diff --git a/README.md b/README.md
index 1fb245cc..55965ffc 100644
--- a/README.md
+++ b/README.md
@@ -37,7 +37,7 @@ npm run build        # writes dist/ and regenerates index.html; the folder is wh
 The browser suite and the three example games need a machine with a GPU:
 
 ```bash
-node tools/seed-e2e.mjs && node tools/e2e.mjs      # the editor, 844 checks (GM_STEPS=20 for one step)
+node tools/seed-e2e.mjs && node tools/e2e.mjs      # the editor, 862 checks (GM_STEPS=20 for one step)
 node tools/seed-jumprun.mjs && node tools/smoke-jumprun.mjs
 node tools/seed-tetris.mjs && node tools/smoke-tetris.mjs
 node tools/seed-actor.mjs && node tools/smoke-actor.mjs
@@ -57,7 +57,7 @@ touches and leave the full run to CI. Details, the GPU requirement and the detac
 | [Colliders](https://git.nockal.com/meleki/game-maker/wiki/Colliders) | Collision events and blocking movement |
 | [Textures](https://git.nockal.com/meleki/game-maker/wiki/Textures) | Images, frames, the filter, upload limits |
 | [Animations](https://git.nockal.com/meleki/game-maker/wiki/Animations) | Animation assets and the Animation tab |
-| [State machines](https://git.nockal.com/meleki/game-maker/wiki/State-machines) | The asset, `State branch` and `Set state` |
+| [State machines](https://git.nockal.com/meleki/game-maker/wiki/State-machines) | The asset, named transitions, `State branch`, `Set state` and `State transition` |
 | [Containers](https://git.nockal.com/meleki/game-maker/wiki/Containers) | Templates, instances, screens |
 | [Keyboard](https://git.nockal.com/meleki/game-maker/wiki/Keyboard) | Every shortcut |
 | [Architecture](https://git.nockal.com/meleki/game-maker/wiki/Architecture) | Stack, source layout, the rules that keep it organised |
diff --git a/src/core/commands/graphCommands.ts b/src/core/commands/graphCommands.ts
index 7ef661a5..8fe4aca2 100644
--- a/src/core/commands/graphCommands.ts
+++ b/src/core/commands/graphCommands.ts
@@ -242,6 +242,39 @@ export class FoldEdgeCommand implements Command {
   }
 }
 
+/** The name a transition answers to. Blank clears it, since an unnamed transition is the normal one. */
+export class NameTransitionCommand implements Command {
+  readonly label = 'Name transition';
+  private previous = '';
+
+  constructor(
+    private readonly assetId: string,
+    private readonly edgeId: string,
+    private readonly name: string,
+  ) {}
+
+  execute(project: Project): void {
+    const edge = this.edge(project);
+    this.previous = edge.label ?? '';
+    this.apply(edge, this.name.trim());
+  }
+
+  undo(project: Project): void {
+    this.apply(this.edge(project), this.previous);
+  }
+
+  private edge(project: Project): GraphEdge {
+    const edge = requireGraph(project, this.assetId).edges.find((e) => e.id === this.edgeId);
+    if (!edge) throw new CommandError(`Edge ${this.edgeId} not found`);
+    return edge;
+  }
+
+  private apply(edge: GraphEdge, name: string): void {
+    if (name) edge.label = name;
+    else delete edge.label;
+  }
+}
+
 /** One undo step for the whole selection; every node is found before any of them changes. */
 export class CollapseNodesCommand implements Command {
   readonly label: string;
diff --git a/src/core/graph/Graph.ts b/src/core/graph/Graph.ts
index 529e7113..12149ada 100644
--- a/src/core/graph/Graph.ts
+++ b/src/core/graph/Graph.ts
@@ -53,6 +53,8 @@ export interface GraphEdge {
   to: PortRef;
   /** Drawn as a stub at each end instead of a curve across the graph. Purely visual. */
   folded?: boolean;
+  /** What a transition between two states is called – the name `State transition` asks for. */
+  label?: string;
 }
 
 export interface Graph {
diff --git a/src/core/graph/GraphInterpreter.ts b/src/core/graph/GraphInterpreter.ts
index 5337491a..8fa0a5e6 100644
--- a/src/core/graph/GraphInterpreter.ts
+++ b/src/core/graph/GraphInterpreter.ts
@@ -105,7 +105,7 @@ export class GraphInterpreter {
     const def = this.def(node);
     if (!def?.run) return;
     const inputs = this.collectInputs(node, ctx);
-    const result = def.run(ctx, inputs, node.params, def, entry);
+    const result = def.run(ctx, inputs, node.params, def, entry, this.lookup);
     const returned = result.call ? this.call(result.call, ctx, depth) : {};
     const produced = { ...result.outputs, ...returned };
     if (!def.read) this.frame.outputCache.set(node.id, produced);
@@ -197,7 +197,8 @@ export class GraphInterpreter {
       throw new Error('Behavior graph exceeded the step limit (data cycle?)');
     // Mark before evaluating so a data cycle reads null instead of recursing forever.
     this.frame.dataCache.set(nodeId, {});
-    const outputs = def.run(ctx, this.collectInputs(source, ctx), source.params, def, '').outputs ?? {};
+    const outputs =
+      def.run(ctx, this.collectInputs(source, ctx), source.params, def, '', this.lookup).outputs ?? {};
     this.frame.dataCache.set(nodeId, outputs);
     this.trace?.onNode(nodeId);
     this.record(nodeId, outputs);
diff --git a/src/core/graph/NodeRegistry.ts b/src/core/graph/NodeRegistry.ts
index 7309aa26..65ddb185 100644
--- a/src/core/graph/NodeRegistry.ts
+++ b/src/core/graph/NodeRegistry.ts
@@ -91,6 +91,12 @@ export interface NodeDef {
   declaresPorts?: 'inputs' | 'outputs' | 'both';
   /** How a declared port becomes a port; without it, named after its key and typed by its kind. */
   declaredPort?(port: DeclaredPort, node: GraphNode): PortDef;
+  /**
+   * Edges between two such nodes are transitions: drawn as a straight arrow instead of the usual
+   * curve, and hung on ports that are never shown. A transition graph is read as directed steps
+   * between whole states, not as signal flowing left to right into a particular socket.
