diff --git a/ccl.yaml b/ccl.yaml
index 24c6b3f..bd0211d 100644
--- a/ccl.yaml
+++ b/ccl.yaml
@@ -6,7 +6,7 @@
 
 defaults:
   # Algorithm to run for this benchmark execution.
-  algorithm: intercube_allreduce
+  algorithm: lrab_hierarchical_allreduce
 
   # IPCQ ring buffer location.
   #   tcm  — PE-local TCM (fast, small, conflicts with compute TCM access)
@@ -37,9 +37,14 @@ algorithms:
   # exchange on root cube, then broadcast back. SIP topology is read
   # from topology.yaml → system.sips.topology. Kernel auto-selects
   # ring / torus / mesh inter-SIP exchange pattern.
-  intercube_allreduce:
-    module: kernbench.ccl.algorithms.intercube_allreduce
+  lrab_hierarchical_allreduce:
+    module: kernbench.ccl.algorithms.lrab_hierarchical_allreduce
     topology: none
     buffer_kind: tcm
     n_elem: 8
+    # root_cube: the kernel currently elects the root dynamically as the
+    # geometric center of the cube mesh (root = (h//2)*w + (w//2)) to
+    # minimize the intra-SIP critical path, so this value is NOT read today.
+    # Kept as a placeholder for a future explicit-root override / runtime
+    # election hook (see ADR-0032 D1 + Non-goals).
     root_cube: 15
diff --git a/docs/adr-ko/ADR-0032-algo-intercube-allreduce.md b/docs/adr-ko/ADR-0032-algo-intercube-allreduce.md
index f89dd77..c5e5689 100644
--- a/docs/adr-ko/ADR-0032-algo-intercube-allreduce.md
+++ b/docs/adr-ko/ADR-0032-algo-intercube-allreduce.md
@@ -31,7 +31,7 @@ pe0만의 same-lane 큐브 간 reduce**, 그 다음 루트 큐브에서 SIP 간
 
 ### 현재 상태
 
-- `src/kernbench/ccl/algorithms/intercube_allreduce.py` — 커널
+- `src/kernbench/ccl/algorithms/lrab_hierarchical_allreduce.py` — 커널
 - `src/kernbench/ccl/sfr_config.py` — `configure_sfr_intercube_multisip`
 - `src/kernbench/runtime_api/distributed.py` — `AhbmCCLBackend`가
   `init_process_group` 시점에 자동으로 와이어링한다.
@@ -42,29 +42,46 @@ pe0만의 same-lane 큐브 간 reduce**, 그 다음 루트 큐브에서 SIP 간
 
 ## Decision
 
-### D1. 알고리즘 구조 — 5단계
+### D1. 알고리즘 구조 — 5단계 (center-root, 양방향)
+
+루트 큐브는 큐브 메시의 기하학적 **중심**에 위치한다:
+
+```
+root_col  = cube_w // 2
+root_row  = cube_h // 2
+root_cube = root_row * cube_w + root_col   # 중심; 4×4 메시에서 10
+```
+
+각 reduce/broadcast 단계는 이 중심을 향해 **양방향으로** 수렴/발산하여,
+corner-root 워크 대비 SIP 내부 임계 경로를 절반으로 줄인다 (4×4 메시:
+reduce 4홉 + broadcast 4홉 vs SE-코너 루트의 6+6).
 
 각 SIP에 대해 (`mp.spawn`으로 동시에 launch):
 
 ```
-Phase 1 — Row reduce W → E (큐브 메시, pe0만):
-    col=0이 E로 송신 → col=1이 누적, E로 송신 → ... → col=3이 row sum 보유.
+Phase 1 — col == root_col에서 수렴하는 Row reduce (큐브 메시, pe0만):
+    좌측 절반(col < root_col)은 W→E로, 우측 절반(col > root_col)은
+    E→W로 진행; root_col 큐브가 양쪽을 병합 → row sum 보유.
 
-Phase 2 — 최우측 열에서 Col reduce N → S (pe0, col = mesh_w-1):
-    row=0이 S로 송신 → row=1이 누적, S로 송신 → ... → 루트 큐브 (15)가
-    전체 SIP sum 보유.
+Phase 2 — col == root_col에서 row == root_row로 수렴하는 Col reduce:
+    위쪽(row < root_row)은 N→S로, 아래쪽(row > root_row)은 S→N로 진행;
+    루트 큐브가 양쪽을 병합 → 전체 SIP sum 보유.
 
-Phase 3 — 루트 큐브에서 SIP 간 교환 (루트 큐브의 pe0만):
+Phase 3 — cube_id == root_cube에서 SIP 간 교환 (pe0만):
     Ring / torus-2d row+col ring / mesh-2d chain reduce+broadcast —
     sip_topo_kind(topology.yaml의 sips.topology)로 선택.
 
-Phase 4 — 최우측 열에서 Col 브로드캐스트 S → N.
+Phase 4 — col == root_col에서 root_row로부터 바깥쪽으로 Col 브로드캐스트.
 
-Phase 5 — 큐브 메시 전반에 걸친 Row 브로드캐스트 E → W.
+Phase 5 — root_col로부터 바깥쪽으로 큐브 메시 전반에 Row 브로드캐스트.
 ```
 
 모든 단계가 끝나면 모든 큐브의 pe0이 전역 sum을 보유한다.
 
+**단일 큐브 fast-path**: `cube_w == cube_h == 1`(rank당 큐브 하나, 일반적인
+TP 케이스)인 경우 SIP 내부 reduce/broadcast 단계를 건너뛰고 곧바로
+Phase 3 SIP 간 교환으로 진행한다.
+
 커널은 `sip_topo_kind ∈ {0, 1, 2}`(ring_1d, torus_2d, mesh_2d_no_wrap)로
 파라미터화된 단일 함수이다. Phase 1-2와 4-5는 토폴로지 전반에서 동일하며,
 phase 3만 분기한다. 헬퍼 함수 `_inter_sip_ring`, `_inter_sip_torus_2d`,
@@ -152,17 +169,19 @@ system:
 
 ```yaml
 defaults:
-  algorithm: intercube_allreduce
+  algorithm: lrab_hierarchical_allreduce
   buffer_kind: tcm
   ...
 
 algorithms:
-  intercube_allreduce:
-    module: kernbench.ccl.algorithms.intercube_allreduce
+  lrab_hierarchical_allreduce:
+    module: kernbench.ccl.algorithms.lrab_hierarchical_allreduce
     topology: none
     buffer_kind: tcm
     n_elem: 8
-    root_cube: 15
+    root_cube: 15   # 현재 사용되지 않음 — 커널이 루트를 기하학적 중심으로
+                    # 동적으로 선출한다 (D1 참조). 향후 명시적 루트 override /
+                    # 런타임 선출 훅을 위한 placeholder로 유지한다.
 ```
 
 `topology.yaml`:
@@ -205,10 +224,11 @@ sip:
 - **비대칭 SIP 토폴로지** (정사각형이 아닌 메시/토러스).
   `torus_2d`와 `mesh_2d_no_wrap`은 `n_sips = k²`를 요구한다.
 - **파이프라인 청크**: 큐브당 단일 타일, 아직 파이프라이닝 없음.
-- **루트 큐브의 런타임 선출**: 커널은 현재 SE 코너로 하드코딩된
-  `root_cube = (mesh_h - 1) * mesh_w + (mesh_w - 1)`을 사용한다. SFR
-  와이어링이 모든 큐브를 커버하므로, 필요해질 때 런타임 선출은 순수
-  커널 변경이다.
+- **루트 큐브의 런타임 선출**: 커널은 현재 SIP 내부 임계 경로를
+  최소화하기 위해 기하학적 중심인
+  `root_cube = (mesh_h // 2) * mesh_w + (mesh_w // 2)`을 사용한다. SFR
+  와이어링이 모든 큐브를 커버하므로, 필요해질 때 다른 루트를 런타임에
+  선출하는 것은 순수 커널 변경이다.
 
