diff --git a/docs/web-ui/README.md b/docs/web-ui/README.md
index 18fadbf0..c0af27d2 100644
--- a/docs/web-ui/README.md
+++ b/docs/web-ui/README.md
@@ -115,7 +115,8 @@ touching the code rather than using the UI:
   [`shape.md`](shape.md) (SSE multiplexing, Worker-death self-heal,
   atomic repaint).
 - **"What does a container row contain?"** →
-  [`dashboard.md`](dashboard.md) (Container row, Selection bar).
+  [`dashboard.md`](dashboard.md) (Container row, Topology tree,
+  Selection bar).
 - **"What endpoints does the dashboard expose?"** →
   [`dashboard.md`](dashboard.md) (Dashboard endpoints, Dashboard event
   channel).
diff --git a/docs/web-ui/dashboard.md b/docs/web-ui/dashboard.md
index 89342d12..9990aa9b 100644
--- a/docs/web-ui/dashboard.md
+++ b/docs/web-ui/dashboard.md
@@ -57,7 +57,8 @@ surfaces, not tab panes.
 ## SW4RM tab
 
 **C0NTAINERS** — live containers as a flat list, one row per
-container, sorted alphabetically by agent name; every container the
+container, sorted alphabetically by agent name. No row nests under
+another, none carries an indent or a tree glyph, and every container the
 rescan reports gets a row. Pulsing red banner at the top
 of this section if any two sub-agents hash to the same port
 (`port_conflicts` from `/api/state`): the operator must rename
@@ -973,6 +974,14 @@ build. (The `hivectl stop --graceful` CLI flag enqueues the same
 `Signal`/`Drain` pair, so the dashboard and CLI paths behave
 identically.)
 
+### Topology tree
+
+Nothing nests. `swarm.js::buildAgentTree` returns every container at
+depth 0 in alphabetical order, and the row builder emits no prefix
+column for a depth-0 row — so a container row carries no indent, no
+joint and no continuation bar, and the SW4RM list reads as a flat
+roster. The `.tree-prefix` lane rules in `dashboard.css` match nothing.
+
 ## Selection bar
 
 Bulk actions (`R3ST4RT` / `ST0P` / `ST4RT` / `P4US3` / `R3SUM3` /
diff --git a/frontend/packages/dashboard/src/dashboard.css b/frontend/packages/dashboard/src/dashboard.css
index e87d1af7..71106782 100644
--- a/frontend/packages/dashboard/src/dashboard.css
+++ b/frontend/packages/dashboard/src/dashboard.css
@@ -200,6 +200,84 @@ body.dashboard-shell {
     opacity 200ms ease,
     border-color 200ms ease;
 }
+/* Topology indent ladder. See docs/web-ui/dashboard.md::Topology tree (Indent
+   + lane geometry paragraph) for the 1.8em-per-depth-level
+   rationale + CSS-attr()-not-yet-portable caveat. */
+.container-row[data-depth] {
+  position: relative;
+}
+.container-row[data-depth="1"] {
+  margin-left: 1.8em;
+}
+.container-row[data-depth="2"] {
+  margin-left: 3.6em;
+}
+.container-row[data-depth="3"] {
+  margin-left: 5.4em;
+}
+.container-row[data-depth="4"] {
+  margin-left: 7.2em;
+}
+.container-row[data-depth="5"] {
+  margin-left: 9em;
+}
+.container-row[data-depth="6"] {
+  margin-left: 10.8em;
+}
+/* Tree prefix lanes — DOM-painted, not text-glyph-painted. */
+.container-row .tree-prefix {
+  position: absolute;
+  top: 0;
+  bottom: -0.4em;
+  display: flex;
+  flex-direction: row;
+  pointer-events: none;
+  user-select: none;
+  color: var(--purple-dim);
+}
+.container-row[data-depth="1"] .tree-prefix {
+  left: -1.8em;
+}
+.container-row[data-depth="2"] .tree-prefix {
+  left: -3.6em;
+}
+.container-row[data-depth="3"] .tree-prefix {
+  left: -5.4em;
+}
+.container-row[data-depth="4"] .tree-prefix {
+  left: -7.2em;
+}
+.container-row[data-depth="5"] .tree-prefix {
+  left: -9em;
+}
+.container-row[data-depth="6"] .tree-prefix {
+  left: -10.8em;
+}
+.tree-prefix .tree-lane {
+  flex: 0 0 1.8em;
+  position: relative;
+}
+.tree-prefix .lane-line::before,
+.tree-prefix .lane-joint::before {
+  content: "";
+  position: absolute;
+  left: 0.6em;
+  top: 0;
+  bottom: 0;
+  border-left: 1px solid currentColor;
+}
+.tree-prefix .lane-joint-last::before {
+  bottom: auto;
+  height: 3.1em;
+}
+.tree-prefix .lane-joint::after {
+  content: "";
+  position: absolute;
+  left: 0.6em;
+  top: 3.1em;
+  width: 2em;
+  border-top: 1px solid currentColor;
+}
 .container-row:not(.tombstone) {
   display: flex;
   align-items: flex-start;
diff --git a/frontend/packages/dashboard/src/swarm.js b/frontend/packages/dashboard/src/swarm.js
index 7ae5c817..69c77bab 100644
--- a/frontend/packages/dashboard/src/swarm.js
+++ b/frontend/packages/dashboard/src/swarm.js
@@ -226,26 +226,89 @@ function derivePortConflicts(containers) {
   return out;
 }
 