+   */
+  transitionEdges?: true;
   /**
    * Ports this node computes beyond the fixed and the declared ones – how many outputs a Sequence
    * offers, which values the behavior a call node names takes. `resolveDef` applies it.
@@ -105,7 +111,8 @@ export interface NodeDef {
   /**
    * Event nodes have no `run` – the interpreter seeds their outputs. `def` is resolved for the node at
    * hand, the only way a node with derived ports knows how many it has. `entry` is the exec input
-   * the pulse arrived through – what a node with one exec input per meaning reads.
+   * the pulse arrived through – what a node with one exec input per meaning reads. `lookup` is the
+   * project around the graph, for a node whose step is written in another asset.
    */
   run?(
     ctx: NodeContext,
@@ -113,6 +120,7 @@ export interface NodeDef {
     params: PropertyBag,
     def: NodeDef,
     entry: string,
+    lookup: GraphLookup,
   ): RunResult;
 }
 
diff --git a/src/core/graph/lookup.ts b/src/core/graph/lookup.ts
index 5462302c..ce244dd9 100644
--- a/src/core/graph/lookup.ts
+++ b/src/core/graph/lookup.ts
@@ -14,9 +14,20 @@ export interface MachineState {
   name: string;
 }
 
+/**
+ * An allowed move between two states, both named by state node id, under the name `State
+ * transition` asks for. The name is empty until someone gives the transition one.
+ */
+export interface MachineTransition {
+  from: string;
+  to: string;
+  name: string;
+}
+
 export interface StateMachine {
   name: string;
   states: MachineState[];
+  transitions: MachineTransition[];
 }
 
 /**
diff --git a/src/core/graph/nodes/flow/StateTransition.ts b/src/core/graph/nodes/flow/StateTransition.ts
new file mode 100644
index 00000000..1095b5ae
--- /dev/null
+++ b/src/core/graph/nodes/flow/StateTransition.ts
@@ -0,0 +1,28 @@
+import { textOf } from '../../../model/Properties';
+import { flatDef } from '../../../properties/PropertySchema';
+import type { NodeDef } from '../../NodeRegistry';
+import { machinePort, STATE_TRANSITION, TRANSITION_PARAM, transitionTo } from '../../stateMachine';
+import { asString } from '../../values';
+import { exec } from '../shared';
+
+/** What the transitions drawn in the machine are for at runtime: one step along a named arrow. */
+export const StateTransition: NodeDef = {
+  type: STATE_TRANSITION,
+  label: 'State transition',
+  category: 'action',
+  description:
+    "Takes the transition of this name out of the machine's current state, then continues. " +
+    'Nothing happens when that state has no transition of the name.',
+  inputs: [exec(), machinePort()],
+  outputs: [exec()],
+  params: [flatDef(TRANSITION_PARAM, 'text', { label: 'Transition', value: '' })],
+  run: (ctx, inputs, params, _def, _entry, lookup) => {
+    const id = asString(inputs.machine);
+    const current = ctx.states[id] ?? '';
+    const machine = current ? lookup.machine(id) : null;
+    const name = textOf(params[TRANSITION_PARAM] ?? '');
+    const target = machine ? transitionTo(machine, current, name) : '';
+    if (target) ctx.states[id] = target;
+    return { next: 'exec' };
+  },
+};
diff --git a/src/core/graph/nodes/index.ts b/src/core/graph/nodes/index.ts
index dd7dc973..7ec17741 100644
--- a/src/core/graph/nodes/index.ts
+++ b/src/core/graph/nodes/index.ts
@@ -89,6 +89,7 @@ import { RunBehavior } from './flow/RunBehavior';
 import { Sequence } from './flow/Sequence';
 import { SetState } from './flow/SetState';
 import { StateBranch } from './flow/StateBranch';
+import { StateTransition } from './flow/StateTransition';
 import { PARTICLE_NODES } from '../../particles/nodes';
 import { SHADER_NODES } from '../../shader/nodes';
 import { State } from '../stateMachine';
@@ -120,6 +121,7 @@ export const BUILT_IN_NODES: readonly NodeDef[] = [
   RunBehavior,
   StateBranch,
   SetState,
+  StateTransition,
   BehaviorEnd,
   Variables,
   Self,
diff --git a/src/core/graph/stateMachine.ts b/src/core/graph/stateMachine.ts
index 398c5bd9..85a1c541 100644
--- a/src/core/graph/stateMachine.ts
+++ b/src/core/graph/stateMachine.ts
@@ -1,27 +1,36 @@
 import { textOf } from '../model/Properties';
 import { flatDef } from '../properties/PropertySchema';
 import { edgesInto, type Graph, type GraphNode } from './Graph';
-import type { MachineState, StateMachine } from './lookup';
+import type { MachineState, MachineTransition, StateMachine } from './lookup';
 import type { NodeDef, PortDef, PortSource } from './NodeRegistry';
 
 export const STATE = 'State';
 export const STATE_MACHINE = 'StateMachine';
+export const STATE_TRANSITION = 'StateTransition';
 export const STATE_NAME_PARAM = 'name';
 /** The input naming the machine on `State branch` and `Set state`. */
 export const MACHINE_PORT = 'machine';
+/** The setting naming the transition on `State transition`. */
+export const TRANSITION_PARAM = 'transition';
+/** The two ports a transition hangs on. A port is the only anchor an edge has – without one it
+ *  cannot be drawn, selected or undone – so a state carries these, and the editor never draws
+ *  them: a transition joins whole states, not sockets. */
+export const STATE_IN = 'in';
+export const STATE_OUT = 'out';
 
 /**
- * One state of a state machine: a node with no ports whose name is its title. Its graph is the
- * machine asset's, never a behavior's – the palette leaves the `state` category out.
