fix: a wire is picked by distance and a refusal is spoken, so the editor answers

A review of the whole node editor. The hit test measured the distance to the
24 curve samples rather than to the segments between them, so a wire spanning
several rows was unpickable between two samples -- the probe now places its
boxes 280 units apart and prints the nearest sample's own 8.4 against a 3.0
tolerance, which the point test would have missed. A refused connection said
nothing: the message is now carried in `MathDialog::refusal` and shown once by
the single writer of the label, and a self-wire is refused through the real
drag-end path instead of only through `math_connect()`.

Two defects were found only by the new assertions. `math_dialog_sync()`
re-entered itself -- `gtk_drop_down_set_selected()` emits `notify::selected`
for a programmatic set too, and the handler answers by syncing again, which
consumed the refusal before it could be drawn -- so the body is now guarded
one level deep. And a deleted node left `selected_wire` naming an index that
afterwards belongs to a different wire, so `Delete` cleared an input on the
wrong node.

A node is placed in the first free grid cell rather than at the end of the
list's own cell, so a node added after a delete no longer lands on top of a
survivor; the label ellipsizes with a tooltip rather than wrapping, because a
wrapped line makes the dialog's height depend on the text in it.

README.md

@@ -706,9 +706,10 @@ and its output the square on its right. Click a box to select it and its paramet
 form beside the canvas; **drag from an output square to an input square to wire them** (the old
 two-click protocol is gone); drag a wired input square off its port to detach it; click a wire and
 press `Delete` to remove it; drag a box to move it. **Wheel zooms about the pointer, drag the
-background to pan, `f` to fit, `Ctrl+0` to reset.** `Tidy` in the toolbar lays out all nodes in
-topological columns. The op is chosen when the node is added — the picker appears at the `+` — so
-there is no opless placeholder to build past. The graph is a *list* walked in order, so a node can
+background to pan, `f` to fit, `Ctrl+0` to reset.** *tidy*, a button in the editor dialog beside
+*fit*, lays out all nodes in topological columns. The op is chosen when the node is added — *add
+node* in the same row of the dialog is a menu button whose popover lists every op — so there is no
+opless placeholder to build past. The graph is a *list* walked in order, so a node can
 only read the ones above it; a wire drawn right to left re-sorts the list silently, so the graph
 stays evaluable without requiring the user to add nodes in order. A cycle is unrepresentable:
 `math_connect()` checks the trial edge set with Kahn's algorithm before writing anything. The node

