docs: handbook states what the code does (fact sweep fixes)

docs/2-handbook/agents/web-page.md

@@ -44,10 +44,16 @@ at a given viewport width. Two columns:
 - **Pills cluster** (`.agent-header-pills`, right-aligned): status
   badges (`StatusChips.tsx`) and flyout triggers together in one row,
   so the header reads as one identity zone + one status/actions zone:
-  - **Alive badge**: `● alive` (green) / `⊘ rate limited` (red) /
-    `◌ needs login` / `◌ logging in` / `○ offline` / `… connecting`.
-  - **State badge**: `💤 idle` / `🧠 thinking` / `📦 compacting` /
-    `○ offline` / `… booting` + age suffix.
+  - **Status badge**, one badge for liveness and turn state: `● alive`
+    (green) / `⊘ rate limited` (red) / `◌ needs login` / `◌ logging in` /
+    `○ offline` / `… connecting` / `💤 idle` / `🧠 thinking` /
+    `📦 compacting` / `… booting` + age suffix, or paused. Selecting it
+    opens a menu: `⏸ pause` / `▶ resume` (via the same hive-c0re-owned
+    `/api/pause/<name>` / `/api/resume/<name>` endpoints the dashboard
+    uses; pausing needs a write this unprivileged process can't make
+    directly), `■ cancel turn` (only while a turn is running),
+    `↻ new session` and `🔓 logout`. Cancel turn, new session and logout
+    need a second selection to confirm.
   - **Model and effort badges** (`model · <name>`, `effort · <level>`):
     display only. Each tooltip says where the value comes from
     (`state.model_source` / `state.effort_source`: set on the swarm,
@@ -65,10 +71,6 @@ at a given viewport width. Two columns:
   - **Ctx / cost badges**: `ctx · 142k` (last inference's prompt size,
     tooltip shows % of context window) / `cost · 1.3M` (cumulative
     tokens billed across every inference in the last turn).
-  - **Pause badge** (`⏸ pause` / `▶ resume`): toggles via the same
-    hive-c0re-owned `/api/pause/<name>` / `/api/resume/<name>`
-    endpoints the dashboard uses (pausing needs a write this
-    unprivileged process can't make directly).
   - **Inbox / todos pills** (`📬 inbox · N` / `📋 todos · N`): hidden
     when empty; selecting it opens the matching flyout in the side panel.
   - **Profile avatar**: the signed-in user's initial, opening a popover with
@@ -162,7 +164,7 @@ If the todo store errors or doesn't answer for any id, the endpoint returns
 ## Live view
 
 Each agent runs an `events::Bus`: a `tokio::sync::broadcast<LiveEvent>`
-plus a sqlite-backed history at `/state/hyperhive-events.sqlite`.
+plus a sqlite-backed history at `/harness/hyperhive-events.sqlite`.
 The harness emits `TurnStart { from, body, unread }`,
 `Stream(value)` (one per parsed stream-json line), `Note`,
 `TurnEnd { ok, note }`. Each event also carries a `ts` (unix
@@ -238,10 +240,9 @@ on this page calls it now.
 
 Successful POSTs return 200 (no 303 redirects). Error responses
 use semantic status codes: **400** for missing/malformed input
-(`body` required, unknown model name, unrecognised effort level),
-**409** for retryable state conflicts (turn in flight when
-`/compact` fires), **500** only for genuine server/transport
-failures. The matching
+(`/api/todos/mark-done` with no todo ids), **500** only for genuine
+server/transport failures. `/compact` never conflicts: it queues
+and runs at the end of the current turn. The matching
 mutations fire `LiveEvent` variants on the per-agent bus, so the
 client doesn't refetch `/api/state` on submit — the SSE stream
 delivers the new state faster anyway.