diff --git a/cmd/mesh-controller/delivery_conditions.go b/cmd/mesh-controller/delivery_conditions.go
index 74b14082..d0a13dc5 100644
--- a/cmd/mesh-controller/delivery_conditions.go
+++ b/cmd/mesh-controller/delivery_conditions.go
@@ -58,8 +58,17 @@ type stalledLine struct {
 	// Severity is "urgent" for a group held or half merged and a refused member (novox/hq issues 1275, 1278); empty
 	// or anything else is a warning, as before.
 	Severity string `json:"severity,omitempty"`
+	// Needs is "new-head" for a delivery whose cure is its author's new head (novox/hq ADR 0505 §5), Author that author
+	// as the operator reads it ("the author of feat/x", with the session that pushed it when its pull request names one)
+	// and Branch its branch. A mesh-delivery from before says none, and the words are as before.
+	Needs  string `json:"needs,omitempty"`
+	Author string `json:"author,omitempty"`
+	Branch string `json:"branch,omitempty"`
 }
 
+// needsNewHead is what a stalled line needs when its cure is its author's new head (ADR 0505 §5).
+const needsNewHead = "new-head"
+
 // severity is the condition's severity a stalled line asks: urgent when it says so, a warning otherwise.
 func (l stalledLine) severity() conditions.Severity {
 	if l.Severity == string(conditions.Urgent) {
diff --git a/cmd/mesh-controller/new_head_words_test.go b/cmd/mesh-controller/new_head_words_test.go
new file mode 100644
index 00000000..86c8a959
--- /dev/null
+++ b/cmd/mesh-controller/new_head_words_test.go
@@ -0,0 +1,40 @@
+package main
+
+import (
+	"strings"
+	"testing"
+
+	"github.com/novox/mesh-controller/internal/conditions"
+)
+
+// novox/hq ADR 0505 §5: a delivery whose cure is its author's new head reaches the operator in words that name its
+// author and say a new head is needed, offer no Stop and never call it the operator's; the line as mesh-delivery-gate
+// says it (ready.go readyLines: needs "new-head", author, branch).
+func TestADeliveryThatNeedsANewHeadNamesItsAuthorAndOffersNoStop(t *testing.T) {
+	l := stalledLine{ID: "novox/mesh-controller@499ff5c21861", Number: 432, State: "rejected", For: "2h1m0s", Bound: "2h0m0s",
+		H2: "none: a new head from its author, or a recheck that passes", Needs: needsNewHead,
+		Author: "the author of feat/quiet-deliveries (quiet-deliveries on shanks)", Branch: "feat/quiet-deliveries",
+		Says: "novox/mesh-controller#432 passed its checks at 499ff5c21861 and is not merged: a conflict"}
+	o := stalledObservations([]stalledLine{l})[0]
+	for _, words := range []string{o.Headline, o.Explanation, o.Resolved, o.Needs} {
+		if why, ok := conditions.Plain(words); !ok {
+			t.Errorf("%q is not plain: %s", words, why)
+		}
+		for _, never := range []string{"stop it", "operator's"} {
+			if strings.Contains(words, never) {
+				t.Errorf("%q says %q", words, never)
+			}
+		}
+	}
+	if o.Headline != "Pull request 432 of mesh-controller needs a new head from its author" ||
+		!strings.Contains(o.Explanation, "until the author of feat/quiet-deliveries (quiet-deliveries on shanks) pushes a new head") ||
+		!strings.Contains(o.Explanation, "for 2 hours") || len(o.Actions) != 0 ||
+		o.Needs != "ask the author of feat/quiet-deliveries (quiet-deliveries on shanks) for a new head." {
+		t.Fatalf("words: %q / %q / %q / %v", o.Headline, o.Explanation, o.Needs, o.Actions)
+	}
+	// A branch in code is not said; the author is then "its author".
+	l.Author = "the author of fix/a1b2c3d4e5f6"
+	if o := stalledObservations([]stalledLine{l})[0]; !strings.Contains(o.Needs, "ask its author") {
+		t.Fatalf("a dotted branch was said: %q", o.Needs)
+	}
+}
diff --git a/cmd/mesh-controller/plain_words.go b/cmd/mesh-controller/plain_words.go
index fce97830..1a954534 100644
--- a/cmd/mesh-controller/plain_words.go
+++ b/cmd/mesh-controller/plain_words.go
@@ -966,6 +966,9 @@ func stalledWords(l stalledLine, o conditions.Observation) (headline, explanatio
 	if l.State == "unanswered" {
 		return unansweredWords(l, o)
 	}
+	if l.Needs == needsNewHead {
+		return newHeadWords(l, name)
+	}
 	held := l.State
 	if held == "" {
 		held = "held"
@@ -999,6 +1002,29 @@ func stalledWords(l stalledLine, o conditions.Observation) (headline, explanatio
 		fmt.Sprintf("Delivery of %s is no longer %s", name, held), needs, actions
 }
 
+// newHeadWords are the words of a delivery whose cure is its author's new head (novox/hq ADR 0505 §5): it names the
+// author and says a new head is needed; it offers no Stop and never calls it the operator's, because the operator
+// hears of it only once the author's own watch has failed, after two hours with no new head.
+func newHeadWords(l stalledLine, name string) (headline, explanation, resolved, needs string, actions []conditions.Action) {
+	pull := "A pull request of " + name
+	if l.Number > 0 {
+		pull = fmt.Sprintf("Pull request %d of %s", l.Number, name)
+	}
+	author := l.Author
+	if _, plain := conditions.Plain(author); !plain {
+		author = "its author" // a branch named in code (a dotted name, a number) is not said
+	}
+	long := "for a long time"
+	if d, err := time.ParseDuration(l.For); err == nil {
+		long = "for " + humanDuration(d)
+	}
+	return pull + " needs a new head from its author",
+		fmt.Sprintf("%s cannot merge until %s pushes a new head: its check failed after its Approve, and no new head "+
+			"came %s.", pull, author, long),
+		pull + " has a new head, or is closed",
+		"ask " + author + " for a new head.", nil
+}
+
 // stoppedNeeds is what ends a delivery that is already stopped, from the stalled line's healer words ("none: a
 // merge that delivers its modules ends it — the operator's"): the part that says what ends it.
 func stoppedNeeds(l stalledLine) string {