A-372 assigner-settles-on-a-mesh-naming-no-branch: the assigner's first pass is told once when the catalog client says the registrations and the source name no branch

Builds: design 47 G A-372 (G-22-lead-answers-2.md, hq design/47-G-lead-answers-31)
Also: Ready reads what the first views hold, since a first view closes before the follower's change is taken into the branches followed; Branches.FirstViews says when both are in.

Claude-Session: https://claude.ai/code/session_01NcbgfGKaxw984XyAPfLm4h

modules/mesh-delivery-assigner/cmd/mesh-delivery-assigner/halves.go

@@ -51,9 +51,39 @@ func (h *halves) follow() error {
 	h.mu.Lock()
 	h.branches = b
 	h.mu.Unlock()
+	h.settleWhenNoBranch()
 	return nil
 }
 
+// settleWhenNoBranch tells the first pass once, when the registrations and the gate's source are answered and name no branch: the
+// trunk is none-yet and the world is empty, as the catalog client's Ready says it (design 47 G, A-372). A mesh that names a branch is
+// told by adopted, when that branch's first view is answered.
+func (h *halves) settleWhenNoBranch() {
+	if h.settled == nil {
+		return
+	}
+	h.mu.Lock()
+	b := h.branches
+	h.mu.Unlock()
+	go func() {
+		select {
+		case <-b.FirstViews(h.ctx):
+		case <-h.ctx.Done():
+			return
+		}
+		if len(b.Followed()) > 0 || b.Ready() != nil {
+			return
+		}
+		h.mu.Lock()
+		told := h.told
+		h.told = true
+		h.mu.Unlock()
+		if !told {
+			h.settled <- struct{}{}
+		}
+	}()
+}
+
 // first is the first watched branch followed, the trunk's: "" while none is.
 func (h *halves) first() string {
 	h.mu.Lock()