+ * One state of a state machine: a node whose name is its title. Its graph is the machine asset's,
+ * never a behavior's – the palette leaves the `state` category out.
  */
 export const State: NodeDef = {
   type: STATE,
   label: 'State',
   category: 'state',
   description: 'One state of a state machine.',
-  inputs: [],
-  outputs: [],
+  inputs: [{ key: STATE_IN, label: '', type: 'exec' }],
+  outputs: [{ key: STATE_OUT, label: '', type: 'exec' }],
   params: [flatDef(STATE_NAME_PARAM, 'text', { label: 'Name', value: 'State' })],
+  transitionEdges: true,
   derivePorts: ({ node }) => ({ label: stateName(node) }),
 };
 
@@ -38,6 +47,31 @@ export function statesOf(graph: Graph): MachineState[] {
   return graph.nodes.filter(isStateNode).map((node) => ({ id: node.id, name: stateName(node) }));
 }
 
+/** The transitions of a machine's graph: every edge between two states, in edge order. */
+export function transitionsOf(graph: Graph): MachineTransition[] {
+  const states = new Set(graph.nodes.filter(isStateNode).map((n) => n.id));
+  return graph.edges
+    .filter((e) => states.has(e.from.node) && states.has(e.to.node))
+    .map((e) => ({ from: e.from.node, to: e.to.node, name: e.label ?? '' }));
+}
+
+/**
+ * Where `State transition` moves from `current`: along the transition of that name leaving it. The
+ * name is matched against the current state alone, so one node asking for "alarm" moves every state
+ * that has an "alarm". Nothing happens when the state has no such transition, or two of the name –
+ * with nothing drawn to pick between them, choosing either would be a guess the graph never made.
+ */
+export function transitionTo(machine: StateMachine, current: string, name: string): string {
+  const out = machine.transitions.filter((t) => t.from === current && t.name === name);
+  const targets = [...new Set(out.map((t) => t.to))];
+  return targets.length === 1 ? targets[0]! : '';
+}
+
+/** The names a machine's transitions carry, deduped and in edge order – what a node may ask for. */
+export function transitionNames(machine: StateMachine | null): string[] {
+  return [...new Set((machine?.transitions ?? []).map((t) => t.name).filter((name) => name))];
+}
+
 /** What a state placed from the palette is called: "State 3" for the third. */
 export function nextStateName(graph: Graph): string {
   return `${State.label} ${statesOf(graph).length + 1}`;
diff --git a/src/core/model/Asset.ts b/src/core/model/Asset.ts
index 864ef665..4c1713c8 100644
--- a/src/core/model/Asset.ts
+++ b/src/core/model/Asset.ts
@@ -83,8 +83,8 @@ export interface AnimationAsset extends AssetBase {
 }
 
 /**
- * The graph holds one `State` node per state and nothing else; a behavior reads the machine's
- * current state through `State branch` and moves it through `Set state`.
+ * The graph holds one `State` node per state and an edge per transition; a behavior reads the
+ * machine's current state through `State branch` and moves it through `Set state` or `State transition`.
  */
 export interface StateMachineAsset extends AssetBase {
   type: 'statemachine';
diff --git a/src/core/model/graphLookup.ts b/src/core/model/graphLookup.ts
index 48e852de..6ba0592c 100644
--- a/src/core/model/graphLookup.ts
+++ b/src/core/model/graphLookup.ts
@@ -1,5 +1,5 @@
 import type { GraphLookup } from '../graph/lookup';
-import { statesOf } from '../graph/stateMachine';
+import { statesOf, transitionsOf } from '../graph/stateMachine';
 import { resolveAssetProps } from '../properties/resolve';
 import { findAssetOf, type Project } from './Project';
 
@@ -16,7 +16,12 @@ export function graphLookup(project: Project): GraphLookup {
     },
     machine: (assetId) => {
       const asset = findAssetOf(project, assetId, 'statemachine');
-      return asset ? { name: asset.name, states: statesOf(asset.graph) } : null;
+      if (!asset) return null;
+      return {
+        name: asset.name,
+        states: statesOf(asset.graph),
+        transitions: transitionsOf(asset.graph),
+      };
     },
   };
 }
diff --git a/src/core/store/serialize.ts b/src/core/store/serialize.ts
index e9b9cb11..ad4a81ad 100644
--- a/src/core/store/serialize.ts
+++ b/src/core/store/serialize.ts
@@ -339,6 +339,8 @@ function normalizeGraph(raw: unknown, keep?: (def: NodeDef) => boolean): Graph {
       to: { node: to.node, port: to.port },
     };
     if (e.folded === true) edge.folded = true;
+    const label = typeof e.label === 'string' ? e.label.trim() : '';
+    if (label) edge.label = label;
     graph.edges.push(edge);
   }
   return graph;
diff --git a/src/editor/debugHook.ts b/src/editor/debugHook.ts
index 5ed94818..dc6f5ed5 100644
--- a/src/editor/debugHook.ts
+++ b/src/editor/debugHook.ts
@@ -1,4 +1,5 @@
 import { type Application, Color, type ColorSource, type Container, Mesh, Rectangle, Text } from 'pixi.js';
