fix: background-delivery ground rules — the dock is the source of truth, delivered content shows the moment it persists

The owner's three-part test of the context-injection flow surfaced
timing/visibility bugs, fixed as standing ground rules for ALL background
processes (owner rules, 2026-09-15):

1. THE JOB STARTS AT SEND. triggerGraphContext moves from onFinish to
   right after the write-ahead persist in handleChatRequest: its only
   input is the first typed message (the topic), just made durable — so
   embedding + cosine scan run CONCURRENT with the prober's turn and
   the dock blob appears the moment the session starts, not after turn
   one finishes. Extraction stays at onFinish (it needs answers
   accumulated DURING the turn).

2. DELIVERED CONTENT SHOWS MID-TURN. Steers inserted server-side
   (claimed at turn start, persisted write-ahead) used to wait for the
   next turn's completion to appear — the full record sync mid-stream
   is forbidden (it breaks the SDK's in-place continuation merge), so
   adoption was deferred to idle. New append-only seam: core
   mergeAdopted() inserts the record's new message ids in canonical
   order (in-flight streaming tail kept last) and never rewrites a
   local message; any other shape bails to the full-sync-at-idle net.
   Wired at three points, no new standing polls:
   - turn-start window: three bounded record fetches (400ms/1s/2s)
     after a send catch the claimed steer while the turn streams;
     self-terminating, survives the submitted->streaming flip.
   - jobs-poll settle: mid-turn settles adopt append-only NOW, the
     owed full sync still runs at idle.
   - wake-adoption poll: each tick adopts persisted wake content, so
     steers show at the wake turn's START, not its finish.
   The dock stays honest with zero gap: jobs hold "running" while
   queued behind a pending question ("delivering context"), then flip
   done at claim/delivery — visible from start to delivery, and the
   turn-start nudge (useActivity().refresh) clears it within ~150ms.

3. THE MARKER IS CLICKABLE (observability). The knowledge-context
   SystemLine becomes GraphContextMarker: quiet line, popover with the
   delivered propositions IN DELIVERY ORDER (most similar first — the
   order the budget filled), each with its folded understanding level;
   Esc / outside pointerdown close. The part data was already the audit
   trail — now it's readable at the seam where it landed.

Tests: mergeAdopted unit pins (6), marker render pins (3) — 468/468,
tsc, eslint, build all green; live-smoked end-to-end: blob at send,
marker at t+500ms mid-turn, popover order + levels, instant dock clear.

src/core/ui-message.ts

@@ -56,3 +56,49 @@ export type TeacherUIDataParts = {
 };
 
 export type TeacherUIMessage = UIMessage<unknown, TeacherUIDataParts, TeacherUITools>;
+
+// ─── Append-only record adoption (background-process ground rules) ──────────
+
+/**
+ * Merge server-added messages into the client's live list WITHOUT the full
+ * snapshot swap (owner ground rules, 2026-09-15: content delivered into the
+ * record — context blocks, sub-agent artifacts, abort notes — must become
+ * visible the moment it persists, mid-turn included; it sits between messages
+ * and nothing about a running turn should hide it).
+ *
+ * Safe against the stale-snapshot lesson (mid-turn full syncs break the SDK's
+ * in-place continuation merge): this NEVER rewrites or removes an existing
+ * message — it returns the RECORD's message order when that order is exactly
+ * the client's persisted core plus new server-added ids (the server appends
+ * only: steers are inserted right after the last persisted user message),
+ * with the client's in-flight streaming assistant message — its last entry,
+ * not yet persisted — kept at the tail. Any other shape (a missing local id
+ * = the record was rewritten/reordered) returns null: the caller defers to
+ * the full sync at idle, the pre-existing safety net.
+ */
+export function mergeAdopted(
+	local: ReadonlyArray<TeacherUIMessage>,
+	record: ReadonlyArray<TeacherUIMessage>,
+): TeacherUIMessage[] | null {
+	const recordIds = new Set(record.map((m) => m.id));
+	// The in-flight tail: the client's last message may legitimately be absent
+	// from the record (the SDK's streaming assistant message persists only at
+	// onFinish). Exactly one such tail is allowed.
+	let core = local;
+	let tail: TeacherUIMessage | undefined;
+	const last = local.at(-1);
+	if (last && !recordIds.has(last.id)) {
+		tail = last;
+		core = local.slice(0, -1);
+	}
+	// No rewrite happened if every core message is still in the record —
+	// otherwise this is not a pure append; bail to the full-sync-at-idle.
+	if (core.some((m) => !recordIds.has(m.id))) return null;
+	// Nothing new → nothing to do.
+	const localIds = new Set(local.map((m) => m.id));
+	if (!record.some((m) => !localIds.has(m.id))) return null;
+	// The record's order is canonical for everything persisted (the server
+	// appends only; plan-block part attachment changes parts, not order) —
+	// merged = record + the in-flight tail.
+	return tail ? [...record, tail] : [...record];
+}