n_sips: int, torch) -> None:
+    """Per-SIP worker: allocate, fill, all_reduce, verify."""
+    from kernbench.policy.placement.dp import DPPolicy
+
+    torch.ahbm.set_device(rank)
+
+    dp = DPPolicy(
+        cube="row_wise", pe="replicate",
+        num_pes=1, num_cubes=N_CUBES,
+    )
+    tensor = torch.zeros(
+        (N_CUBES, N_ELEM), dtype="f16", dp=dp,
+        name=f"sip{rank}",
+    )
+
+    init_arr = np.full((N_CUBES, N_ELEM), float(rank + 1), dtype=np.float16)
+    tensor.copy_(torch.from_numpy(init_arr))
+
+    print(f"[SIP {rank}] input  cube0[:4] = {tensor.numpy()[0][:4].tolist()}")
+
+    torch.distributed.all_reduce(tensor, op="sum")
+
+    arr = tensor.numpy()
+    expected = float(N_CUBES * sum(range(1, n_sips + 1)))
+
+    print(f"[SIP {rank}] output cube0[:4]  = {arr[0][:4].tolist()}")
+    print(f"[SIP {rank}] output cube15[:4] = {arr[15][:4].tolist()}")
+
+    for cube_id in range(N_CUBES):
+        assert np.allclose(arr[cube_id], expected, rtol=1e-1, atol=1e-1), (
+            f"SIP{rank} cube {cube_id}: "
+            f"got {arr[cube_id][:4]}, expected {expected}"
+        )
+
+    if rank == 0:
+        print(f"\n  lrab_hierarchical_allreduce (ws={n_sips}): "
+              f"{n_sips * N_CUBES} OK")
+
+
+def test_distributed_lrab_hierarchical_allreduce(tmp_path, monkeypatch):
+    """Full distributed path: init_process_group → mp.spawn → all_reduce."""
+    from kernbench.runtime_api.context import RuntimeContext
+    from kernbench.runtime_api.types import DeviceSelector
+    from kernbench.sim_engine.engine import GraphEngine
+    from kernbench.topology.builder import resolve_topology
+
+    monkeypatch.chdir(_write_ccl_yaml(tmp_path))
+
+    topo = resolve_topology(str(TOPOLOGY_PATH))
+    engine = GraphEngine(topo.topology_obj, enable_data=True)
+    spec = topo.topology_obj.spec
+    n_sips = int(spec["system"]["sips"]["count"])
+
+    with RuntimeContext(
+        engine=engine,
+        target_device=DeviceSelector("all"),
+        correlation_id="dist_intercube_ar",
+        spec=spec,
+    ) as ctx:
+        ctx.distributed.init_process_group(backend="ahbm")
+
+        assert ctx.distributed.get_world_size() == n_sips
+
+        t_start = engine._env.now
+
+        ctx.multiprocessing.spawn(
+            _worker, args=(n_sips, ctx), nprocs=n_sips,
+        )
+
+        t_end = engine._env.now
+        print(f"\n[distributed] sim latency = "
+              f"{t_end - t_start:.1f} ns ({(t_end - t_start) / 1000:.3f} us)")