+import { NameTransitionCommand } from '../core/commands/graphCommands';
 import { resolveObjects } from '../core/model/instance';
 import { findObjectHolder } from '../core/model/Project';
 import type { FrameRect } from '../core/model/texture';
@@ -287,6 +288,21 @@ export function installDebugHook(app: Application, state: EditorState, editor: E
       canvasRect: () => editor.stateMachineEditor.canvas.canvasRect(),
       center: () => centreOf(editor.stateMachineEditor.canvas),
       snapping: () => editor.stateMachineEditor.canvas.snapEnabled,
+      /** Where a state's hidden pin sits. It is no longer grabbable – `portGrabbable` is the check. */
+      portAt: (nodeId: string, port: string, isOutput: boolean) =>
+        editor.stateMachineEditor.canvas.portGlobal(nodeId, port, isOutput),
+      portGrabbable: (nodeId: string, port: string, isOutput: boolean) =>
+        editor.stateMachineEditor.canvas.portGrabbable(nodeId, port, isOutput),
+      edgeDrawn: (edgeId: string) => editor.stateMachineEditor.canvas.edgeDrawn(edgeId),
+      transitionLabel: (edgeId: string) => editor.stateMachineEditor.canvas.transitionLabelDrawn(edgeId),
+      hint: () => editor.stateMachineEditor.canvas.shownHint(),
+      /** Names a transition the way the inspector row does, for steps that need one already named. */
+      nameTransition: (edgeId: string, name: string) =>
+        state.execute(new NameTransitionCommand(editor.stateMachineEditor.currentAssetId, edgeId, name)),
+      dropTarget: () => editor.stateMachineEditor.canvas.pendingDropTarget(),
+      danglingEdge: () => editor.stateMachineEditor.canvas.danglingEdgeVisible(),
+      emptySpot: () => editor.stateMachineEditor.canvas.emptySpotGlobal(),
+      selected: () => state.selectedNodeIds,
     },
     particles: {
       current: () => editor.particlesEditor.currentAssetId,
diff --git a/src/editor/graph/EdgeLayer.ts b/src/editor/graph/EdgeLayer.ts
index 2e637c9a..c25c74ba 100644
--- a/src/editor/graph/EdgeLayer.ts
+++ b/src/editor/graph/EdgeLayer.ts
@@ -1,6 +1,8 @@
 import { Container, Graphics, Text } from 'pixi.js';
 import { type GraphEdge, portsCompatible } from '../../core/graph';
 import { Theme, textStyle, truncate } from '../../ui';
+import { dashedLine } from '../../viewport/symbols';
+import { arrowCorners, arrowShaft, type Point, transitionEnds, transitionOffsets } from './transitions';
 import {
   buildFoldMarks,
   foldedEdgeShown,
@@ -17,6 +19,7 @@ import { type NodeView, portColor } from './NodeView';
 const FOLD_STUB = 16;
 const FOLD_MARK_RADIUS = 5;
 const FOLD_LABEL_WIDTH = 96;
+const TRANSITION_LABEL_WIDTH = 110;
 const BEAD_RADIUS = 4.5;
 /** Dash pattern and sampling of an edge hanging on a port that is gone. */
 const GHOST_DASH = 7;
@@ -48,6 +51,9 @@ export class EdgeLayer extends Container {
   /** Edges the last draw really stroked as a curve – a hidden one is missing from it. */
   private readonly stroked = new Set<string>();
   private beadsDrawn: { edgeId: string; progress: number; x: number; y: number }[] = [];
+  /** Sideways shift per transition, so two between the same states do not lie on top of each other. */
+  private offsets = new Map<string, number>();
+  private transitionLabels: { edgeId: string; text: string; x: number; y: number }[] = [];
 
   constructor() {
     super();
@@ -69,6 +75,12 @@ export class EdgeLayer extends Container {
     this.ends = [];
     this.labelCount = 0;
     this.stroked.clear();
+    this.transitionLabels = [];
+    this.offsets = transitionOffsets(
+      edges
+        .filter((e) => isTransition(e, views))
+        .map((e) => ({ id: e.id, from: e.from.node, to: e.to.node })),
+    );
     for (const edge of edges) this.drawEdge(edge, views, isHot(edge.id), selected, beads(edge.id));
     // After the curves, so no line drawn later crosses a mark that stands for a hidden one.
     this.drawFoldMarks();
@@ -111,14 +123,25 @@ export class EdgeLayer extends Container {
     const ghost = out?.ghost === true || inp?.ghost === true;
     const valid = !ghost && portsCompatible(type, inType);
     const color = hot ? Theme.colors.hot : valid ? portColor(type) : Theme.colors.danger;
-    const start = { x: from.x + a.x, y: from.y + a.y };
-    const end = { x: to.x + b.x, y: to.y + b.y };
+    const pins = {
+      start: { x: from.x + a.x, y: from.y + a.y },
+      end: { x: to.x + b.x, y: to.y + b.y },
+    };
+    const transition = isTransition(edge, views)
+      ? transitionEnds(from, to, this.offsets.get(edge.id) ?? 0)
+      : null;
+    const { start, end } = transition ?? pins;
     if (edge.folded) {
-      this.addFoldEnd(edge, views, start, true, to.def.label, color, hot);
-      this.addFoldEnd(edge, views, end, false, from.def.label, color, hot);
+      // The fold mark belongs on the port, whatever the line between the nodes does.
