feat: Last Seen column tracking Alertmanager re-send heartbeat

The alert list showed only Started, which comes from Prometheus and
never changes for the lifetime of an alert instance. A firing alert
that started 12 days ago looked identical whether Alertmanager
refreshed it 30 seconds ago or went silent a week ago.

terdut-server already tracks this: the webhook upsert sets
received_at on every accepted payload, including the periodic
re-sends issued at repeat_interval, and its archiver treats the
field as a liveness heartbeat. The field was already decoded into
api.Alert.ReceivedAt and simply never rendered.

Add a Last Seen column to the alert tables, rendered with the
existing humanAgo helper. The Alerts and Archived tabs share
alertColumns/alertRows, so both pick it up. The width budget is
re-derived for five columns; the slack constant now accounts for
all of bubbles' per-cell padding, so the table lands exactly on
the terminal width instead of overflowing by two columns as it
did with four.

The detail view gains a matching Last Seen line, with the timeline
labels widened to keep values aligned. Since received_at stops
advancing once an alert resolves, also pull through the server's
resolution_source and show it in the status header
(RESOLVED · alertmanager vs RESOLVED · expiry) so a frozen
timestamp is explained.

CLAUDE.md

@@ -66,3 +66,16 @@ go build -ldflags="-X main.version=v0.1.0" -o terdut-tui .
 | 3 | Alert detail: acknowledge, comment, statistics charts |
 | 4 | On-call schedule calendar view |
 | 5 | User management and API key lifecycle |
+
+<!-- graymatter:instructions:begin — managed by `graymatter init`; edits inside this block are overwritten -->
+## Memory (GrayMatter)
+
+This project has persistent agent memory via the `graymatter` MCP tools:
+
+- `memory_search` (`agent_id`, `query`) — call at the **start of a task** when prior context might matter.
+- `memory_add` (`agent_id`, `text`) — call whenever you learn something **durable**: user preferences, decisions, conventions, gotchas.
+- `memory_reflect` (`action`, `agent`, `text`/`target`) — update or forget stale facts. ⚠ takes `agent`, not `agent_id`.
+- `checkpoint_save` / `checkpoint_resume` (`agent_id`) — snapshot/restore session state before major refactors or across restarts.
+
+Use a stable `agent_id` of the form `<project>-<role>` (e.g. `myapp-backend`). Store conclusions, not conversation logs. Err on the side of remembering.
+<!-- graymatter:instructions:end -->

internal/api/types.go

@@ -17,6 +17,11 @@ type Alert struct {
 	AcknowledgedBy   string            `json:"acknowledged_by"`
 	AcknowledgedAt   *time.Time        `json:"acknowledged_at"`
 	ArchivedAt       *time.Time        `json:"archived_at,omitempty"`
+
+	// ResolutionSource records why a resolved alert left the firing state:
+	// "alertmanager" for a real resolved webhook, "expiry" when the server
+	// inferred it after the alert stopped being refreshed.
+	ResolutionSource *string `json:"resolution_source,omitempty"`
 }
 
 type AlertStats struct {

internal/tui/model.go

@@ -340,18 +340,21 @@ func (m Model) detailViewportHeight() int {
 // ── Column definitions ─────────────────────────────────────────────────────
 
 func alertColumns(width int) []table.Column {
-	nameW := width/2 - 8
+	const statusW, timeW = 10, 12
+	nameW := width/2 - 14
 	if nameW < 20 {
 		nameW = 20
 	}
-	ackW := width - nameW - 10 - 12 - 6
+	// 10 = bubbles' Padding(0, 1) on each of the five cells.
+	ackW := width - nameW - statusW - 2*timeW - 10
 	if ackW < 8 {
 		ackW = 8
 	}
 	return []table.Column{
 		{Title: "Name", Width: nameW},
-		{Title: "Status", Width: 10},
+		{Title: "Status", Width: statusW},
-		{Title: "Started", Width: 12},
+		{Title: "Started", Width: timeW},
+		{Title: "Last Seen", Width: timeW},
 		{Title: "Ack By", Width: ackW},
 	}
 }
@@ -400,7 +403,7 @@ func alertRows(alerts []api.Alert) []table.Row {
 	now := time.Now()
 	rows := make([]table.Row, len(alerts))
 	for i, a := range alerts {
-		rows[i] = table.Row{a.Name, a.Status, humanAgo(now, a.StartsAt), a.AcknowledgedBy}
+		rows[i] = table.Row{a.Name, a.Status, humanAgo(now, a.StartsAt), humanAgo(now, a.ReceivedAt), a.AcknowledgedBy}
 	}
 	return rows
 }

internal/tui/view.go

@@ -381,7 +381,11 @@ func buildDetailContent(alert api.Alert, comments []api.Comment, cursor, width i
 	if alert.Status == "firing" {
 		statusStr = styleFiring.Render("● FIRING")
 	} else {
-		statusStr = styleResolved.Render("✓ RESOLVED")
+		label := "✓ RESOLVED"
+		if alert.ResolutionSource != nil {
+			label += " · " + *alert.ResolutionSource
+		}
+		statusStr = styleResolved.Render(label)
 	}
 	nameGap := contentW - lipgloss.Width(name) - lipgloss.Width(statusStr)
 	if nameGap < 1 {
@@ -392,6 +396,8 @@ func buildDetailContent(alert api.Alert, comments []api.Comment, cursor, width i
 	// Timeline
 	b.WriteString(fmt.Sprintf("  Started:    %s  (%s)\n",
 		alert.StartsAt.UTC().Format("2006-01-02 15:04 UTC"), humanAgo(now, alert.StartsAt)))
+	b.WriteString(fmt.Sprintf("  Last Seen:  %s  (%s)\n",
+		alert.ReceivedAt.UTC().Format("2006-01-02 15:04 UTC"), humanAgo(now, alert.ReceivedAt)))
 	if alert.EndsAt != nil {
 		b.WriteString(fmt.Sprintf("  Ended:      %s\n", alert.EndsAt.UTC().Format("2006-01-02 15:04 UTC")))
 	}