-// ─── container ordering ──────────────────────────────────────────────────────
-// Flat alphabetical sort — see docs/web-ui/dashboard.md::C0NTAINERS.
+// ─── topology tree ───────────────────────────────────────────────────────────
+// See docs/web-ui/dashboard.md::Topology tree for the rendering contract
+// (forest walk, alphabetical sort, orphan + cycle handling).
 
-function sortedContainerRows(containers) {
+function buildAgentTree(containers) {
   // Close any open context menu before replacing the DOM tree — the
   // previous dropdown element would otherwise be a stale reference.
   closeAllMenus();
-  return [...containers].sort((a, b) => a.name.localeCompare(b.name));
+  const byName = new Map();
+  for (const c of containers) byName.set(c.name, c);
+  const children = new Map(); // parent_name -> [child_name, ...]
+  const roots = [];
+  for (const c of containers) {
+    const p = c.parent || null;
+    if (p == null || !byName.has(p)) {
+      roots.push(c.name);
+    } else {
+      const list = children.get(p) || [];
+      list.push(c.name);
+      children.set(p, list);
+    }
+  }
+  roots.sort();
+  for (const list of children.values()) list.sort();
+  const out = [];
+  const visited = new Set();
+  function visit(name, depth, ancestorIsLast, isLast) {
+    if (visited.has(name)) return;
+    visited.add(name);
+    const c = byName.get(name);
+    if (!c) return;
+    out.push({
+      container: c,
+      depth,
+      ancestorIsLast: [...ancestorIsLast],
+      isLast,
+    });
+    const kids = children.get(name) || [];
+    kids.forEach((kid, i) =>
+      visit(kid, depth + 1, [...ancestorIsLast, isLast], i === kids.length - 1),
+    );
+  }
+  roots.forEach((name, i) => visit(name, 0, [], i === roots.length - 1));
+  // Cycle safety: anything not reached lands at root level so no
+  // agent silently disappears when a config is malformed.
+  for (const c of containers) {
+    if (!visited.has(c.name)) visit(c.name, 0, [], true);
+  }
+  return out;
+}
+// Builds the .tree-prefix DOM for a row at the given depth.
+// See docs/web-ui/dashboard.md::Topology tree for why this is DOM-painted
+// (one positioned <span> per lane) rather than text-glyph-painted.
+function treePrefixDom({ depth, ancestorIsLast, isLast }) {
+  if (depth === 0) return null;
+  const prefix = el("span", { class: "tree-prefix", "aria-hidden": "true" });
+  // Ancestor columns (depth 1..depth-1). Skip depth 0 (root has no
+  // continuation column — top-level rows are separated visually as
+  // top-level rows already).
+  for (let d = 1; d < depth; d++) {
+    const cls = ancestorIsLast[d]
+      ? "tree-lane lane-blank"
+      : "tree-lane lane-line";
+    prefix.append(el("span", { class: cls }));
+  }
+  const jointCls =
+    "tree-lane lane-joint " +
+    (isLast ? "lane-joint-last" : "lane-joint-branch");
+  prefix.append(el("span", { class: jointCls }));
+  return prefix;
 }
 
