ui: the node editor offers the de-noise node and persists its window

The form gains a `median samples` row, shown only for `DeNoise`; the corner row widens to
anything that reads `fc` (`math_op_uses_fc()`) while `q` stays band-pass-only, and the wiring
row keeps its place at the end so the form's order is unchanged for every existing op.

The session format gains a thirteenth field, `med_n`, after `y`. A twelve-field node -- a file
written before this node existed -- still loads, with `med_n` left at the struct's default,
which is what such a file meant; the reader's `return number(...) && ...` chain had to become a
guarded sequence so the thirteenth field could be read conditionally.

The math probe enables the channel it builds its graphs from, the same self-sufficiency rule
the noise and measurement probes already follow: `enable_all_probe` ends by switching one
signal off, and with `sine` gone the graphs landed on `square`, changing a documented line for
reasons unrelated to the math.

Readings: `[math-probe] 2 math channels on 'sine' and 'noise'`, `pane add: 'math3' sources
'sine'`, `graph edit: stored_slots 31000 -> 32000`, `dialog build: nodes=2, output after add=1`
and the rest of the suite unchanged; no `Gtk-CRITICAL`.

src/layout_store.cpp

@@ -366,7 +366,7 @@ std::string math_node_text(const MathNode& node) {
   std::ostringstream o;
   o << kind << '|' << node.source << '|' << node.in_a << '|' << node.in_b << '|' << node.gain << '|'
     << node.offset << '|' << node.fc << '|' << node.q << '|' << node.lo << '|' << node.hi << '|'
-    << node.x << '|' << node.y;
+    << node.x << '|' << node.y << '|' << node.med_n;
   return o.str();
 }
 
@@ -382,7 +382,9 @@ bool math_node_from_text(const std::string& text, MathNode& out) {
     }
   }
   f.push_back(cur);
-  if (f.size() != 12u) return false;
+  // Twelve fields is a session file written before the de-noise node existed; its `med_n` stays at the
+  // struct's default, which is what that file meant.
+  if (f.size() != 12u && f.size() != 13u) return false;
   const auto number = [&](std::size_t i, double& v) {
     try {
       v = std::stod(f[i]);
@@ -402,8 +404,16 @@ bool math_node_from_text(const std::string& text, MathNode& out) {
   out.source = f[1];
   out.in_a = static_cast<int>(in_a);
   out.in_b = static_cast<int>(in_b);
-  return number(4, out.gain) && number(5, out.offset) && number(6, out.fc) && number(7, out.q) &&
+  if (!(number(4, out.gain) && number(5, out.offset) && number(6, out.fc) && number(7, out.q) &&
-         number(8, out.lo) && number(9, out.hi) && number(10, out.x) && number(11, out.y);
+        number(8, out.lo) && number(9, out.hi) && number(10, out.x) && number(11, out.y))) {
+    return false;
+  }
+  if (f.size() == 13u) {
+    double med = 0.0;
+    if (!number(12, med)) return false;
+    out.med_n = static_cast<int>(med);
+  }
+  return true;
 }
 
 bool load_layout(const std::string& path, LayoutState& out) {

src/ui.cpp

@@ -2140,6 +2140,14 @@ void open_math_dialog(App& app, int edit) {
     gtk_box_append(GTK_BOX(form), clamp_rows);
   }
 
+  // Odd, 3..9. The engine rounds up to odd anyway, but a step of 2 means the widget never offers an even
+  // one.
+  d->med = gtk_spin_button_new_with_range(3.0, 9.0, 2.0);
+  gtk_spin_button_set_digits(GTK_SPIN_BUTTON(d->med), 0);
+  gtk_spin_button_set_value(GTK_SPIN_BUTTON(d->med), 5.0);
+  g_signal_connect(d->med, "value-changed", G_CALLBACK(on_math_param_changed), d);
+  gtk_box_append(GTK_BOX(form), math_row("median samples", d->med, &d->rows[6]));
+
   d->inputs = gtk_label_new("");
   gtk_label_set_wrap(GTK_LABEL(d->inputs), true);
   gtk_widget_add_css_class(d->inputs, "dim-label");
@@ -2159,7 +2167,7 @@ void open_math_dialog(App& app, int edit) {
   gtk_widget_set_visible(d->problem, FALSE);
   gtk_box_append(GTK_BOX(form), d->problem);
 