 ---
 
@@ -241,15 +261,15 @@ sip:
 
 | File | Change |
 |---|---|
-| `src/kernbench/ccl/algorithms/intercube_allreduce.py` (신규) | 커널 + `_inter_sip_*` 헬퍼 + `TOPO_NAME_TO_KIND` |
+| `src/kernbench/ccl/algorithms/lrab_hierarchical_allreduce.py` (신규) | 커널 + `_inter_sip_*` 헬퍼 + `TOPO_NAME_TO_KIND` |
 | `src/kernbench/ccl/sfr_config.py` (신규) | `configure_sfr_intercube_multisip` |
 | `src/kernbench/ccl/topologies.py` | `torus_2d`, `mesh_2d_no_wrap` 추가 |
 | `src/kernbench/ccl/install.py` | `_OPPOSITE_DIR`을 `global_*` 쌍으로 확장 |
 | `src/kernbench/runtime_api/distributed.py` | `AhbmCCLBackend`가 `configure_sfr_intercube_multisip` 사용 + sip_rank/topo 인자 추가 |
-| `ccl.yaml` | 단일 `intercube_allreduce` 항목 |
+| `ccl.yaml` | 단일 `lrab_hierarchical_allreduce` 항목 |
 | `topology.yaml` | `system.sips.topology` 추가 |
 | `benches/ccl_allreduce.py` | Row-wise 큐브-메시 텐서 레이아웃 |
 | `tests/test_allreduce_multidevice.py` (신규) | 구성 기반 ring/torus/mesh |
-| `tests/test_distributed_intercube_allreduce.py` (신규) | 전체 `dist.all_reduce` 경로 |
+| `tests/test_distributed_lrab_hierarchical_allreduce.py` (신규) | 전체 `dist.all_reduce` 경로 |
 | `tests/test_intercube_sfr_config.py` (신규) | SFR 와이어링 검증 |
 | 제거 | `ring_allreduce.py`, `mesh_allreduce.py`, `tree_allreduce.py`, `hierarchical_allreduce.py`, `hello_send.py`, `testing.py` 및 그 테스트 |
diff --git a/docs/adr/ADR-0032-algo-intercube-allreduce.md b/docs/adr/ADR-0032-algo-intercube-allreduce.md
index bb6ba3c..3171cd7 100644
--- a/docs/adr/ADR-0032-algo-intercube-allreduce.md
+++ b/docs/adr/ADR-0032-algo-intercube-allreduce.md
@@ -32,7 +32,7 @@ bandwidth characteristics for the common per-cube DP workload.
 
 ### Current state
 
-- `src/kernbench/ccl/algorithms/intercube_allreduce.py` — kernel
+- `src/kernbench/ccl/algorithms/lrab_hierarchical_allreduce.py` — kernel
 - `src/kernbench/ccl/sfr_config.py` — `configure_sfr_intercube_multisip`
 - `src/kernbench/runtime_api/distributed.py` — `AhbmCCLBackend` wires this
   automatically at `init_process_group` time.
@@ -43,29 +43,46 @@ bandwidth characteristics for the common per-cube DP workload.
 
 ## Decision
 
-### D1. Algorithm structure — 5 phases
+### D1. Algorithm structure — 5 phases (center-root, bidirectional)
+
+The root cube sits at the geometric **center** of the cube mesh:
+
+```
+root_col  = cube_w // 2
+root_row  = cube_h // 2
+root_cube = root_row * cube_w + root_col   # center; 10 on a 4×4 mesh
+```
+
+Each reduce/broadcast phase converges/diverges **bidirectionally** toward
+this center, halving the intra-SIP critical path versus a corner-root walk
+(4×4 mesh: 4 hops reduce + 4 hops broadcast vs 6+6 with an SE-corner root).
 
 For each SIP (launched concurrently by `mp.spawn`):
 
 ```
-Phase 1 — Row reduce W → E (cube mesh, pe0 only):
-    col=0 sends E → col=1 accumulates, sends E → ... → col=3 holds row sum.
+Phase 1 — Row reduce converging at col == root_col (cube mesh, pe0 only):
+    left half (col < root_col) walks W→E; right half (col > root_col)
+    walks E→W; the root_col cube merges both sides → holds row sum.
 
-Phase 2 — Col reduce N → S on rightmost column (pe0, col = mesh_w-1):
-    row=0 sends S → row=1 accumulates, sends S → ... → root cube (15)
-    holds the full SIP sum.
+Phase 2 — Col reduce on col == root_col converging at row == root_row:
+    above (row < root_row) walks N→S; below (row > root_row) walks S→N;
+    the root cube merges both → holds the full SIP sum.
 
-Phase 3 — Inter-SIP exchange on root cube (pe0 of root cube only):
+Phase 3 — Inter-SIP exchange on cube_id == root_cube (pe0 only):
     Ring / torus-2d row+col ring / mesh-2d chain reduce+broadcast —
     selected by sip_topo_kind (from topology.yaml sips.topology).
 
-Phase 4 — Col broadcast S → N on rightmost column.
+Phase 4 — Col broadcast on col == root_col, outward from root_row.
 
-Phase 5 — Row broadcast E → W across the cube mesh.
+Phase 5 — Row broadcast outward from root_col across the cube mesh.
 ```
 
 After all phases every cube's pe0 holds the global sum.
 