 // ─── container row ───────────────────────────────────────────────────────────
 
 // Serialise the visible state of a container row into a stable string
 // for change-detection. Includes everything that affects what the row
-// renders — container fields, derived pending/selection state, and
-// link-base context. The async dashboard-state (nav strip, ctx badge,
-// status text) is intentionally excluded: it populates in-place and is
-// preserved when a row is reused.
+// renders — container fields, derived pending/selection state, tree
+// position, and link-base context. The async dashboard-state (nav
+// strip, ctx badge, status text) is intentionally excluded: it
+// populates in-place and is preserved when a row is reused.
 function containerRowFingerprint(
   c,
+  node,
   pending,
   opRunning,
   selected,
@@ -263,6 +326,9 @@ function containerRowFingerprint(
     pending,
     opRunning,
     selected,
+    depth: node.depth,
+    isLast: node.isLast,
+    ancestorIsLast: node.ancestorIsLast,
     gatewayLinks,
     hostname,
   });
@@ -272,7 +338,7 @@ function containerRowFingerprint(
 // renderContainers can call this only for rows whose fingerprint
 // changed (keyed cache), skipping the build + async dashboard-state
 // fetch for stable rows.
-function buildContainerLi(c, opts) {
+function buildContainerLi(c, node, opts) {
   const { pending, opRunning, selected, url, containerBase, forgeBase, s } =
     opts;
   // A single `pending-running` class covers any active transient
@@ -284,6 +350,13 @@ function buildContainerLi(c, opts) {
       (opRunning ? " pending-running" : "") +
       (selected ? " selected" : ""),
   });
+  // Topology: depth contributes left-padding; the glyph string in
+  // the .tree-prefix span draws the ├─ / └─ joint + continuation
+  // lines (`│  `) for ancestors whose subtree extends below this
+  // row. A depth-0 row gets neither — no glyph, no indent.
+  if (node.depth > 0) li.dataset.depth = String(node.depth);
+  const prefix = treePrefixDom(node);
+  if (prefix) li.prepend(prefix);
 
   // Agent icon: 5em square wrapper with an absolutely-positioned
   // <img> + fire-and-forget load with /favicon.svg fallback. The
@@ -671,12 +744,13 @@ export function renderContainers(s) {
   // rather than emit a possibly-wrong one.
   const forgeBase = (s && s.forge_public_url) || null;
   const ul = existingUl ?? el("ul", { class: "containers" });
-  const rows = sortedContainerRows(containers);
+  const tree = buildAgentTree(containers);
 
   // Build the ordered list of <li> elements, reusing cached rows
   // whose displayed state hasn't changed.
   const orderedLis = [];
-  for (const c of rows) {
+  for (const node of tree) {
+    const c = node.container;
     const url = gatewayLinks
       ? `/agent/${encodeURIComponent(c.name)}/`
       : `http://${hostname}:${c.port}/`;
@@ -700,6 +774,7 @@ export function renderContainers(s) {
 
     const fp = containerRowFingerprint(
       c,
+      node,
       pending,
       opRunning,
       selected,
@@ -715,7 +790,7 @@ export function renderContainers(s) {
       // intact from the previous build, avoiding a redundant fetch.
       li = cached.el;
     } else {
-      li = buildContainerLi(c, {
+      li = buildContainerLi(c, node, {
         pending,
         opRunning,
         selected,