docs/claude/invariants-math-channels.md

@@ -23,9 +23,9 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
   The editor is the *compact graph*: nodes as boxes on a `GtkDrawingArea`, click to select (its
   parameters in the form beside it), **drag from an output port to an input port to wire** (the old
   two-click protocol is gone), drag a box to move it; **wheel zooms about the pointer, background
-  drag pans, `f` fits, `Ctrl+0` resets**. Its widgets are created once and only shown, hidden and set by `math_dialog_sync()`,
-  so no rebuild can invalidate a live callback handle -- the same shape the measurements dialog
-  uses. `UDPSCOPE_PROBE_MATH_MS` defines two graphs and opens the editor (a construction crash test
+  drag pans, `f` fits, `Ctrl+0` resets**.
+  Its widgets are created once and only shown, hidden and set by `math_dialog_sync()`, so no rebuild
+  can invalidate a live callback handle -- the same shape the measurements dialog uses. `UDPSCOPE_PROBE_MATH_MS` defines two graphs and opens the editor (a construction crash test
   as much as a state check), and the dump prints each derived channel's extremes beside the
   source's. Read it on the fast mock, where the two assertions that matter are **`gaps=0`** (the
   math is on the producer thread, so what it can break is packet capture, never the frame rate)
@@ -59,11 +59,30 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
   * `[math-probe] wire: connect mode=2 in_a=0 (want 2 0)`,
     `[math-probe] detach: emptied_at_begin=-1 in_a=-1 (want -1 -1)`,
     `[math-probe] detach: escape restores in_a=0 (want 0)`.
-  * `[math-probe] wire: pick node=1 which=0 -> in_a=-1 (want 1 0 -1)`.
+  * `[math-probe] wire: pick node=1 which=0 -> in_a=-1 off_sample=8.4 tol=3.0 (want 1 0 -1,
+    off_sample > tol)` — the pick is taken at `t = 0.52`, **between** samples 12 and 13 of the 24 the
+    curve is walked at, on a wire whose two boxes are several rows apart. `off_sample` is the measured
+    distance from the pick to the nearest sample point and `tol` the pick radius in the same units:
+    with `off_sample` the larger, a hit test that measured to the sample *points* rather than to the
+    *segments* between them would miss. Taken at `t = 0.5` — exactly sample 12 — the line passed for
+    both implementations and asserted nothing, the same mistake as a hit test taken at the identity
+    view.
   * `[math-probe] wire: backwards ok=1 order=[0:-1,1:0,2:1] output=2 valid=1 why=[] (want 1 ... 1 [])` —
     the re-sort. `valid=1` is the assertion; the `order=` string is the reading that explains it.
-  * `[math-probe] wire: self refused=1 why=[...]` and
-    `[math-probe] wire: cycle refused=1 why=[...]` — and **nothing is written** on either.
+  * `[math-probe] wire: self refused=1 why=[a node cannot read itself]` and
+    `[math-probe] wire: cycle refused=1 why=[that wire would make a loop]` — and **nothing is
+    written** on either. Both call `math_connect()` directly, so both assert its out-parameter and
+    neither says anything about the UI.
+  * `[math-probe] wire: self through drag-end node=1 problem=[a node cannot read itself] (want the
+    refusal text, not empty)` — the other half, and the one that matters: the refusal has to reach
+    the **validation line**. The UI path used to screen the self case out before `math_connect()` and
+    then drop its `why` on the floor, so the user drew a wire, nothing appeared and nothing was said
+    while the two lines above passed. No synthetic GTK gesture is reachable headlessly, so the probe
+    sets `drag_mode`/`wire_from`/`press_cx`/`press_cy` and calls `math_canvas_drag_end()` — which is
+    still the handler under test. An empty `problem=[]` here is also how the sync **re-entrancy** was
+    found: setting the op dropdown emits `notify::selected`, whose handler syncs, so the form's own
+    write re-entered `math_dialog_sync()` and the inner call rewrote the label the outer had just
+    written. `MathDialog::syncing` guards it.
   * `[math-probe] validate: broken problem=[..] label=[..] apply=0; fixed problem=[] apply=1 (want non-empty 0; empty 1)`,
     `[math-probe] validate: no-selection label=[..] (want non-empty)` — the label is written
     **above** `math_dialog_sync()`'s early return; a stale message when there is no selection to
@@ -72,7 +91,14 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
     dropdown lists exactly the acquired channels, not all signals.
   * `[math-probe] op pick: nodes 3->4 op_index=7 q_row=1 (want 4 7 1)` and
     `[math-probe] op pick: index round trip=1 (want 1)`.
-  * `[math-probe] tidy: xs=[24,204,384,564] overlaps=0 (want 0)`.
+  * `[math-probe] add node: after a delete cells=[(24,20) (24,78) (184,78) (184,20)] overlaps=0
+    (want 0)` — the boxes are put back on the grid, the middle one deleted and one added. The new box
+    takes cell 1, `(184,20)`, which the deletion freed; placing by `nodes.size()` would have put it on
+    `(184,78)`, which is occupied, and an overlapped box is an unclickable one. `overlaps` is the
+    assertion, `cells` the reading that explains it.
+  * `[math-probe] tidy: xs=[24,24,204,384] overlaps=0 (want 0)` — four nodes in three depth columns
+    (the delete above left two roots), so two share the first column and the x values repeat. Only
+    `overlaps=0` is the assertion.
   Four rules here were wrong first and are worth keeping:
   * **A `Source` may only name an *acquired* channel** -- `ScopeModel::channels()`, which is what the
     dialog's dropdown lists, **and both places that create a node must take one from there**.
@@ -103,10 +129,15 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
   * **Boxes must not overlap on the canvas.** The first auto-place staggered nodes by 24 px for a
     132 px box, so every box sat on the one before it, `math_node_at()`'s topmost-first search always
     returned the last, and a drag or a click landed on the wrong node -- which reads as the dialog
-    ignoring the pointer. The **add-node grid** places in two columns spaced 160 px apart, rows 58;
-    the **tidy layout** uses a column pitch of `kNodeW + 48` (narrower), which is enough clearance
-    for a wire's 40-unit horizontal tread — at 160 the bezier's control points cross and the wire
-    doubles back on itself. The probe prints the box the drag *began over* for exactly this reason.
+    ignoring the pointer. The **add-node grid** places in two columns spaced 160 px apart, rows 58,
+    and `math_add_node()` takes the **first free cell** rather than cell `nodes.size()`: placing by
+    the count reuses an occupied cell as soon as anything has been deleted — delete the middle of
+    three and add one and the new box lands exactly on an existing one. The free-cell search uses the
+    same overlap test the tidy probe asserts with, and falls through to cell `nodes.size()` after 64
+    cells rather than searching for ever. The **tidy layout** uses a column pitch of `kNodeW + 48` =
+    180, which is *wider* than that 160 and is what gives a wire's 40-unit horizontal tread its
+    clearance — at 160 the bezier's control points cross and the wire doubles back on itself. The
+    probe prints the box the drag *began over* for exactly this reason.
     Offering the whole signal list let a graph name something nobody is acquiring (no data for ever)
     and put the stream's timestamp signal, which has no samples, in it.
   * **`prepare_math_locked()` runs from `rebuild_locked()`, so *every* plan change re-prepares the
@@ -158,6 +189,17 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
   * **The validation line is written above `math_dialog_sync()`'s early return.** An out-of-range
     selection is exactly the state in which a stale message misleads most: the graph can still be
     broken and there is no form to read instead.
+  * **The line is written from `math_dialog_sync()` and from nowhere else, it ellipsizes, and its
+    tooltip carries the full text.** Three consequences. (1) A *refusal* — "a node cannot read
+    itself", a cycle — is not a state `math_dialog_problem()` can describe, since it is a thing that
+    did not happen, so `drag-end` leaves it on `MathDialog::refusal`, which the sync shows in
+    preference to the graph's own problem and **consumes as it writes**: the message lasts until the
+    next sync, and every mutation syncs. `Apply`'s sensitivity still follows the graph alone, because
+    a refused wire wrote nothing. (2) The label **ellipsizes rather than wraps**, and the tooltip is
+    set beside the text so the two cannot disagree — layout must not depend on content, and this
+    label sits in a dialog whose canvas is `hexpand`. (3) The sync is **not re-entrant**
+    (`MathDialog::syncing`): writing the op dropdown emits `notify::selected`, whose handler syncs,
+    and the inner call rewrote the label the outer one had just written.
   * **`math_op_index()`, never a cast.** `math_op_at()`'s order is the dialog's — what a dropdown
     lists and what a session file stores — and `static_cast<guint>(op)` worked only because the
     two happen to agree today. The session-file rule in this file already says an op is written as

