diff --git a/docs/web-ui/agent.md b/docs/web-ui/agent.md
index 24d7f420..8714090e 100644
--- a/docs/web-ui/agent.md
+++ b/docs/web-ui/agent.md
@@ -219,7 +219,8 @@ SSE frame and the replayed history rows. The web UI:
 - terminal-themed: phosphor mauve glow, Crust bg,
   backdrop-filter blur, row fade-in slide-up.
 
-Per-stream rendering:
+Per-stream rendering (see [`docs/terminal-rendering.md`](../terminal-rendering.md) for
+the full row taxonomy and dispatch logic):
 
 - `Stream` `tool_use` →
   - `Write` / `Edit`: collapsed `<details>` with a +/- diff body
@@ -227,13 +228,18 @@ Per-stream rendering:
     `input.new_string` or every line of `input.content`).
     Summary carries the path + line counts.
   - others (`Read /path`, `Bash $ cmd`, `mcp__hyperhive__send →
-    operator: "..."`, etc.): flat one-line per-tool format.
+    operator: "..."`, etc.): flat one-line per-tool format with
+    per-tool salient-arg extraction (`fmtToolUse`).
 - `Stream` `tool_result` short → flat `← ...`; long → collapsed
   `<details>` `▸ ← Nl · headline` (click to expand full body).
-- `Stream` `thinking` → text content if claude provided one,
-  otherwise the bare `· thinking …` indicator.
-- `Stream` `system init`, `result`, `rate_limit_event` are
-  dropped — too noisy.
+- `Stream` `thinking` → `.thinking` row with a `💭 thinking …`
+  indicator.
+- `Stream` `system` → handled by subtype: `plugin_install` and
+  `compact_boundary` emit muted notes; `commands_changed` emits an
+  expandable details row listing slash commands; `thinking_tokens`
+  updates a single in-place `🧠` counter; `init`, `result`, and
+  `rate_limit_event` are dropped (noise / used elsewhere); other
+  subtypes → muted `⚙ <subtype>` note.
 - `Note` → `· text`.
 - `TurnStart` → `◆ TURN ← <from>` with the wake-prompt body; a
   muted `· HH:MM:SS` time suffix from the event `ts`.