+      this.addFoldEnd(edge, views, pins.start, true, to.def.label, color, hot);
+      this.addFoldEnd(edge, views, pins.end, false, from.def.label, color, hot);
       if (!foldedEdgeShown(edge, selected, hot)) return;
     }
-    if (ghost) dashedBezier(this.curves, start.x, start.y, end.x, end.y, GHOST_DASH, GHOST_GAP);
+    const shaft = transition ? arrowShaft(start, end) : end;
+    if (ghost && transition)
+      dashedLine(this.curves, start.x, start.y, shaft.x, shaft.y, GHOST_DASH, GHOST_GAP);
+    else if (ghost) dashedBezier(this.curves, start.x, start.y, end.x, end.y, GHOST_DASH, GHOST_GAP);
+    else if (transition) this.curves.moveTo(start.x, start.y).lineTo(shaft.x, shaft.y);
     else bezier(this.curves, start.x, start.y, end.x, end.y);
     this.curves.stroke({
       width: hot ? 4 : type === 'exec' ? 2.5 : 2,
@@ -126,6 +149,8 @@ export class EdgeLayer extends Container {
       // Dimmed while folded, so a curve that is only on loan is not mistaken for a plain one.
       alpha: (type === 'exec' || hot ? 1 : 0.85) * (edge.folded ? 0.6 : 1),
     });
+    if (transition) arrowHead(this.curves, start, end, color);
+    if (transition && edge.label) this.drawTransitionLabel(edge, start, end);
     this.stroked.add(edge.id);
     for (const progress of beads) {
       const { x, y } = curvePoint(start.x, start.y, end.x, end.y, progress);
@@ -138,6 +163,23 @@ export class EdgeLayer extends Container {
     }
   }
 
+  /** The transition's name at the middle of its arrow, on a plate so the line does not run through it. */
+  private drawTransitionLabel(edge: GraphEdge, start: Point, end: Point): void {
+    const label = this.nextLabel();
+    label.text = truncate(edge.label ?? '', textStyle('small'), TRANSITION_LABEL_WIDTH);
+    const x = (start.x + end.x) / 2 - label.width / 2;
+    const y = (start.y + end.y) / 2 - label.height / 2;
+    label.position.set(x, y);
+    this.chips
+      .roundRect(x - 3, y - 1, label.width + 6, label.height + 2, 3)
+      .fill({ color: Theme.colors.node, alpha: 0.85 });
+    this.transitionLabels.push({ edgeId: edge.id, text: label.text, x, y });
+  }
+
+  drawnTransitionLabels(): readonly { edgeId: string; text: string; x: number; y: number }[] {
+    return this.transitionLabels;
+  }
+
   private addFoldEnd(
     edge: GraphEdge,
     views: ReadonlyMap<string, NodeView>,
@@ -195,6 +237,21 @@ export class EdgeLayer extends Container {
   }
 }
 
+function isTransition(edge: GraphEdge, views: ReadonlyMap<string, NodeView>): boolean {
+  return (
+    views.get(edge.from.node)?.def.transitionEdges === true &&
+    views.get(edge.to.node)?.def.transitionEdges === true
+  );
+}
+
+/** The filled triangle at the target end of a transition. */
+export function arrowHead(g: Graphics, start: Point, end: Point, color: number): void {
+  const corners = arrowCorners(start, end);
+  if (!corners) return;
+  const [tip, left, right] = corners;
+  g.moveTo(tip.x, tip.y).lineTo(left.x, left.y).lineTo(right.x, right.y).closePath().fill(color);
+}
+
 /** Horizontal S-curve between two points. */
 export function bezier(g: Graphics, x1: number, y1: number, x2: number, y2: number): void {
   const dx = curveReach(x1, x2);
diff --git a/src/editor/graph/GraphCanvas.ts b/src/editor/graph/GraphCanvas.ts
index e5afeab5..7c17946b 100644
--- a/src/editor/graph/GraphCanvas.ts
+++ b/src/editor/graph/GraphCanvas.ts
@@ -27,6 +27,8 @@ import {
   portTypeOf,
   resolveDef,
   RUN_BEHAVIOR,
+  STATE_IN,
+  STATE_OUT,
 } from '../../core/graph';
 import type { GraphAsset } from '../../core/model/Asset';
 import { graphLookup } from '../../core/model/graphLookup';
@@ -44,16 +46,19 @@ import {
   endDrag,
   onDragChange,
   pressCount,
+  type MenuItem,
   type Size,
   Theme,
   textStyle,
   truncate,
+  ui,
   Widget,
   zoomFactor,
 } from '../../ui';
 import { type EditorState, nodeSelection } from '../state';
 import { type Box, boxesInBand, dragOffset, frameBoxes } from '../framing';
-import { bezier, EdgeLayer } from './EdgeLayer';
+import { arrowHead, bezier, EdgeLayer } from './EdgeLayer';
+import { arrowShaft, type Point, transitionPreview } from './transitions';
 import { openLinkMenu, openNodeMenu } from './graphMenus';
 import { NodePalette } from './NodePalette';
 import { type PaletteEntry, paletteEntries } from './paletteEntries';
@@ -112,6 +117,10 @@ export class GraphCanvas extends Widget {
   /** A finished drag whose palette is still open – drawn like the running one, so the connection
    *  being made stays visible while the node type is chosen. */
   private pendingDrop: { from: PortSide; pointer: { x: number; y: number } } | null = null;
+  /** A transition begun from a state's menu, waiting for the click that names its target. It takes
+   *  the shape of a drag because it is one in everything but the held button – that way the running
+   *  preview draws it without a second code path. `release` takes the Escape handler back off. */
+  private armed: { from: PortSide; pointer: { x: number; y: number }; release: () => void } | null = null;
   /** Where the running drag would land, recomputed on every move so the drop holds no surprise. */
   private dropTarget: PortSide | null = null;
   /** Whether the last redraw actually stroked the dangling edge. */
@@ -173,6 +182,8 @@ export class GraphCanvas extends Widget {
   /** Switching refits the view, since the next graph is a new subject. */
   show(assetId: string): void {
     if (this.assetId === assetId) return;
+    // Its source node is in the graph being left, so the click that finished it would land nowhere.