docs/claude/verification.md

@@ -17,10 +17,14 @@ Two baselines every run is read against. A clean build emits **four** warnings a
 `-Wmissing-field-initializers` on `MathNode::source` and `-Woverlength-strings` on **both**
 generated GResource `.c` files — the help pages' and the icons', whose blob crossed C99's
 4095-byte string-literal limit when the two app icons joined the four action ones (a note about a
-generated file, which GCC itself supports). The fifth warning that used to appear here was an
-unused `output_built` in `on_math_apply()` — Task 6's live validation check reads that value, so
-the variable is no longer unused. And an exit-dump run emits **no** `Gtk-CRITICAL` at all. A
-fifth warning, or any critical, is a finding.
+generated file, which GCC itself supports). The fifth warning that used to appear here was an unused
+`output_built` in `math_probe()`; it was **deleted** as dead code — redundant with the
+`output_after_add` already printed on the same line — and that deletion is what dropped the baseline
+from five to four. Nothing started reading it. And an exit-dump run emits **no** `Gtk-CRITICAL` at
+all. A fifth warning, or any critical, is a finding.
+
+An *incremental* build reads **two** of those four: the generated GResource `.c` files are not
+recompiled when only `src/` changed, so their `-Woverlength-strings` do not reappear.
 
 That second baseline used to be "exactly two, `gtk_widget_get_height` and `gtk_widget_get_width`,
 from the dump asking a destroyed widget for its size", and tolerating them was a mistake: the dump

src/help/11-math.txt

@@ -5,22 +5,24 @@ nodes, operations, one output — and udpscope then treats the result as an ordi
 
 <b>How to reach it</b>
 
-The math button in the toolbar, or <tt>g</tt>. The pane's <tt>+</tt> adds a channel — a picker
-chooses the op — and opening one shows the graph editor: nodes as boxes, click a box to select it
-and edit its parameters beside the canvas.
+The math button in the toolbar, or <tt>g</tt>. The pane's <tt>+</tt> adds a channel, and opening
+one shows the graph editor: nodes as boxes, click a box to select it and edit its parameters beside
+the canvas. Inside the editor, <i>add node</i> is a menu button whose popover picks the op, so the
+node arrives as the operation you asked for.
 
 <b>Graph gestures:</b> <b>drag</b> from an output port to an input port to wire them; drag a
 wired input port off its connection to detach it; click a wire and press <tt>Delete</tt> to remove
 it; drag a box to move it. <b>Wheel</b> zooms about the pointer. <b>Drag the background</b> to
-pan. <tt>f</tt> fits all nodes into view; <tt>Ctrl+0</tt> resets the view. <tt>Tidy</tt> in the
-toolbar lays the graph out in topological columns. The orange dot marks the output node; click
-<i>set as output</i> to move it.
+pan. <tt>f</tt> fits all nodes into view; <tt>Ctrl+0</tt> resets the view. <i>tidy</i>, the button
+beside <i>fit</i> in the editor, lays the graph out in topological columns and frames it. The orange
+dot marks the output node; click <i>set as output</i> to move it.
 