+**Single-cube fast-path**: when `cube_w == cube_h == 1` (one cube per rank,
+the common TP case), the intra-SIP reduce/broadcast phases are skipped and
+the kernel goes straight to the Phase 3 inter-SIP exchange.
+
 The kernel is a single function parameterised by `sip_topo_kind ∈ {0, 1, 2}`
 (ring_1d, torus_2d, mesh_2d_no_wrap). Phases 1-2 and 4-5 are identical
 across topologies; only phase 3 branches. Helper functions
@@ -154,17 +171,19 @@ At each `dist.all_reduce(tensor)` call:
 
 ```yaml
 defaults:
-  algorithm: intercube_allreduce
+  algorithm: lrab_hierarchical_allreduce
   buffer_kind: tcm
   ...
 
 algorithms:
-  intercube_allreduce:
-    module: kernbench.ccl.algorithms.intercube_allreduce
+  lrab_hierarchical_allreduce:
+    module: kernbench.ccl.algorithms.lrab_hierarchical_allreduce
     topology: none
     buffer_kind: tcm
     n_elem: 8
-    root_cube: 15
+    root_cube: 15   # NOT read today — the kernel elects the root dynamically
+                    # as the geometric center (see D1). Kept as a placeholder
+                    # for a future explicit-root override / runtime election.
 ```
 
 `topology.yaml`:
@@ -207,9 +226,10 @@ Modules loaded via `cfg["module"]` must export:
   `mesh_2d_no_wrap` require `n_sips = k²`.
 - **Pipelined chunks**: single-tile per cube, no pipelining yet.
 - **Root cube runtime election**: the kernel currently uses
-  `root_cube = (mesh_h - 1) * mesh_w + (mesh_w - 1)` hardcoded to the SE
-  corner. SFR wiring covers all cubes, so runtime election is a pure kernel
-  change when needed.
+  `root_cube = (mesh_h // 2) * mesh_w + (mesh_w // 2)` — the geometric
+  center, chosen to minimize the intra-SIP critical path. SFR wiring
+  covers all cubes, so electing a different root at runtime is a pure
+  kernel change when needed.
 
 ---
 
@@ -242,15 +262,15 @@ Modules loaded via `cfg["module"]` must export:
 