+    this.cancelTransition();
     this.assetId = assetId;
     this.sync();
     this.needsFit = true;
@@ -216,6 +227,7 @@ export class GraphCanvas extends Widget {
     if (!asset) {
       // An asset that was deleted (or undone away) must not linger as a graph.
       this.assetId = '';
+      this.cancelTransition();
       for (const view of this.views.values()) view.destroy({ children: true });
       this.views.clear();
       this.redraw();
@@ -317,6 +329,11 @@ export class GraphCanvas extends Widget {
       return;
     }
     if (e.target !== this) return;
+    // Away from every state, so there is nothing to transition to: the click drops the attempt.
+    if (this.armed && (e.button === 0 || e.button === 2)) {
+      this.finishTransition(e.global.x, e.global.y, false);
+      return;
+    }
     // Shift-drag on empty space pans as well, as it does in the scene view.
     if (e.button === 0 && e.shiftKey) {
       startPan();
@@ -346,6 +363,12 @@ export class GraphCanvas extends Widget {
     if (e.button === 1) return;
     if (!this.assetId) return;
     e.stopPropagation();
+    // An armed transition eats the next click whole: on another state it lands, anywhere else it
+    // is dropped. Selecting or dragging the node underneath would be a second meaning for one click.
+    if (this.armed && (e.button === 0 || e.button === 2)) {
+      this.finishTransition(e.global.x, e.global.y, e.button === 0);
+      return;
+    }
     const local = view.toLocal(e.global);
     const hit = view.portAt(local.x, local.y);
     if (e.button === 2) {
@@ -356,7 +379,13 @@ export class GraphCanvas extends Widget {
       } else {
         // Right-clicking inside a multi-selection acts on all of it; outside it, on that node alone.
         if (!this.state.selectedNodeIds.includes(id)) this.state.select(nodeSelection(this.assetId, [id]));
-        openNodeMenu(this.state, this.assetId, this.selectedNodes(), e.global.x, e.global.y);
+        const at = this.toLocal(e.global);
+        const graphPoint = this.screenToGraph(at.x, at.y);
+        const extras: MenuItem[] =
+          view.def.transitionEdges === true
+            ? [{ label: 'Make transition', onSelect: () => this.armTransition(id, graphPoint) }]
+            : [];
+        openNodeMenu(this.state, this.assetId, this.selectedNodes(), e.global.x, e.global.y, extras);
       }
       return;
     }
@@ -446,6 +475,10 @@ export class GraphCanvas extends Widget {
       this.connecting.pointer = g;
       this.dropTarget = this.resolveDrop(e.global.x, e.global.y);
       this.redraw();
+    } else if (this.armed) {
+      this.armed.pointer = g;
+      this.dropTarget = this.armedTarget(e.global.x, e.global.y);
+      this.redraw();
     } else if (this.marquee) {
       this.marquee.current = g;
       const d = Math.hypot(g.x - this.marquee.start.x, g.y - this.marquee.start.y) * this.zoom;
@@ -607,6 +640,18 @@ export class GraphCanvas extends Widget {
     return null;
   }
 
+  /** Null unless the drag started on a state: only those draw as a straight arrow. */
+  private transitionPreviewOf(
+    from: PortSide,
+    target: PortSide | null,
+    pointer: Point,
+  ): { start: Point; end: Point } | null {
+    const source = this.views.get(from.nodeId);
+    if (source?.def.transitionEdges !== true) return null;
+    const to = target ? this.views.get(target.nodeId) : undefined;
+    return transitionPreview(source, to?.def.transitionEdges === true ? to : null, pointer);
+  }
+
   private nodeUnder(globalX: number, globalY: number): string | null {
     for (const view of this.topDownViews()) {
       const p = view.toLocal({ x: globalX, y: globalY });
@@ -666,6 +711,59 @@ export class GraphCanvas extends Widget {
     if (graph) openLinkMenu(this.state, this.assetId, pick(graph), at.x, at.y);
   }
 
+  /** Begin a transition out of this state; the next click on another one completes it. */
+  private armTransition(nodeId: string, pointer: { x: number; y: number }): void {
+    this.cancelTransition();
+    const handlers = ui().focus.globalHandlers;
+    const onKey = (event: KeyboardEvent): boolean => {
+      if (event.key !== 'Escape' || !this.armed) return false;
+      this.cancelTransition();
+      this.redraw();
+      return true;
+    };
+    handlers.push(onKey);
+    this.armed = {
+      from: { nodeId, port: STATE_OUT, isOutput: true },
+      pointer,
+      release: () => {
+        const at = handlers.indexOf(onKey);
+        if (at >= 0) handlers.splice(at, 1);
+      },
+    };
+    this.dropTarget = null;
+    this.redraw();
+  }
+
+  private cancelTransition(): void {
+    this.armed?.release();
+    this.armed = null;
+  }
+
+  /**
+   * Where an armed transition would land: any other state under the pointer. A state cannot
+   * transition to itself, which is what `ConnectCommand` says about every node.