 <b>Worth knowing</b>
 
 • The graph is evaluated as an ordered list, so a node may only read ones <i>above</i> it. A
   wire drawn right to left re-sorts the list silently so the graph stays valid. A cycle is
-  unrepresentable: the connection is refused rather than created.
+  unrepresentable: the connection is refused rather than created, and the line beneath the form
+  says why — a loop, or a node asked to read itself.
 • A derived channel <i>is</i> a channel. It appears in the signal panel, can be plotted,
   measured, exported, and used as a source for another math channel.
 • The math runs on the <b>stored</b> samples — decimated and averaged — so a cutoff you type in

src/ui.cpp

@@ -3282,8 +3282,10 @@ void add_math_channel(App& app) {
 // the output the square on its right. Click a box to select it (its parameters appear in the form
 // beside the canvas), drag from an output square to an input square to wire them, drag a wired
 // input off to detach it, drag a box to move it. The graph is a *list*, walked in order, so a node
-// may only read ones above it -- which is why an input square offers only the nodes before it and a
-// cycle cannot be drawn at all.
+// may only read ones above it -- but that order is the *evaluator's* contract, not a restriction on
+// the gesture: a wire may be drawn in either direction and `math_connect()` re-sorts the list
+// (Kahn's algorithm) so the contract still holds. Only a wire that cannot be ordered at all, i.e.
+// one that closes a cycle, is refused, and it is refused at connect time with a message.
 constexpr double kNodeW = 132.0;
 constexpr double kNodeH = 46.0;
 constexpr double kPort = 10.0;
@@ -3351,10 +3353,25 @@ struct MathDialog {
   GtkWidget* hi = nullptr;
   GtkWidget* rows[6] = {nullptr, nullptr, nullptr, nullptr, nullptr, nullptr};
   GtkWidget* inputs = nullptr;
-  /// The validation line and the button it governs. Both are set from `math_dialog_problem()` and
-  /// from nowhere else, so what the line says and what the button allows cannot disagree.
+  /// 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.
   GtkWidget* problem = nullptr;
   GtkWidget* apply = nullptr;
+  /// Why the last gesture was *refused* -- "a node cannot read itself", or a cycle. A refusal has no
+  /// standing state to be read back from: it is a thing that did not happen, so `math_dialog_problem()`
+  /// cannot describe it and a refused wire otherwise just fails to appear, which reads as the editor
+  /// being broken. `math_dialog_sync()` shows this in preference to the graph's own problem and
+  /// **consumes it as it writes**, so the next sync -- and every mutation syncs -- replaces it with
+  /// the graph's state. `Apply`'s sensitivity still follows `math_dialog_problem()` alone: a refused
+  /// wire changed nothing, so a graph that was saveable still is.
+  std::string refusal;
+  /// True while the form is being written. `gtk_drop_down_set_selected()` emits `notify::selected`
+  /// for a programmatic set exactly as for a user one, and the op handler answers a notify by
+  /// syncing -- so writing the form **re-entered** `math_dialog_sync()`, and the inner call rewrote
+  /// the validation label the outer one had just written. That is how a refusal vanished in the same
+  /// call that put it up (the probe's `wire: self through drag-end` read an empty line). A
+  /// programmatic set is not a user edit.
+  bool syncing = false;
 };
 
 /// The channels a math channel may read: the ones the model actually acquires. Offering the whole
@@ -3580,12 +3597,36 @@ int math_node_at_canvas(const MathDialog* d, double cx, double cy) {
   return math_node_at(d, gx, gy);
 }
 
+/// The squared distance from a point to a line *segment* -- clamped to the segment, so the ends do
+/// not extend it. A degenerate segment falls back to the distance to its first point.
+double math_seg_dist2(double px, double py, double ax, double ay, double bx, double by) {
+  const double dx = bx - ax;
+  const double dy = by - ay;
+  const double len2 = dx * dx + dy * dy;
+  double t = 0.0;
+  if (len2 > 0.0) t = std::clamp(((px - ax) * dx + (py - ay) * dy) / len2, 0.0, 1.0);
+  const double cx = px - (ax + t * dx);
+  const double cy = py - (ay + t * dy);
+  return cx * cx + cy * cy;
+}
+
 /// The wire under a graph position, or `{-1, 0}`. The wire is the cubic the draw lays down, so it
 /// is *sampled* rather than solved: 24 segments is well under a pixel of chord error at the scales
 /// this canvas allows, and a closed form for "nearest point on a cubic" is a quartic root find for
-/// no gain. Topmost-first, matching every other hit test here.
+/// no gain.
+///
+/// The 24 samples are the ends of 24 **segments**, and it is the distance to the segment that is
+/// measured. Testing the sample *points* instead leaves a gap wherever two of them are more than
+/// `2 * tol` apart -- which a wire spanning several rows of a tidied graph is, in y -- and in that
+/// gap a click lands on the drawn wire and picks nothing. That is half of "it is not possible to
+/// delete edges".
+///
+/// The *nearest* wire wins rather than the first one found, so a crossing picks the one actually
+/// under the pointer; topmost-first iteration is the tie-break, matching every other hit test here.
 MathWireRef math_wire_at(const MathDialog* d, double gx, double gy, double tol) {
   constexpr int kSamples = 24;
+  MathWireRef best{-1, 0};
+  double best_d2 = tol * tol;
   for (int i = static_cast<int>(d->nodes.size()) - 1; i >= 0; --i) {
     const MathNode& n = d->nodes[static_cast<std::size_t>(i)];
     const int ins[2] = {n.in_a, n.in_b};
@@ -3600,18 +3641,24 @@ MathWireRef math_wire_at(const MathDialog* d, double gx, double gy, double tol)
       math_input_pos(n, k, bx, by);
       const double c1x = ax + 40.0;
       const double c2x = bx - 40.0;
-      for (int s = 0; s <= kSamples; ++s) {
+      double prev_x = ax;
+      double prev_y = ay;
+      for (int s = 1; s <= kSamples; ++s) {
         const double t = static_cast<double>(s) / kSamples;
         const double u = 1.0 - t;
         const double px = u * u * u * ax + 3 * u * u * t * c1x + 3 * u * t * t * c2x + t * t * t * bx;
         const double py = u * u * u * ay + 3 * u * u * t * ay + 3 * u * t * t * by + t * t * t * by;
-        if (std::fabs(gx - px) <= tol && std::fabs(gy - py) <= tol) {
-          return MathWireRef{i, k};
+        const double d2 = math_seg_dist2(gx, gy, prev_x, prev_y, px, py);
+        if (d2 < best_d2) {
+          best_d2 = d2;
+          best = MathWireRef{i, k};
         }
+        prev_x = px;
+        prev_y = py;
       }
     }
   }
-  return MathWireRef{-1, 0};
+  return best;
 }
 
 /// The pick radius for a wire, in screen pixels. Smaller than a port's, so a wire that passes
@@ -3944,15 +3991,23 @@ void math_canvas_drag_end(GtkGestureDrag*, double dx, double dy, gpointer user)
   // node may be a column away from the press point.
   int which = kPortOut;
   const int target = math_port_at_canvas(d, d->press_cx + dx, d->press_cy + dy, which);
-  if (target >= 0 && which != kPortOut && target != d->wire_from) {
+  // Released on *any* input port, `wire_from`'s own included: the self case has to reach
+  // `math_connect()` to be refused there by name. Screening it out here meant the one refusal the
+  // user is most likely to provoke never got a message at all.
+  if (target >= 0 && which != kPortOut) {
     std::string why;
     if (math_connect(d, d->wire_from, target, which, &why)) {
       // `math_connect()` may have permuted the list, so the target's index is no longer `target`.
       math_dialog_sync(d);
-    } else if (d->wire_detach >= 0) {
+    } else {
       // A refused wire must not also lose the one the drag detached to start with.
-      MathNode& back = d->nodes[static_cast<std::size_t>(d->wire_detach)];
-      (d->wire_detach_which == 0 ? back.in_a : back.in_b) = d->wire_from;
+      if (d->wire_detach >= 0 && d->wire_detach < static_cast<int>(d->nodes.size())) {
+        MathNode& back = d->nodes[static_cast<std::size_t>(d->wire_detach)];
+        (d->wire_detach_which == 0 ? back.in_a : back.in_b) = d->wire_from;
+      }
+      // And it must *say* why. `why` used to be filled and dropped here, so neither "a node cannot
+      // read itself" nor the cycle refusal ever reached the user.
+      d->refusal = why.empty() ? std::string("that wire cannot be made") : why;
       math_dialog_sync(d);
     }
   }
@@ -4009,6 +4064,10 @@ gboolean math_canvas_key(GtkEventControllerKey*, guint keyval, guint, GdkModifie
     d->drag_mode = MathDrag::None;
     d->wire_from = -1;
     d->wire_detach = -1;
+    // Restoring the input is a mutation like any other, so the validation line has to be
+    // re-evaluated: `drag-begin` emptied the input and synced, leaving "input is not connected" on
+    // screen with `Apply` insensitive, and without this the undo left both there.
+    math_dialog_sync(d);
     gtk_widget_queue_draw(d->canvas);
     return TRUE;
   }
@@ -4038,8 +4097,33 @@ void math_add_node(MathDialog* d, MathOp op) {
   MathNode n;
   n.op = op;
   const std::size_t k = d->nodes.size();
-  n.x = 24.0 + 160.0 * static_cast<double>(k % 2u);
-  n.y = 20.0 + 58.0 * static_cast<double>(k / 2u);
+  // The first *free* cell of the grid, not cell `k`. Placing by `nodes.size()` reuses an occupied
+  // cell as soon as anything has been deleted -- delete the middle of three and add one and the new
+  // box lands exactly on an existing one, which breaks the documented rule that boxes must not
+  // overlap: `math_node_at()` searches topmost-first, so the covered box becomes unclickable. Same
+  // 160/58 pitch and two-column wrap as before; only the choice of cell changes. A graph that has
+  // taken every cell up to the bound falls through to cell `k` rather than searching for ever.
+  constexpr std::size_t kCellLimit = 64;
+  std::size_t cell = k;
+  for (std::size_t c = 0; c < kCellLimit; ++c) {
+    const double cx = 24.0 + 160.0 * static_cast<double>(c % 2u);
+    const double cy = 20.0 + 58.0 * static_cast<double>(c / 2u);
+    bool free_cell = true;
+    for (const MathNode& other : d->nodes) {
+      if (cx < other.x + kNodeW && other.x < cx + kNodeW && cy < other.y + kNodeH &&
+          other.y < cy + kNodeH) {
+        free_cell = false;
+        break;
+      }
+    }
+    if (free_cell) {
+      cell = c;
+      break;
+    }
+  }
+  n.x = 24.0 + 160.0 * static_cast<double>(cell % 2u);
+  n.y = 20.0 + 58.0 * static_cast<double>(cell / 2u);
+  // `k`, not `cell`: the new node's *index* is the end of the list whatever cell it was drawn in.
   const int arity = math_op_arity(n.op);
   if (arity >= 1 && k > 0) n.in_a = static_cast<int>(k) - 1;
   if (arity >= 2 && k > 0) n.in_b = static_cast<int>(k) - 1;
@@ -4083,6 +4167,11 @@ void on_math_node_deleted(GtkButton*, gpointer user) {
   d->drag_mode = MathDrag::None;
   d->wire_from = -1;
   d->wire_detach = -1;
+  // `MathWireRef::node` is an index into `d->nodes`, so a selection held across the erase names a
+  // *different* wire afterwards and `Delete` would clear an input on the wrong node. Cleared rather
+  // than remapped because the selected wire may have been one of the deleted node's own: a selection
+  // the user can no longer see, pointing at a surviving edge, is worse than no selection.
+  d->selected_wire = MathWireRef{-1, 0};
   math_dialog_sync(d);
 }
 
@@ -4141,15 +4230,24 @@ void on_math_op_changed(GObject* object, GParamSpec*, gpointer user) {
 }
 
 /// The form and the canvas from the selected node: which rows an op uses, what they hold, and which
-/// nodes its inputs are wired to.
-void math_dialog_sync(MathDialog* d) {
+/// nodes its inputs are wired to. Called only through `math_dialog_sync()`, which guards it against
+/// the re-entry the dropdowns' `notify::selected` would otherwise cause.
+void math_dialog_sync_form(MathDialog* d) {
   // Before the early return below: an out-of-range selection is exactly the state in which a stale
   // validation line is most misleading -- a graph with no node selected can still be broken, and the
   // user has no form to read instead.
   if (d->problem != nullptr) {
     const std::string why = math_dialog_problem(d);
-    gtk_label_set_text(GTK_LABEL(d->problem), why.c_str());
-    gtk_widget_set_visible(d->problem, !why.empty());
+    // A refusal from the last gesture wins the *text*, because nothing in the graph's state records
+    // it; `Apply` still follows `why`, since a refused wire wrote nothing. Consumed here, so the
+    // message lasts exactly until the next sync.
+    const std::string shown = d->refusal.empty() ? why : d->refusal;
+    d->refusal.clear();
+    gtk_label_set_text(GTK_LABEL(d->problem), shown.c_str());
+    // The label ellipsizes (see its construction), so the tooltip is the only place the full text
+    // can be read. Set here, beside the text, so the two cannot disagree.
+    gtk_widget_set_tooltip_text(d->problem, shown.empty() ? nullptr : shown.c_str());
+    gtk_widget_set_visible(d->problem, !shown.empty());
     if (d->apply != nullptr) gtk_widget_set_sensitive(d->apply, why.empty());
   }
   if (d->selected < 0 || d->selected >= static_cast<int>(d->nodes.size())) {
@@ -4221,6 +4319,20 @@ void math_dialog_sync(MathDialog* d) {
   gtk_widget_queue_draw(d->canvas);
 }
 
+/// The one entry point, and the re-entrancy guard: setting the op dropdown emits `notify::selected`,
+/// whose handler syncs, so the form's own write re-entered the sync and the inner call rewrote the
+/// validation label -- erasing a refusal in the same call that displayed it. One level only; the
+/// flag is reset by a scope guard, so the early return inside cannot leave it set.
+void math_dialog_sync(MathDialog* d) {
+  if (d->syncing) return;
+  struct Guard {
+    MathDialog* d;
+    ~Guard() { d->syncing = false; }
+  } guard{d};
+  d->syncing = true;
+  math_dialog_sync_form(d);
+}
+
 void on_math_apply(GtkButton*, gpointer user) {
   MathDialog* d = static_cast<MathDialog*>(user);
   on_math_param_changed(nullptr, d);
@@ -4483,10 +4595,14 @@ void open_math_dialog(App& app, int edit) {
   gtk_widget_set_halign(d->inputs, GTK_ALIGN_START);
   gtk_box_append(GTK_BOX(form), math_row("wired", d->inputs, &d->rows[5]));
 