 | File | Change |
 |---|---|
-| `src/kernbench/ccl/algorithms/intercube_allreduce.py` (new) | Kernel + `_inter_sip_*` helpers + `TOPO_NAME_TO_KIND` |
+| `src/kernbench/ccl/algorithms/lrab_hierarchical_allreduce.py` (new) | Kernel + `_inter_sip_*` helpers + `TOPO_NAME_TO_KIND` |
 | `src/kernbench/ccl/sfr_config.py` (new) | `configure_sfr_intercube_multisip` |
 | `src/kernbench/ccl/topologies.py` | Added `torus_2d`, `mesh_2d_no_wrap` |
 | `src/kernbench/ccl/install.py` | Extended `_OPPOSITE_DIR` with `global_*` pairs |
 | `src/kernbench/runtime_api/distributed.py` | `AhbmCCLBackend` uses `configure_sfr_intercube_multisip` + appends sip_rank/topo args |
-| `ccl.yaml` | Single `intercube_allreduce` entry |
+| `ccl.yaml` | Single `lrab_hierarchical_allreduce` entry |
 | `topology.yaml` | Added `system.sips.topology` |
 | `benches/ccl_allreduce.py` | Row-wise cube-mesh tensor layout |
 | `tests/test_allreduce_multidevice.py` (new) | Config-driven ring/torus/mesh |
-| `tests/test_distributed_intercube_allreduce.py` (new) | Full `dist.all_reduce` path |
+| `tests/test_distributed_lrab_hierarchical_allreduce.py` (new) | Full `dist.all_reduce` path |
 | `tests/test_intercube_sfr_config.py` (new) | SFR wiring verification |
 | Removed | `ring_allreduce.py`, `mesh_allreduce.py`, `tree_allreduce.py`, `hierarchical_allreduce.py`, `hello_send.py`, `testing.py` and their tests |
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diff --git a/docs/diagrams/pe2pe_latency_plots/summary.csv b/docs/diagrams/pe2pe_latency_plots/summary.csv
index 3b7e0ef..ac08aca 100644
--- a/docs/diagrams/pe2pe_latency_plots/summary.csv
+++ b/docs/diagrams/pe2pe_latency_plots/summary.csv
@@ -1,81 +1,81 @@
 hop,label,size_bytes,path,total_ns
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),128,ipcq,24.88749999999891
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),128,raw,33.57999999999811
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),256,ipcq,28.13749999999891
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),256,raw,36.07999999999811
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),384,ipcq,29.88749999999891
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),384,raw,37.07999999999811
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),512,ipcq,31.63749999999891
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),512,raw,38.07999999999811
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),768,ipcq,35.13749999999891
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),768,raw,40.07999999999811
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),1024,ipcq,38.63749999999891
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),1024,raw,42.07999999999811
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),2048,ipcq,52.63749999999891
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),2048,raw,50.07999999999811
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),4096,ipcq,80.63750000000073
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),4096,raw,66.08000000000175
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),8192,ipcq,136.63750000000073
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),8192,raw,98.08000000000175
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),10240,ipcq,164.63750000000073
-h1_intra_horizontal,Intra-cube horizontal (pe0 to pe1),10240,raw,114.08000000000175
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),128,ipcq,38.49749999999585
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),128,raw,47.18999999999505
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),256,ipcq,43.24749999999585
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),256,raw,51.18999999999505
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),384,ipcq,44.99749999999585
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),384,raw,52.18999999999505
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),512,ipcq,46.74749999999585
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),512,raw,53.18999999999505
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),768,ipcq,50.24749999999585
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),768,raw,55.18999999999505
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),1024,ipcq,53.74749999999585
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),1024,raw,57.18999999999505
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),2048,ipcq,67.74749999999585
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),2048,raw,65.18999999999505
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),4096,ipcq,95.74750000000131
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),4096,raw,81.19000000000233
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),8192,ipcq,151.7475000000013
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),8192,raw,113.19000000000233
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),10240,ipcq,179.7475000000013
-h2_intra_vertical,Intra-cube vertical (pe0 to pe4),10240,raw,129.19000000000233
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),128,ipcq,81.15999999999804
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),128,raw,89.28999999999724
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),256,ipcq,88.65999999999804
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),256,raw,95.53999999999724
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),384,ipcq,90.90999999999804
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),384,raw,96.53999999999724
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),512,ipcq,93.15999999999804
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),512,raw,97.53999999999724
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),768,ipcq,97.65999999999804
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),768,raw,99.53999999999724
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),1024,ipcq,103.15999999999804
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),1024,raw,102.53999999999724
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),2048,ipcq,125.15999999999804
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),2048,raw,114.53999999999724
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),4096,ipcq,169.15999999999985
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),4096,raw,138.54000000000087
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),8192,ipcq,257.15999999999985
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),8192,raw,186.54000000000087
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),10240,ipcq,301.15999999999985
-h3_inter_cube_horizontal,Inter-cube horizontal (cube0 to cube1),10240,raw,210.54000000000087
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),128,ipcq,103.15999999999804
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),128,raw,111.28999999999724
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),256,ipcq,112.65999999999804
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),256,raw,119.53999999999724
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),384,ipcq,114.90999999999804
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),384,raw,120.53999999999724
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),512,ipcq,117.15999999999804
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),512,raw,121.53999999999724
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),768,ipcq,121.65999999999804
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),768,raw,123.53999999999724
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),1024,ipcq,127.15999999999804
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),1024,raw,126.53999999999724
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),2048,ipcq,149.15999999999804
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),2048,raw,138.53999999999724
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),4096,ipcq,193.15999999999985
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),4096,raw,162.54000000000087
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),8192,ipcq,281.15999999999985
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),8192,raw,210.54000000000087
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),10240,ipcq,325.15999999999985
-h4_inter_cube_vertical,Inter-cube vertical (cube0 to cube4),10240,raw,234.54000000000087
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),128,ipcq,24.88749999999891
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),128,raw,33.57999999999811
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),256,ipcq,28.13749999999891
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),256,raw,36.07999999999811
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),384,ipcq,29.88749999999891
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),384,raw,37.07999999999811
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),512,ipcq,31.63749999999891
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),512,raw,38.07999999999811
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),768,ipcq,35.13749999999891
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),768,raw,40.07999999999811
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),1024,ipcq,38.63749999999891
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),1024,raw,42.07999999999811
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),2048,ipcq,52.63749999999891
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),2048,raw,50.07999999999811
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),4096,ipcq,80.63750000000073
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),4096,raw,66.08000000000175
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),8192,ipcq,136.63750000000073
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),8192,raw,98.08000000000175
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),10240,ipcq,164.63750000000073
+latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),10240,raw,114.08000000000175
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),128,ipcq,38.49749999999585
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),128,raw,47.18999999999505
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),256,ipcq,43.24749999999585
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),256,raw,51.18999999999505
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),384,ipcq,44.99749999999585
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),384,raw,52.18999999999505
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),512,ipcq,46.74749999999585
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),512,raw,53.18999999999505
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),768,ipcq,50.24749999999585
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),768,raw,55.18999999999505
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),1024,ipcq,53.74749999999585
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),1024,raw,57.18999999999505
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),2048,ipcq,67.74749999999585
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),2048,raw,65.18999999999505
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),4096,ipcq,95.74750000000131
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),4096,raw,81.19000000000233
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),8192,ipcq,151.7475000000013
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),8192,raw,113.19000000000233
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),10240,ipcq,179.7475000000013
+latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),10240,raw,129.19000000000233
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),128,ipcq,81.15999999999804
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),128,raw,89.28999999999724
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),256,ipcq,88.65999999999804
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),256,raw,95.53999999999724
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),384,ipcq,90.90999999999804
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),384,raw,96.53999999999724
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),512,ipcq,93.15999999999804
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),512,raw,97.53999999999724
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),768,ipcq,97.65999999999804
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),768,raw,99.53999999999724
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),1024,ipcq,103.15999999999804
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),1024,raw,102.53999999999724
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),2048,ipcq,125.15999999999804
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),2048,raw,114.53999999999724
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),4096,ipcq,169.15999999999985
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),4096,raw,138.54000000000087
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),8192,ipcq,257.15999999999985
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),8192,raw,186.54000000000087
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),10240,ipcq,301.15999999999985
+latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),10240,raw,210.54000000000087
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),128,ipcq,103.15999999999804
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),128,raw,111.28999999999724
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),256,ipcq,112.65999999999804
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),256,raw,119.53999999999724
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),384,ipcq,114.90999999999804
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),384,raw,120.53999999999724
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),512,ipcq,117.15999999999804
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),512,raw,121.53999999999724
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),768,ipcq,121.65999999999804
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),768,raw,123.53999999999724
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),1024,ipcq,127.15999999999804
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),1024,raw,126.53999999999724
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),2048,ipcq,149.15999999999804
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),2048,raw,138.53999999999724
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),4096,ipcq,193.15999999999985
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),4096,raw,162.54000000000087
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),8192,ipcq,281.15999999999985
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),8192,raw,210.54000000000087
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),10240,ipcq,325.15999999999985
+latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),10240,raw,234.54000000000087
diff --git a/scripts/build_overview_slides.py b/scripts/build_overview_slides.py
index 8ccfded..c2f6b9a 100644
--- a/scripts/build_overview_slides.py
+++ b/scripts/build_overview_slides.py
@@ -4,8 +4,8 @@ Slides:
   1. Overall architecture — how PEs are connected (cube_mesh_view)
   2. Model correctness — DMA vs P2P latency (pe2pe overview)
   3. PE-to-PE IPCQ communication (ipcq_two_pe_dma)
-  4. 6-device allreduce — model vs theoretical vs ext-sim (overview_broken)
-  5. IPCQ buffer-kind sweep — TCM vs SRAM vs HBM (buffer_kind_sweep)
+  4. 6-device allreduce — model vs theoretical vs FSIM (comparison_…_fsim)
+  5. IPCQ buffer-kind sweep — TCM vs SRAM vs HBM (…_with_TCM_SRAM_HBM)
   6. PE_accelerator data path (composite GEMM pipeline structure)
   7. matmul(32, 128, 32) — composite GEMM execution sequence
   8. matmul(32, 128, 128) — pipeline scaling and HBM contention
@@ -63,7 +63,7 @@ SLIDES = [
     },
     {
         "title": "4. 6-Device Allreduce: Model vs Theoretical vs External Simulator",
-        "image": DIAG / "allreduce_latency_plots" / "overview_broken.png",
+        "image": DIAG / "allreduce_latency_plots" / "comparison_mesh_vs_ring_vs_2DTorus_vs_theoretical_vs_fsim.png",
         "bullets": [
             "Three SIP topologies (ring / torus / mesh) swept 16 B → 96 KB per PE",
             "Dashed red curve: hand-derived theoretical model for torus_2d (6 SIPs)",
@@ -73,7 +73,7 @@ SLIDES = [
     },
     {
         "title": "5. IPCQ Slot Memory: TCM vs SRAM vs HBM",
-        "image": DIAG / "allreduce_latency_plots" / "buffer_kind_sweep.png",
+        "image": DIAG / "allreduce_latency_plots" / "AllReduce_LRAB_2Dtorus_6SiP_2x3_with_TCM_SRAM_HBM.png",
         "bullets": [
             "Same allreduce with slot memory swapped: TCM (per-PE local) / SRAM / HBM (cube-shared, behind router link)",
             "Cost = NoC drain + slot-IO + PE↔bank hop; only TCM skips the bank hop",
diff --git a/scripts/emit_overview_with_external_ref.py b/scripts/emit_overview_with_external_ref.py
index a8a2863..8877bbc 100644
--- a/scripts/emit_overview_with_external_ref.py
+++ b/scripts/emit_overview_with_external_ref.py
@@ -1,6 +1,7 @@
-"""One-shot: render overview.png with an external 366 µs reference, in two
-variants — log scale and broken y-axis. Reads docs/diagrams/allreduce_latency_plots/summary.csv
-and writes overview_log.png and overview_broken.png alongside it.
+"""One-shot: render the broken-y-axis allreduce comparison with the FSIM
+single-device reference. Reads docs/diagrams/allreduce_latency_plots/summary.csv
+and writes comparison_mesh_vs_ring_vs_2DTorus_vs_theoretical_vs_fsim.png
+alongside it.
 
 This is a derived-artifact generator (per CLAUDE.md): plotting only, no production
 or test logic touched.
@@ -17,7 +18,7 @@ ROOT = Path(__file__).resolve().parent.parent
 PLOT_DIR = ROOT / "docs" / "diagrams" / "allreduce_latency_plots"
 CSV_PATH = PLOT_DIR / "summary.csv"
 
-EXT_LABEL = "ext-sim single-device reduce: 366 µs"
+EXT_LABEL = "FSIM (single device): 366 µs"
 EXT_LATENCY_NS = 366_000.0
 
 COLORS = {
@@ -26,6 +27,15 @@ COLORS = {
     "mesh_2d_no_wrap": "tab:green",
 }
 
+# Display labels (data keys above stay as the summary.csv sip_topology
+# values; these are only the human-readable legend strings). All non-FSIM
+# runs use 6 devices; the grid differs per topology.
+DISPLAY = {
+    "ring_1d": "Ring 1x6 (6 devices)",
+    "torus_2d": "2D Torus 2x3 (6 devices)",
+    "mesh_2d_no_wrap": "2D Mesh 2x3 (6 devices)",
+}
+
 # Hand-derived theoretical model for torus_2d (6 SIPs). Mirrors
 # _aggregate_sweep_plots in tests/test_allreduce_multidevice.py.
 NOC_PACKET_BYTES = 128
@@ -51,7 +61,7 @@ def _plot_theoretical(ax, records):
         [r["bytes_per_pe"] for r in torus_rs],
         [_theoretical_torus_2d_ns(r["bytes_per_pe"]) for r in torus_rs],
         color="tab:red", linestyle="--", linewidth=1.6, marker="x",
-        label="theoretical torus_2d (6 SIPs)",
+        label="Theoretical 2D Torus 2x3",
     )
 
 
@@ -91,36 +101,11 @@ def _plot_curves(ax, records, topologies):
             [r["bytes_per_pe"] for r in rs],
             [r["latency_ns"] for r in rs],
             marker="o",
-            label=f"{topo}",
+            label=DISPLAY.get(topo, topo),
             color=COLORS.get(topo),
         )
 
 
-def emit_log(records):
-    topologies = sorted({r["sip_topology"] for r in records})
-    fig, ax = plt.subplots(figsize=(9, 6))
-    _plot_curves(ax, records, topologies)
-    _plot_theoretical(ax, records)
-    ax.scatter(
-        [_ext_x(records)], [EXT_LATENCY_NS],
-        marker="*", s=220, color="tab:red", zorder=5,
-        label=EXT_LABEL,
-    )
-    ax.set_xscale("log", base=2)
-    ax.set_yscale("log")
-    ax.set_xlabel("Bytes per PE (log scale)")
-    ax.set_ylabel("Time (ns) — log scale")
-    ax.set_title("Multi-device allreduce latency vs external single-device reference")
-    ax.grid(True, which="both", alpha=0.3)
-    ax.xaxis.set_major_formatter(mticker.FuncFormatter(_bytes_fmt))
-    ax.legend(loc="upper left")
-    fig.tight_layout()
-    out = PLOT_DIR / "overview_log.png"
-    fig.savefig(out, dpi=120)
-    plt.close(fig)
-    print(f"wrote {out}")
-
-
 def emit_broken(records):
     topologies = sorted({r["sip_topology"] for r in records})
     max_local = max(r["latency_ns"] for r in records)
@@ -172,9 +157,9 @@ def emit_broken(records):
     ax_bot.legend(handles_bot + handles_top, labels_bot + labels_top,
                   loc="upper left")
 
-    fig.suptitle("Multi-device allreduce latency vs external single-device reference (broken y-axis)")
+    fig.suptitle("Multidevice allreduce (ring, Mesh, 2DTorus) vs FSIM latency")
     fig.tight_layout()
-    out = PLOT_DIR / "overview_broken.png"
+    out = PLOT_DIR / "comparison_mesh_vs_ring_vs_2DTorus_vs_theoretical_vs_fsim.png"
     fig.savefig(out, dpi=120)
     plt.close(fig)
     print(f"wrote {out}")
@@ -184,7 +169,6 @@ def main():
     records = _load_records()
     if not records:
         raise SystemExit(f"no rows in {CSV_PATH}")
-    emit_log(records)
     emit_broken(records)
 
 
diff --git a/src/kernbench/ccl/algorithms/intercube_allreduce.py b/src/kernbench/ccl/algorithms/lrab_hierarchical_allreduce.py
similarity index 100%
rename from src/kernbench/ccl/algorithms/intercube_allreduce.py
rename to src/kernbench/ccl/algorithms/lrab_hierarchical_allreduce.py
diff --git a/tests/test_allreduce_buffer_kind_sweep.py b/tests/test_allreduce_buffer_kind_sweep.py
index 9e8aab9..48d53aa 100644
--- a/tests/test_allreduce_buffer_kind_sweep.py
+++ b/tests/test_allreduce_buffer_kind_sweep.py
@@ -3,7 +3,8 @@
 Parametrized over (buffer_kind, n_elem). Each case runs the standard
 config-driven allreduce app and writes a JSON row to a shared staging
 dir; the conftest sessionfinish hook (added in Phase 1) aggregates
-rows into ``docs/diagrams/allreduce_latency_plots/buffer_kind_sweep.png``.
+rows into ``docs/diagrams/allreduce_latency_plots/
+AllReduce_LRAB_2Dtorus_6SiP_2x3_with_TCM_SRAM_HBM.png``.
 
 Pre-Phase-2: the three buffer-kind lines overlap exactly because slot
 access is latency-free today. Post-Phase-2 they spread out (tcm
@@ -36,6 +37,8 @@ _ELEM_BYTES_F16 = 2
 _OUT_DIR = (Path(__file__).parent.parent / "docs" / "diagrams"
             / "allreduce_latency_plots")
 _ROWS_DIR = _OUT_DIR / "_buffer_kind_rows"
+# Descriptive output stem (shared by the .png and .csv).
+_OUT_STEM = "AllReduce_LRAB_2Dtorus_6SiP_2x3_with_TCM_SRAM_HBM"
 
 
 def _bk_params():
@@ -55,7 +58,7 @@ def test_buffer_kind_allreduce_one(tmp_path, buffer_kind, n_elem):
         sub,
         sip_topology="torus_2d",
         n_sips=6,
-        algorithm="intercube_allreduce",
+        algorithm="lrab_hierarchical_allreduce",
         sip_w=3, sip_h=2,
         n_elem_override=n_elem,
     )
@@ -64,7 +67,7 @@ def test_buffer_kind_allreduce_one(tmp_path, buffer_kind, n_elem):
         ccl_cfg = yaml.safe_load(f)
     ccl_cfg.setdefault("defaults", {})["buffer_kind"] = buffer_kind
     ccl_cfg.setdefault("algorithms", {}).setdefault(
-        "intercube_allreduce", {},
+        "lrab_hierarchical_allreduce", {},
     )["buffer_kind"] = buffer_kind
     with open(ccl_path, "w") as f:
         yaml.dump(ccl_cfg, f, default_flow_style=False)
@@ -81,7 +84,7 @@ def test_buffer_kind_allreduce_one(tmp_path, buffer_kind, n_elem):
     ) as ctx:
         result = run_allreduce(
             ctx, engine, spec,
-            algorithm="intercube_allreduce", ccl_yaml=ccl_path,
+            algorithm="lrab_hierarchical_allreduce", ccl_yaml=ccl_path,
         )
         assert result["ok_cubes"] > 0
 
@@ -108,7 +111,7 @@ def test_buffer_kind_allreduce_one(tmp_path, buffer_kind, n_elem):
 
 
 def aggregate_buffer_kind_plot() -> bool:
-    """Read per-config rows and emit buffer_kind_sweep.png + CSV.
+    """Read per-config rows and emit the descriptive .png + .csv (_OUT_STEM).
 