+   */
+  private armedTarget(globalX: number, globalY: number): PortSide | null {
+    const from = this.armed?.from;
+    if (!from) return null;
+    const node = this.nodeUnder(globalX, globalY);
+    if (!node || node === from.nodeId) return null;
+    const view = this.views.get(node);
+    return view?.def.transitionEdges === true ? { nodeId: node, port: STATE_IN, isOutput: false } : null;
+  }
+
+  /** Finish or abandon an armed transition. True when the click belonged to it. */
+  private finishTransition(globalX: number, globalY: number, connect: boolean): boolean {
+    const armed = this.armed;
+    if (!armed) return false;
+    const target = connect ? this.armedTarget(globalX, globalY) : null;
+    this.cancelTransition();
+    this.dropTarget = null;
+    if (target) this.connect(armed.from, target);
+    this.redraw();
+    return true;
+  }
+
   /** Shortened to the canvas: since the Particles tab put a preview beside it, a canvas can be narrow. */
   private setHint(text: string): void {
     this.hint.text = truncate(text, this.hint.style, this.w - Theme.padding * 2);
@@ -688,7 +786,15 @@ export class GraphCanvas extends Widget {
       return;
     }
     const playing = this.state.mode === 'play';
-    this.setHint(asset.graph.nodes.length === 0 ? 'Right-click to add a node' : playing ? 'live' : '');
+    this.setHint(
+      this.armed
+        ? 'Click the state to transition to – anywhere else, or Escape, cancels'
+        : asset.graph.nodes.length === 0
+          ? 'Right-click to add a node'
+          : playing
+            ? 'live'
+            : '',
+    );
 
     const trace = playing ? this.traceProvider(asset.id) : null;
     const now = this.timeProvider();
@@ -721,14 +827,21 @@ export class GraphCanvas extends Widget {
 
     this.tempEdge.clear();
     this.tempEdgeShown = false;
-    const drag = this.connecting ?? this.pendingDrop;
+    const drag = this.connecting ?? this.pendingDrop ?? this.armed;
     const a = drag && this.anchorPoint(drag.from);
     if (drag && a) {
       // Snapping to the resolved port makes the prediction the ring shows unmistakable.
       const b = this.anchorPoint(target) ?? drag.pointer;
-      const [from, to] = drag.from.isOutput ? [a, b] : [b, a];
-      bezier(this.tempEdge, from.x, from.y, to.x, to.y);
+      // Dragged off a state, the line already looks like the transition it is about to become.
+      const preview = this.transitionPreviewOf(drag.from, target, drag.pointer);
+      const ends = preview ? [preview.start, preview.end] : [a, b];
+      const [from, to] = (drag.from.isOutput ? ends : [ends[1], ends[0]]) as [Point, Point];
+      if (preview) {
+        const shaft = arrowShaft(from, to);
+        this.tempEdge.moveTo(from.x, from.y).lineTo(shaft.x, shaft.y);
+      } else bezier(this.tempEdge, from.x, from.y, to.x, to.y);
       this.tempEdge.stroke({ width: 2, color: c.textMuted, alpha: 0.9 });
+      if (preview) arrowHead(this.tempEdge, from, to, c.textMuted);
       this.tempEdgeShown = true;
     }
 
@@ -799,6 +912,23 @@ export class GraphCanvas extends Widget {
     return this.edgeLayer.wasStroked(edgeId);
   }
 
+  /** The name drawn on a transition, or null when nothing is drawn on it. */
+  transitionLabelDrawn(edgeId: string): string | null {
+    return this.edgeLayer.drawnTransitionLabels().find((l) => l.edgeId === edgeId)?.text ?? null;
+  }
+
+  /** Whether a pin can be grabbed on this node at all – false for a state, whose ports are hidden. */
+  portGrabbable(nodeId: string, port: string, isOutput: boolean): boolean {
+    const view = this.views.get(nodeId);
+    const p = view?.portPosition(port, isOutput);
+    return view !== undefined && p !== null && p !== undefined && view.portAt(p.x, p.y) !== null;
+  }
+
+  /** The line at the bottom of the canvas – what tells the user an armed transition is waiting. */
+  shownHint(): string {
+    return this.hint.text;
+  }
+
   foldMarksDrawn(): { links: number; label: string; isOutput: boolean }[] {
     return this.edgeLayer
       .drawnMarks()
diff --git a/src/editor/graph/NodeView.ts b/src/editor/graph/NodeView.ts
index 56982e10..8c1a7530 100644
--- a/src/editor/graph/NodeView.ts
+++ b/src/editor/graph/NodeView.ts
@@ -199,7 +199,9 @@ export class NodeView extends Widget {
     return this.toGlobal({ x: PAD + CHEVRON_SLOT / 2, y: TITLE_HEIGHT / 2 });
   }
 
+  /** Rows of ports, which set the node's height – none on a state, whose ports are never drawn. */
   private rowCount(): number {
+    if (this.def.transitionEdges === true) return 0;
     return Math.max(this.def.inputs.length, this.def.outputs.length);
   }
 
@@ -275,9 +277,12 @@ export class NodeView extends Widget {
     return this.headerHeight() + index * ROW_HEIGHT + ROW_HEIGHT / 2;
   }
 
-  /** Every port with its local centre – none while collapsed, so none can be grabbed. */
+  /**
+   * Every port with its local centre – none while collapsed, and none on a state, so neither can
+   * be drawn or grabbed. `portPosition` stays open either way: the edges still need their anchor.