-  // Why the graph cannot be saved, in the form column where the user is already reading. Wrapped,
-  // so a long channel name does not widen the dialog, and hidden when there is nothing to say.
+  // Why the graph cannot be saved, in the form column where the user is already reading. Hidden
+  // when there is nothing to say, and **ellipsized rather than wrapped**, with the full text on the
+  // tooltip (`math_dialog_sync()` sets both together): layout must not depend on content. This label
+  // sits in a dialog whose canvas is `hexpand`, so a wrapping message re-heights the form -- and a
+  // long channel name in it would widen the dialog -- on a mere change of graph. The same rule the
+  // status bar and the y gutter are built to.
   d->problem = gtk_label_new("");
-  gtk_label_set_wrap(GTK_LABEL(d->problem), TRUE);
+  gtk_label_set_ellipsize(GTK_LABEL(d->problem), PANGO_ELLIPSIZE_END);
   gtk_label_set_xalign(GTK_LABEL(d->problem), 0.0f);
   gtk_widget_add_css_class(d->problem, "error");
   gtk_widget_set_visible(d->problem, FALSE);
@@ -7521,27 +7637,53 @@ gboolean math_probe(gpointer user) {
       p->view_x = 50.0;
       p->view_y = 20.0;
       p->nodes[1].in_a = 0;
-      // Halfway along the wire in *graph* units: the bezier's own midpoint, which for a cubic
-      // with these control points is the average of the two ends plus three eighths of the
-      // tread -- so sampling the curve is the only honest way to find a point on it.
+      // The two boxes are put several rows apart on purpose: that is the geometry a tidied graph
+      // has, and it is the only one in which the pick can fail. Where consecutive curve samples are
+      // close together, a hit test that measures to the sample *points* and one that measures to the
+      // *segments* between them give the same answer, so a probe taken on a short wire asserts
+      // nothing about either.
+      p->nodes[0].x = 24.0;
+      p->nodes[0].y = 20.0;
+      p->nodes[1].x = 260.0;
+      p->nodes[1].y = 300.0;
       double ax = 0.0;
       double ay = 0.0;
       double bx = 0.0;
       double by = 0.0;
       math_output_pos(p->nodes[0], ax, ay);
       math_input_pos(p->nodes[1], 0, bx, by);
-      const double t = 0.5;
-      const double u = 1.0 - t;
-      const double mx = u * u * u * ax + 3 * u * u * t * (ax + 40.0) +
-                        3 * u * t * t * (bx - 40.0) + t * t * t * bx;
-      const double my = u * u * u * ay + 3 * u * u * t * ay + 3 * u * t * t * by + t * t * t * by;
+      // **Between two samples, not at one.** `math_wire_at()` samples the cubic at `s / 24`, so
+      // `t = 0.5` is exactly sample 12 and a point-distance test passes there by construction --
+      // the same mistake as a hit test taken at the identity view. `t = 0.52` falls between samples
+      // 12 and 13, and `off_sample` below is the measured distance from the pick to the nearest of
+      // the 25 sample points, in graph units, beside the tolerance the pick is allowed: it reads
+      // off_sample=8.4 against tol=3.0, so a point test misses and only a segment test can hit.
+      const auto curve_at = [&](double t, double& px, double& py) {
+        const double u = 1.0 - t;
+        px = u * u * u * ax + 3 * u * u * t * (ax + 40.0) + 3 * u * t * t * (bx - 40.0) +
+             t * t * t * bx;
+        py = u * u * u * ay + 3 * u * u * t * ay + 3 * u * t * t * by + t * t * t * by;
+      };
+      const double t = 0.52;
+      double mx = 0.0;
+      double my = 0.0;
+      curve_at(t, mx, my);
+      double off_sample = 1e300;
+      for (int s = 0; s <= 24; ++s) {
+        double sx = 0.0;
+        double sy = 0.0;
+        curve_at(static_cast<double>(s) / 24.0, sx, sy);
+        off_sample = std::min(off_sample, std::max(std::fabs(mx - sx), std::fabs(my - sy)));
+      }
       const MathWireRef hit = math_wire_at_canvas(p, mx * p->view_scale + p->view_x,
                                                   my * p->view_scale + p->view_y);
       p->selected_wire = hit;
       math_canvas_key(nullptr, GDK_KEY_Delete, 0, static_cast<GdkModifierType>(0), p);
       std::fprintf(stderr,
-                   "[math-probe] wire: pick node=%d which=%d -> in_a=%d (want 1 0 -1)\n",
-                   hit.node, hit.which, p->nodes[1].in_a);
+                   "[math-probe] wire: pick node=%d which=%d -> in_a=%d off_sample=%.1f tol=%.1f "
+                   "(want 1 0 -1, off_sample > tol)\n",
+                   hit.node, hit.which, p->nodes[1].in_a, off_sample,
+                   kWirePick / p->view_scale);
       p->nodes[1].in_a = 0;
       p->selected_wire = MathWireRef{-1, 0};
     }
@@ -7591,6 +7733,43 @@ gboolean math_probe(gpointer user) {
       std::fprintf(stderr, "[math-probe] wire: self refused=%d why=[%s] (want 1)\n",
                    self_ok ? 0 : 1, self_why.c_str());
 