     Called from conftest.pytest_sessionfinish (controller-only).
     Returns True if rows were aggregated.
@@ -141,7 +144,7 @@ def aggregate_buffer_kind_plot() -> bool:
     _bytes_fmt = FuncFormatter(_fmt_bytes)
 
     _OUT_DIR.mkdir(parents=True, exist_ok=True)
-    with open(_OUT_DIR / "buffer_kind_sweep.csv", "w",
+    with open(_OUT_DIR / f"{_OUT_STEM}.csv", "w",
               newline="", encoding="utf-8") as f:
         w = csv.DictWriter(f, fieldnames=[
             "buffer_kind", "sip_topology", "n_sips", "n_elem",
@@ -172,13 +175,13 @@ def aggregate_buffer_kind_plot() -> bool:
     ax.set_xlabel("Bytes per PE (log scale)")
     ax.set_ylabel("Time (ns)")
     ax.set_title(
-        "Allreduce torus_2d (6 SIPs, 3×2) — IPCQ slot memory tier"
+        "AllReduce_LRAB_2Dtorus_6SiP(2x3) — IPCQ memory (SRAM, TCM, HBM)"
     )
     ax.grid(True, alpha=0.3)
     ax.legend()
     ax.xaxis.set_major_formatter(_bytes_fmt)
     fig.tight_layout()
-    fig.savefig(_OUT_DIR / "buffer_kind_sweep.png", dpi=130)
+    fig.savefig(_OUT_DIR / f"{_OUT_STEM}.png", dpi=130)
     plt.close(fig)
 
     for p in row_files:
@@ -191,6 +194,6 @@ def aggregate_buffer_kind_plot() -> bool:
     except OSError:
         pass
 
-    print(f"\nWrote {_OUT_DIR / 'buffer_kind_sweep.png'} "
+    print(f"\nWrote {_OUT_DIR / f'{_OUT_STEM}.png'} "
           f"from {len(records)} rows")
     return True
diff --git a/tests/test_allreduce_multidevice.py b/tests/test_allreduce_multidevice.py
index 351f03b..a270b3f 100644
--- a/tests/test_allreduce_multidevice.py
+++ b/tests/test_allreduce_multidevice.py
@@ -189,15 +189,15 @@ TOPOLOGY_PATH = Path(__file__).parent.parent / "topology.yaml"
 
 CONFIGS = [
     pytest.param(
-        "intercube_allreduce", "ring_1d", 6, None, None,
+        "lrab_hierarchical_allreduce", "ring_1d", 6, None, None,
         id="ring_6sip",
     ),
     pytest.param(
-        "intercube_allreduce", "torus_2d", 6, 2, 3,
+        "lrab_hierarchical_allreduce", "torus_2d", 6, 2, 3,
         id="torus_6sip_2x3",
     ),
     pytest.param(
-        "intercube_allreduce", "mesh_2d_no_wrap", 6, 2, 3,
+        "lrab_hierarchical_allreduce", "mesh_2d_no_wrap", 6, 2, 3,
         id="mesh_6sip_2x3",
     ),
 ]
@@ -280,9 +280,9 @@ _SWEEP_N_ELEM = [
 _ELEM_BYTES_F16 = 2
 
 _SWEEP_TOPOLOGIES = [
-    ("intercube_allreduce", "ring_1d", 6, None, None),
-    ("intercube_allreduce", "torus_2d", 6, 2, 3),
-    ("intercube_allreduce", "mesh_2d_no_wrap", 6, 2, 3),
+    ("lrab_hierarchical_allreduce", "ring_1d", 6, None, None),
+    ("lrab_hierarchical_allreduce", "torus_2d", 6, 2, 3),
+    ("lrab_hierarchical_allreduce", "mesh_2d_no_wrap", 6, 2, 3),
 ]
 
 # Shared on-disk staging dir for parametrized sweep rows. Each
@@ -440,10 +440,22 @@ def _aggregate_sweep_plots() -> bool:
             continue
         xs = [r["bytes_per_pe"] for r in rs]
         ys = [r["latency_ns"] for r in rs]
-        title = (
-            f"Allreduce latency — {topo_name} "
-            f"(n_sips={rs[0]['n_sips']})"
+        _per_topo_titles = {
+            "ring_1d": "AllReduce_LRAB_Ring1D_6SiP(1x6)",
+            "torus_2d": "AllReduce_LRAB_2Dtorus_6SiP(2x3)",
+            "mesh_2d_no_wrap": "AllReduce_LRAB_2DMesh_6SiP(2x3)",
+        }
+        # Descriptive output filenames (parens → underscores for
+        # markdown/URL safety; topo key stays the summary.csv value).
+        _per_topo_files = {
+            "ring_1d": "AllReduce_LRAB_Ring1D_6SiP_1x6",
+            "torus_2d": "AllReduce_LRAB_2Dtorus_6SiP_2x3",
+            "mesh_2d_no_wrap": "AllReduce_LRAB_2DMesh_6SiP_2x3",
+        }
+        title = _per_topo_titles.get(
+            topo_name, f"Allreduce latency — {topo_name}"
         )
+        out_stem = _per_topo_files.get(topo_name, topo_name)
         fig, ax = plt.subplots(figsize=(8, 5))
         ax.plot(xs, ys, marker="o", color="tab:blue")
         ax.set_xscale("log", base=2)
@@ -453,75 +465,14 @@ def _aggregate_sweep_plots() -> bool:
         ax.grid(True, alpha=0.3)
         ax.xaxis.set_major_formatter(_bytes_fmt)
         fig.tight_layout()
-        fig.savefig(_SWEEP_OUT_DIR / f"{topo_name}.png", dpi=120)
+        fig.savefig(_SWEEP_OUT_DIR / f"{out_stem}.png", dpi=120)
         plt.close(fig)
 
-    colors = {"ring_1d": "tab:blue", "torus_2d": "tab:orange",
-              "mesh_2d_no_wrap": "tab:green"}
-
-    # ── Hand-derived theoretical model for torus_2d (6 SIPs) ──
-    # Critical-path analysis (per packet, packet = 128 B at NoC):
-    #   local intra-SIP reduce + broadcast = 8 hops × 57 ns = 456 ns
-    #   global X-direction reduce          = 5 UCIe + 1 UAL = 445 ns
-    #   global Y-direction reduce          = 5 UCIe + 1 UAL = 445 ns
-    #   per-packet startup latency         = 456 + 445 + 445 = 1346 ns
-    # Packet count is PER CUBE (8 PEs/cube cooperate on the cube tile).
-    # At 6144 packets/cube the pipelined total is 8741 ns, so the
-    # bottleneck-stage interval τ = (8741 − 1346) / (6144 − 1) ≈ 1.204 ns.
-    # T_theoretical(N) = 1346 + (N − 1) × τ
-    #   where N = ceil((bytes_per_pe × 8) / 128) = ceil(bytes_per_pe / 16)
-    NOC_PACKET_BYTES = 128
-    PES_PER_CUBE = 8
-    T_STARTUP_NS = 1346.0
-    TAU_NS = (8741.0 - 1346.0) / (6144 - 1)  # ≈ 1.2038 ns/packet
-
-    def _theoretical_torus_2d_ns(bytes_per_pe: int) -> float:
-        bytes_per_cube = int(bytes_per_pe) * PES_PER_CUBE
-        n_packets = max(1, -(-bytes_per_cube // NOC_PACKET_BYTES))  # ceil
-        return T_STARTUP_NS + (n_packets - 1) * TAU_NS
-
-    fig, ax = plt.subplots(figsize=(9, 6))
-    for topo_name in topologies:
-        rs = sorted(
-            [r for r in records if r["sip_topology"] == topo_name],
-            key=lambda r: r["bytes_per_pe"],
-        )
-        if not rs:
-            continue
-        ax.plot(
-            [r["bytes_per_pe"] for r in rs],
-            [r["latency_ns"] for r in rs],
-            marker="o",
-            label=f"{topo_name} (n_sips={rs[0]['n_sips']})",
-            color=colors.get(topo_name),
-        )
-
-    # Theoretical torus_2d curve across all payload sizes.
-    torus_rs = sorted(
-        [r for r in records if r["sip_topology"] == "torus_2d"],
-        key=lambda r: r["bytes_per_pe"],
-    )
-    if torus_rs:
-        xs_th = [r["bytes_per_pe"] for r in torus_rs]
-        ys_th = [_theoretical_torus_2d_ns(r["bytes_per_pe"]) for r in torus_rs]
-        ax.plot(
-            xs_th, ys_th,
-            color="tab:red", linestyle="--", linewidth=1.6, marker="x",
-            label="theoretical torus_2d (6 SIPs)",
-        )
-
-    ax.set_xscale("log", base=2)
-    ax.set_xlabel("Bytes per PE (log scale)")
-    ax.set_ylabel("Time (ns)")
-    ax.set_title("Multi-device allreduce latency by topology")
-    ax.grid(True, alpha=0.3)
-    ax.set_xlim(left=min(r["bytes_per_pe"] for r in records) / 2,
-                right=max(r["bytes_per_pe"] for r in records) * 1.5)
-    ax.legend()
-    ax.xaxis.set_major_formatter(_bytes_fmt)
-    fig.tight_layout()
-    fig.savefig(_SWEEP_OUT_DIR / "overview.png", dpi=120)
-    plt.close(fig)
+    # Combined overview.png is no longer emitted — the broken-y-axis
+    # comparison (scripts/emit_overview_with_external_ref.py →
+    # comparison_mesh_vs_ring_vs_2DTorus_vs_theoretical_vs_fsim.png)
+    # supersedes it. Per-topology plots above and summary.csv are still
+    # produced.
 
     # Cleanup row staging dir so a partial future run doesn't pick up
     # stale rows.
@@ -535,7 +486,7 @@ def _aggregate_sweep_plots() -> bool:
     except OSError:
         pass
 
-    print(f"\nWrote {_SWEEP_OUT_DIR / 'overview.png'} "
+    print(f"\nWrote per-topology plots + summary.csv to {_SWEEP_OUT_DIR} "
           f"from {len(records)} rows")
     return True
 
diff --git a/tests/test_distributed_intercube_allreduce.py b/tests/test_distributed_lrab_hierarchical_allreduce.py
similarity index 91%
rename from tests/test_distributed_intercube_allreduce.py
rename to tests/test_distributed_lrab_hierarchical_allreduce.py
index 81bdc57..1f9d78a 100644
--- a/tests/test_distributed_intercube_allreduce.py
+++ b/tests/test_distributed_lrab_hierarchical_allreduce.py
@@ -25,7 +25,7 @@ N_ELEM = 8
 def _write_ccl_yaml(tmp_path) -> str:
     body = textwrap.dedent("""\
         defaults:
-          algorithm: intercube_allreduce
+          algorithm: lrab_hierarchical_allreduce
           buffer_kind: tcm
           backpressure: sleep
           n_slots: 4
@@ -34,8 +34,8 @@ def _write_ccl_yaml(tmp_path) -> str:
           ipcq_credit_size_bytes: 16
 
         algorithms:
-          intercube_allreduce:
-            module: kernbench.ccl.algorithms.intercube_allreduce
+          lrab_hierarchical_allreduce:
+            module: kernbench.ccl.algorithms.lrab_hierarchical_allreduce
             topology: none
             buffer_kind: tcm
             n_elem: 8
@@ -80,11 +80,11 @@ def _worker(rank: int, n_sips: int, torch) -> None:
         )
 
     if rank == 0:
-        print(f"\n  intercube_allreduce (ws={n_sips}): "
+        print(f"\n  lrab_hierarchical_allreduce (ws={n_sips}): "
               f"{n_sips * N_CUBES} OK")
 
 
-def test_distributed_intercube_allreduce(tmp_path, monkeypatch):
+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
diff --git a/tests/test_intercube_root_center.py b/tests/test_intercube_root_center.py
index ef3c72c..7267b37 100644
--- a/tests/test_intercube_root_center.py
+++ b/tests/test_intercube_root_center.py
@@ -1,7 +1,7 @@
-"""Phase 1 test for moving the intercube_allreduce root cube from the
+"""Phase 1 test for moving the lrab_hierarchical_allreduce root cube from the
 bottom-right corner (3,3) to the geometric center (2,2).
 
-Today's algorithm (intercube_allreduce.py) hardcodes
+Today's algorithm (lrab_hierarchical_allreduce.py) hardcodes
 ``root_cube = (cube_h-1) * cube_w + (cube_w-1)`` (= cube 15 in 4×4).
 The intra-SIP critical path for one allreduce is therefore::
 
@@ -55,7 +55,7 @@ def _run_torus_96kb(tmp_path: Path) -> float:
         sub,
         sip_topology="torus_2d",
         n_sips=6,
-        algorithm="intercube_allreduce",
+        algorithm="lrab_hierarchical_allreduce",
         sip_w=3, sip_h=2,
         n_elem_override=49152,   # 49152 × 2 = 96 KB / slot
     )
@@ -70,7 +70,7 @@ def _run_torus_96kb(tmp_path: Path) -> float:
     ) as ctx:
         result = run_allreduce(
             ctx, engine, spec,
-            algorithm="intercube_allreduce", ccl_yaml=ccl_path,
+            algorithm="lrab_hierarchical_allreduce", ccl_yaml=ccl_path,
         )
         assert result["ok_cubes"] > 0
     pe_exec_vals = [
@@ -121,7 +121,7 @@ def test_correctness_preserved(tmp_path):
         sub,
         sip_topology="torus_2d",
         n_sips=6,
-        algorithm="intercube_allreduce",
+        algorithm="lrab_hierarchical_allreduce",
         sip_w=3, sip_h=2,
         n_elem_override=128,   # tiny payload to keep this fast
     )
@@ -136,7 +136,7 @@ def test_correctness_preserved(tmp_path):
     ) as ctx:
         result = run_allreduce(
             ctx, engine, spec,
-            algorithm="intercube_allreduce", ccl_yaml=ccl_path,
+            algorithm="lrab_hierarchical_allreduce", ccl_yaml=ccl_path,
         )
     n_cubes = 6 * 16  # 6 SIPs × 16 cubes/SIP
     assert result["ok_cubes"] == n_cubes, (
diff --git a/tests/test_intercube_sfr_config.py b/tests/test_intercube_sfr_config.py
index bdf0cea..b4c7474 100644
--- a/tests/test_intercube_sfr_config.py
+++ b/tests/test_intercube_sfr_config.py
@@ -28,7 +28,7 @@ def _engine_and_spec():
 
 def _merged_cfg():
     cfg = load_ccl_config()
-    return resolve_algorithm_config(cfg, name="intercube_allreduce")
+    return resolve_algorithm_config(cfg, name="lrab_hierarchical_allreduce")
 
 
 class TestConfigureSfrNeighborTables:
diff --git a/tests/test_ipcq_buffer_kind_latency.py b/tests/test_ipcq_buffer_kind_latency.py
index 20e26d7..e356e64 100644
--- a/tests/test_ipcq_buffer_kind_latency.py
+++ b/tests/test_ipcq_buffer_kind_latency.py
@@ -81,7 +81,7 @@ def _run_torus_allreduce(
         sub,
         sip_topology="torus_2d",
         n_sips=6,
-        algorithm="intercube_allreduce",
+        algorithm="lrab_hierarchical_allreduce",
         sip_w=3, sip_h=2,
         n_elem_override=n_elem,
     )
@@ -92,7 +92,7 @@ def _run_torus_allreduce(
         ccl_cfg = yaml.safe_load(f)
     ccl_cfg.setdefault("defaults", {})["buffer_kind"] = buffer_kind
     ccl_cfg.setdefault("algorithms", {}).setdefault(
-        "intercube_allreduce", {},
+        "lrab_hierarchical_allreduce", {},
     )["buffer_kind"] = buffer_kind
     with open(ccl_path, "w") as f:
         yaml.dump(ccl_cfg, f, default_flow_style=False)
@@ -109,7 +109,7 @@ def _run_torus_allreduce(
     ) as ctx:
         result = run_allreduce(
             ctx, engine, spec,
-            algorithm="intercube_allreduce", ccl_yaml=ccl_path,
+            algorithm="lrab_hierarchical_allreduce", ccl_yaml=ccl_path,
         )
         assert result["ok_cubes"] > 0, "allreduce did not validate"
 
diff --git a/tests/test_ipcq_buffer_kind_locations.py b/tests/test_ipcq_buffer_kind_locations.py
index b7b4270..0bb278f 100644
--- a/tests/test_ipcq_buffer_kind_locations.py
+++ b/tests/test_ipcq_buffer_kind_locations.py
@@ -68,7 +68,7 @@ def _run_allreduce_with_buffer_kind(
         sub,
         sip_topology="torus_2d",
         n_sips=6,
-        algorithm="intercube_allreduce",
+        algorithm="lrab_hierarchical_allreduce",
         sip_w=3, sip_h=2,
         n_elem_override=n_elem,
     )
@@ -77,7 +77,7 @@ def _run_allreduce_with_buffer_kind(
         ccl_cfg = yaml.safe_load(f)
     ccl_cfg.setdefault("defaults", {})["buffer_kind"] = buffer_kind
     ccl_cfg.setdefault("algorithms", {}).setdefault(
-        "intercube_allreduce", {},
+        "lrab_hierarchical_allreduce", {},
     )["buffer_kind"] = buffer_kind
     with open(ccl_path, "w") as f:
         yaml.dump(ccl_cfg, f, default_flow_style=False)
@@ -94,7 +94,7 @@ def _run_allreduce_with_buffer_kind(
     ) as ctx:
         result = run_allreduce(
             ctx, engine, spec,
-            algorithm="intercube_allreduce", ccl_yaml=ccl_path,
+            algorithm="lrab_hierarchical_allreduce", ccl_yaml=ccl_path,
         )
         assert result["ok_cubes"] > 0, "allreduce did not validate"
 
diff --git a/tests/test_pe_to_pe_diagnostic.py b/tests/test_pe_to_pe_diagnostic.py
index 4d7bc2f..8d0c653 100644
--- a/tests/test_pe_to_pe_diagnostic.py
+++ b/tests/test_pe_to_pe_diagnostic.py
@@ -472,7 +472,7 @@ def _run_ipcq():
         dst_sip, dst_cube, dst_pe = DST
 
         cfg = load_ccl_config()
-        merged = resolve_algorithm_config(cfg, name="intercube_allreduce")
+        merged = resolve_algorithm_config(cfg, name="lrab_hierarchical_allreduce")
         merged["slot_size"] = max(int(merged.get("slot_size", 4096)), NBYTES)
 
         with RuntimeContext(
diff --git a/tests/test_pe_to_pe_latency.py b/tests/test_pe_to_pe_latency.py
index 8af2896..1e911a9 100644
--- a/tests/test_pe_to_pe_latency.py
+++ b/tests/test_pe_to_pe_latency.py
@@ -56,13 +56,17 @@ class Hop:
 
 
 HOPS = [
-    Hop("h1_intra_horizontal", "Intra-cube horizontal (pe0 to pe1)",
+    Hop("latency_intracube_PE0_to_PE1_horizontal",
+        "Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal)",
         (0, 0, 0), (0, 0, 1), "intra_E", "intra_W", True),
-    Hop("h2_intra_vertical", "Intra-cube vertical (pe0 to pe4)",
+    Hop("latency_intracube_PE0_to_PE4_vertical",
+        "Intra-cube PE-to-PE latency: PE0 → PE4 (vertical)",
         (0, 0, 0), (0, 0, 4), "intra_S", "intra_N", True),
-    Hop("h3_inter_cube_horizontal", "Inter-cube horizontal (cube0 to cube1)",
+    Hop("latency_intercube_C0PE0_to_C1PE0_horizontal",
+        "Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal)",
         (0, 0, 0), (0, 1, 0), "E", "W", True),
-    Hop("h4_inter_cube_vertical", "Inter-cube vertical (cube0 to cube4)",
+    Hop("latency_intercube_C0PE0_to_C4PE0_vertical",
+        "Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical)",
         (0, 0, 0), (0, 4, 0), "S", "N", True),
 ]
 
@@ -80,7 +84,7 @@ def _measure_ipcq(hop: Hop, nbytes: int) -> float:
     engine, spec = _make_engine()
 
     cfg = load_ccl_config()
-    merged = resolve_algorithm_config(cfg, name="intercube_allreduce")
+    merged = resolve_algorithm_config(cfg, name="lrab_hierarchical_allreduce")
     merged["slot_size"] = max(int(merged.get("slot_size", 4096)), nbytes)
 
     n_elem = nbytes // ELEM_BYTES