-  // A menu of the twelve ops rather than one button that always makes a gain: building anything
+  // A menu of the thirteen ops rather than one button that always makes a gain: building anything
   // else was add-then-change-the-dropdown, which is two steps for the common case.
   GtkWidget* add = gtk_menu_button_new();
   gtk_menu_button_set_label(GTK_MENU_BUTTON(add), "add node");

src/ui_app.hpp

@@ -978,9 +978,10 @@ struct MathDialog {
   GtkWidget* offset = nullptr;
   GtkWidget* fc = nullptr;
   GtkWidget* q = nullptr;
+  GtkWidget* med = nullptr;  ///< MathNode::med_n
   GtkWidget* lo = nullptr;
   GtkWidget* hi = nullptr;
-  GtkWidget* rows[6] = {nullptr, nullptr, nullptr, nullptr, nullptr, nullptr};
+  GtkWidget* rows[7] = {nullptr, nullptr, nullptr, nullptr, nullptr, nullptr, nullptr};
   GtkWidget* inputs = nullptr;
   /// The validation line and the button it governs. Both are set from `math_dialog_sync()` and from
   /// nowhere else, so what the line says and what the button allows cannot disagree.

src/ui_math.cpp

@@ -835,6 +835,7 @@ void on_math_param_changed(GtkWidget*, gpointer user) {
   n.offset = gtk_spin_button_get_value(GTK_SPIN_BUTTON(d->offset));
   n.fc = gtk_spin_button_get_value(GTK_SPIN_BUTTON(d->fc));
   n.q = gtk_spin_button_get_value(GTK_SPIN_BUTTON(d->q));
+  n.med_n = static_cast<int>(gtk_spin_button_get_value(GTK_SPIN_BUTTON(d->med)));
   n.lo = gtk_spin_button_get_value(GTK_SPIN_BUTTON(d->lo));
   n.hi = gtk_spin_button_get_value(GTK_SPIN_BUTTON(d->hi));
   if (d->source_drop != nullptr) {
@@ -930,14 +931,18 @@ void math_dialog_sync_form(MathDialog* d) {
   const bool source = op == MathOp::Source;
   gtk_widget_set_visible(d->rows[0], source);  // the source channel
   gtk_widget_set_visible(d->rows[1], gain);
-  gtk_widget_set_visible(d->rows[2], filter);
+  // The corner row is shown for anything that reads `fc`, which is now the three biquads *and* the
+  // de-noise node; `q` stays a band-pass-only row.
+  gtk_widget_set_visible(d->rows[2], math_op_uses_fc(op));
   gtk_widget_set_visible(d->rows[3], filter && op == MathOp::BandPass);
   gtk_widget_set_visible(d->rows[4], clamp);
   gtk_widget_set_visible(d->rows[5], true);  // the inputs, always: they say what is wired
+  gtk_widget_set_visible(d->rows[6], math_op_uses_median(op));
   gtk_spin_button_set_value(GTK_SPIN_BUTTON(d->gain), n.gain);
   gtk_spin_button_set_value(GTK_SPIN_BUTTON(d->offset), n.offset);
   gtk_spin_button_set_value(GTK_SPIN_BUTTON(d->fc), n.fc);
   gtk_spin_button_set_value(GTK_SPIN_BUTTON(d->q), n.q);
+  gtk_spin_button_set_value(GTK_SPIN_BUTTON(d->med), static_cast<double>(n.med_n));
   gtk_spin_button_set_value(GTK_SPIN_BUTTON(d->lo), n.lo);
   gtk_spin_button_set_value(GTK_SPIN_BUTTON(d->hi), n.hi);
   if (d->source_drop != nullptr) {

src/ui_probe.cpp

@@ -281,6 +281,16 @@ gboolean eventzoom_probe(gpointer user) {
 gboolean math_probe(gpointer user) {
   App* a = static_cast<App*>(user);
   if (a->window == nullptr) return G_SOURCE_REMOVE;
+  // The channel the graphs are built from is enabled *here*, for the reason the noise and measurement
+  // probes give: `enable_all_probe` finishes by switching one signal off, and with `sine` gone the graphs
+  // land on `square`, which turns the documented "2 math channels on 'sine' and 'noise'" into a different
+  // line for reasons that have nothing to do with the math.
+  {
+    const std::vector<SignalInfo>& signals = a->model->signals();
+    for (std::size_t i = 0; i < signals.size(); ++i) {
+      if (signals[i].name == "sine") a->model->set_signal_enabled(i, true);
+    }
+  }
   std::string name;
   std::string late_name;
   {