+      // The same refusal again, through the **handler**. The line above asserts only
+      // `math_connect()`'s out-parameter: the UI path used to screen the self case out before the
+      // call and then drop `why` on the floor, so a user drew the wire, nothing appeared and nothing
+      // was said -- which is the whole of "the editor is broken" -- while the direct call passed.
+      // This half asserts what the *validation line* reads after `drag-end`, which is the only place
+      // that defect is visible. A synthetic GTK gesture is not reachable headlessly, so the drag's
+      // state is set up by hand and the real handler called: `press_cx`/`press_cy` plus a zero offset
+      // is a release exactly on the input port of `wire_from` itself.
+      for (std::size_t i = 0; i < c->nodes.size(); ++i) {
+        // Spread out, so the release point belongs to one port and not to three stacked at (0,0).
+        c->nodes[i].x = 24.0 + 200.0 * static_cast<double>(i);
+        c->nodes[i].y = 20.0;
+      }
+      math_set_scale(c, 1.0);
+      c->view_x = 0.0;
+      c->view_y = 0.0;
+      int self_node = -1;
+      for (std::size_t i = 0; i < c->nodes.size() && self_node < 0; ++i) {
+        if (math_op_arity(c->nodes[i].op) >= 1) self_node = static_cast<int>(i);
+      }
+      if (self_node >= 0) {
+        double sx = 0.0;
+        double sy = 0.0;
+        math_input_pos(c->nodes[static_cast<std::size_t>(self_node)], 0, sx, sy);
+        c->drag_mode = MathDrag::Wire;
+        c->wire_from = self_node;
+        c->wire_detach = -1;
+        c->press_cx = sx;
+        c->press_cy = sy;
+        math_canvas_drag_end(nullptr, 0.0, 0.0, c);
+        const char* line = gtk_label_get_text(GTK_LABEL(c->problem));
+        std::fprintf(stderr,
+                     "[math-probe] wire: self through drag-end node=%d problem=[%s] "
+                     "(want the refusal text, not empty)\n",
+                     self_node, line != nullptr ? line : "(null)");
+      }
+
       // A cycle: the node that already feeds the other is asked to read it back.
       const int reader_idx = c->nodes[1].in_a == 0 ? 2 : 1;
       const int feeder_idx = reader_idx == 2 ? 1 : 2;
@@ -7680,6 +7859,39 @@ gboolean math_probe(gpointer user) {
         if (math_op_index(math_op_at(i)) != i) round = 0;
       }
       std::fprintf(stderr, "[math-probe] op pick: index round trip=%d (want 1)\n", round);
+
+      // And placement: the first *free* grid cell, not cell `nodes.size()`. The boxes are put back
+      // on the grid, the middle one deleted and one added -- under the old placement the new box
+      // landed on the cell the deleted node's *successor* had moved out of the count for, i.e. on an
+      // occupied one, and `math_node_at()` searches topmost-first, so the covered box becomes
+      // unclickable. `cells=` is where the boxes ended up; `overlaps` is the assertion.
+      if (o->nodes.size() >= 3) {
+        for (std::size_t i = 0; i < o->nodes.size(); ++i) {
+          o->nodes[i].x = 24.0 + 160.0 * static_cast<double>(i % 2u);
+          o->nodes[i].y = 20.0 + 58.0 * static_cast<double>(i / 2u);
+        }
+        o->selected = 1;
+        on_math_node_deleted(nullptr, o);
+        math_add_node(o, MathOp::Gain);
+        int overlaps = 0;
+        std::string cells;
+        for (std::size_t i = 0; i < o->nodes.size(); ++i) {
+          const MathNode& p2 = o->nodes[i];
+          cells += (i != 0 ? " " : "");
+          cells += "(" + std::to_string(static_cast<int>(p2.x)) + "," +
+                   std::to_string(static_cast<int>(p2.y)) + ")";
+          for (std::size_t j = i + 1; j < o->nodes.size(); ++j) {
+            const MathNode& q2 = o->nodes[j];
+            if (p2.x < q2.x + kNodeW && q2.x < p2.x + kNodeW && p2.y < q2.y + kNodeH &&
+                q2.y < p2.y + kNodeH) {
+              ++overlaps;
+            }
+          }
+        }
+        std::fprintf(stderr,
+                     "[math-probe] add node: after a delete cells=[%s] overlaps=%d (want 0)\n",
+                     cells.c_str(), overlaps);
+      }
     }
   }
     if (a->math_dialog != nullptr) {