+   */
   private *portCentres(): Iterable<{ port: PortDef; isOutput: boolean; x: number; y: number }> {
-    if (this.collapsed) return;
+    if (this.collapsed || this.def.transitionEdges === true) return;
     for (const [list, isOutput] of [
       [this.def.inputs, false],
       [this.def.outputs, true],
diff --git a/src/editor/graph/graphMenus.ts b/src/editor/graph/graphMenus.ts
index da3b2db4..eab09cf2 100644
--- a/src/editor/graph/graphMenus.ts
+++ b/src/editor/graph/graphMenus.ts
@@ -13,6 +13,7 @@ export function openNodeMenu(
   nodes: readonly GraphNode[],
   x: number,
   y: number,
+  extras: readonly MenuItem[] = [],
 ): void {
   const ids = state.selectedNodeIds;
   const fold = (list: readonly GraphNode[], verb: string, to: boolean): MenuItem[] => {
@@ -24,6 +25,7 @@ export function openNodeMenu(
   const expanded = nodes.filter((n) => !n.collapsed);
   const collapsed = nodes.filter((n) => n.collapsed);
   new Menu([
+    ...extras,
     ...fold(expanded, 'Collapse', true),
     ...fold(collapsed, 'Expand', false),
     {
diff --git a/src/editor/graph/transitions.ts b/src/editor/graph/transitions.ts
new file mode 100644
index 00000000..926dec83
--- /dev/null
+++ b/src/editor/graph/transitions.ts
@@ -0,0 +1,134 @@
+/**
+ * Geometry of a transition: the straight arrow drawn between two states. It runs border to border
+ * rather than pin to pin, because a diagonal line into a port would pass under the target node and
+ * take its arrowhead with it – the usual curve never does, since it swings in horizontally.
+ */
+
+export interface Point {
+  x: number;
+  y: number;
+}
+
+export interface Rect {
+  x: number;
+  y: number;
+  w: number;
+  h: number;
+}
+
+/** Length of an arrowhead along the line, and half its width across. */
+export const ARROW = 10;
+export const ARROW_HALF_WIDTH = 4.5;
+/** Air between a node's border and the end of the arrow touching it. */
+export const BORDER_GAP = 7;
+/** How far apart two transitions between the same pair of states are pushed. */
+export const PARALLEL_SEP = 14;
+
+export function centreOf(box: Rect): Point {
+  return { x: box.x + box.w / 2, y: box.y + box.h / 2 };
+}
+
+/** Null when the two points coincide: there is no direction to draw along. */
+export function direction(a: Point, b: Point): Point | null {
+  const length = Math.hypot(b.x - a.x, b.y - a.y);
+  return length === 0 ? null : { x: (b.x - a.x) / length, y: (b.y - a.y) / length };
+}
+
+/** Where a ray leaving the box's centre crosses its border. */
+export function boxExit(box: Rect, dir: Point): Point {
+  const centre = centreOf(box);
+  const tx = dir.x === 0 ? Infinity : box.w / 2 / Math.abs(dir.x);
+  const ty = dir.y === 0 ? Infinity : box.h / 2 / Math.abs(dir.y);
+  const t = Math.min(tx, ty);
+  return { x: centre.x + dir.x * t, y: centre.y + dir.y * t };
+}
+
+/** The normal of a direction, pointing to its right. */
+function normal(dir: Point): Point {
+  return { x: -dir.y, y: dir.x };
+}
+
+function shift(point: Point, out: Point, along: number, n: Point, across: number): Point {
+  return { x: point.x + out.x * along + n.x * across, y: point.y + out.y * along + n.y * across };
+}
+
+/**
+ * The two points a transition between these nodes runs between: each a border crossing, pushed
+ * `BORDER_GAP` clear of the node and `offset` sideways. Null when the boxes share a centre.
+ */
+export function transitionEnds(from: Rect, to: Rect, offset = 0): { start: Point; end: Point } | null {
+  const dir = direction(centreOf(from), centreOf(to));
+  if (!dir) return null;
+  const back = { x: -dir.x, y: -dir.y };
+  const n = normal(dir);
+  return {
+    start: shift(boxExit(from, dir), dir, BORDER_GAP, n, offset),
+    end: shift(boxExit(to, back), back, BORDER_GAP, n, offset),
+  };
+}
+
+/** One transition as the offsets care about it: which states it joins, under which edge id. */
+export interface TransitionLink {
+  id: string;
+  from: string;
+  to: string;
+}
+
+/**
+ * How far each transition is pushed sideways, so several between the same two states lie next to
+ * each other instead of on top. The fan is computed in the canonical direction of the pair, and a
+ * transition running the other way takes the opposite sign – which is what puts a there-and-back
+ * pair on either side of the line rather than both on the same one.
+ */
+export function transitionOffsets(links: readonly TransitionLink[]): Map<string, number> {
+  const groups = new Map<string, TransitionLink[]>();
+  for (const link of links) {
+    const [a, b] = link.from < link.to ? [link.from, link.to] : [link.to, link.from];
+    const key = `${a}\u0000${b}`;
+    const group = groups.get(key);
+    if (group) group.push(link);
+    else groups.set(key, [link]);
+  }
+  const offsets = new Map<string, number>();
+  for (const group of groups.values()) {
+    for (const [i, link] of group.entries()) {
+      const canonical = (i - (group.length - 1) / 2) * PARALLEL_SEP;
+      offsets.set(link.id, link.from <= link.to ? canonical : -canonical);
+    }
+  }
+  return offsets;
+}
+
+/**
+ * The line drawn while a transition is being dragged: out of the source's border towards the
+ * pointer, or border to border once the drag has found another state.
+ */
+export function transitionPreview(
+  source: Rect,
+  target: Rect | null,
+  pointer: Point,
+): {
+  start: Point;
+  end: Point;
+} {
+  if (target) return transitionEnds(source, target) ?? { start: centreOf(source), end: pointer };
+  const dir = direction(centreOf(source), pointer);
+  if (!dir) return { start: centreOf(source), end: pointer };
+  return { start: shift(boxExit(source, dir), dir, BORDER_GAP, normal(dir), 0), end: pointer };
+}
+
+/** Where the line stops: at the head's base, so the stroke does not blunt its tip. */
+export function arrowShaft(start: Point, end: Point): