a turn hands back its trace id, and one wire op corrects it (V-630)

The correction is the only supervised signal in the box, so the cost of
giving one has to be near zero. That means the surface needs the trace id of
the turn it is showing, which it had no way to learn: handleText returns one
string and the trace was written after the reply left.

The id rides back on ChatReply through the same context sink querySource
uses, so the mic, telegram and the web keep the one signature they share.
CorrectTurn takes a trace id and an optional target, which is deliberately
reach-agnostic: nothing about it assumes a browser.

store.ErrNoSuchTrace gets a wire twin. A turn past the retention bound is
gone, and that is the expected outcome of correcting an old turn, not a
broken database.

internal/ipc/api.go

@@ -724,8 +724,15 @@ type chatReq struct {
 	Conversation string `json:"conversation,omitempty"`
 }
 type chatResp struct {
-	Reply  string `json:"reply"`
-	Source string `json:"source,omitempty"`
+	Reply   string `json:"reply"`
+	Source  string `json:"source,omitempty"`
+	TraceID int64  `json:"trace_id,omitempty"`
+}
+
+// correctTurnReq — the owner correcting one persisted turn (V-630).
+type correctTurnReq struct {
+	TraceID  int64  `json:"trace_id"`
+	ShouldBe string `json:"should_be,omitempty"`
 }
 
 // ChatReply — one text turn's answer plus which query source claimed it.
@@ -738,6 +745,12 @@ type chatResp struct {
 type ChatReply struct {
 	Reply  string
 	Source string
+	// TraceID is the persisted routing trace for this turn (V-629), and it is
+	// what makes a correction one gesture: the surface already has the id, so
+	// saying "that was wrong" costs a button and no lookup. 0 ⇒ nothing was
+	// persisted, which is a box with no database, and the surface offers no
+	// correction rather than a broken one.
+	TraceID int64
 }
 
 type proposeToolReq struct {
@@ -937,6 +950,12 @@ var ErrTaskDuplicate = errors.New("ipc: another live task already has this text"
 // is down" must not read the same to a caller deciding whether to store an id.
 var ErrNoEntity = errors.New("ipc: no such entity")
 
+// ErrNoSuchTrace — the turn a correction names is not in routing_traces. Given
+// a wire twin because it is the expected outcome of correcting a turn older than
+// the retention bound, and "that turn is gone" and "the database is broken" must
+// not read the same to the surface offering the gesture.
+var ErrNoSuchTrace = errors.New("ipc: no such routing trace")
+
 // ErrTaskResolved — a resolved task is not editable.
 var ErrTaskResolved = errors.New("ipc: task is resolved")