compaction: the usage-anchored trigger + visible session state (round 15)

The relational-databases incident, diagnosed and fixed:

TRIGGER — pi's estimator law, adopted exactly: anchor on the last
assistant message's provider-reported usage (totalTokens || the field
sum) and chars/4-estimate ONLY what was appended after it. The anchor
scan skips aborted/zero-usage assistants and STOPS at the newest
compaction marker (pre-cut usage described context the next request
will not carry — pi's distrust rule). The old estimator
(JSON.stringify of every message /4) tripled the true context
(measured: 84,412 'tokens' estimated vs 38,799 provider-reported on
the incident record) — scaffolding, escaped LaTeX, thinking blocks
and app-side details all counted. estimateMessageTokens now counts
wire text only (text + thinking + toolCall name/args; content text
for user/toolResult/custom). The unanchored fallback runs the plain
heuristic over the CUT-HONORED projection plus the additive prompt
term; the anchored path adds nothing (usage already billed prompt
and tools).

OBSERVABILITY — compaction is a visible session-wide state (owner
spec): the transcript-bottom placeholder register gains COMPACTING
CONTEXT… (BrailleSpinner + Shimmer, the THINKING placeholder's twin,
mutually exclusive by construction — the gate precedes beginTurn),
and the sidebar row shows 'Compacting context · <ago>' with the
spinner (sessionMeta outranks busy; compacting-changed joins
turn-started/turn-settled as refresh triggers). Liveness rides the
API like turn-busy: ChatListItem.compacting + compactionInFlight on
both GET /api/chats and GET /api/chats/[id] (initiallyCompacting
covers the navigate-back-mid-compaction mount — the event already
fired), exported through the server barrel.

Also: the relational-databases record rolled back to pre-compaction
(marker, post-marker turns, tree reset; backup in /tmp) for a clean
retest. The summarizer-usage 'gap' was a misread — steps[] was
populated all along.

components/chat.tsx

@@ -183,6 +183,7 @@ export function Chat({
 	initialMessages,
 	initialPrompt,
 	initiallyInFlight,
+	initiallyCompacting = false,
 	initialConfigured = false,
 	kind = "teach",
 }: {
@@ -197,6 +198,11 @@ export function Chat({
 	/** A teacher turn is running server-side but attached to no client
 	 * (navigated away mid-turn, returned while in flight). */
 	initiallyInFlight?: boolean;
+	/** A compaction holds the chat's model gate at mount (navigated away
+	 * mid-compaction — the registry is live server state, the
+	 * compaction-changed event already fired). The transcript spinner
+	 * and send gates key on it. */
+	initiallyCompacting?: boolean;
 	/** slotsConfigured(server record) — the persistent setup CTA keys on
 	 *  it (BYOK, owner 2026-09-22). The server gate stays the truth; this
 	 *  only decides whether the pill rides the composer. */
@@ -623,7 +629,7 @@ export function Chat({
 	// flips it; the send paths, canSend, and the docks gate on it (the
 	// server's registry mutex is the structural gate; this is the
 	// affordance). The summary dialog state rides with it.
-	const [compacting, setCompacting] = useState(false);
+	const [compacting, setCompacting] = useState(initiallyCompacting);
 	const [compactionSummary, setCompactionSummary] = useState<CompactionDividerData | null>(null);
 	const canSend =
 		(text.trim().length > 0 || dictation.active) && !pending && !activeProblem && !compacting;
@@ -1425,6 +1431,17 @@ export function Chat({
 							    provider-connect gap. turnInFlight: the same state
 							    entered by external discovery (wake) / the poll
 							    fallback. Never collapsible itself. */}
+							{/* Compaction (owner round 15): the same register as the
+						    thinking placeholder — a visible session-wide state while
+						    the summarizer holds the model gate. Mutually exclusive with
+						    the THINKING placeholder by construction (the gate sits
+						    BEFORE beginTurn; the settle kick runs after endTurn). */}
+							{compacting && (
+								<span className="flex items-center gap-2 font-ui text-xs font-medium uppercase tracking-wide text-muted-foreground">
+									<BrailleSpinner label="Compacting context" />
+									<Shimmer duration={1}>COMPACTING CONTEXT…</Shimmer>
+								</span>
+							)}
 							{(status === "submitted" || turnInFlight) && (
 								<span className="flex items-center gap-2 font-ui text-xs font-medium uppercase tracking-wide text-muted-foreground">
 									<BrailleSpinner label="Thinking" />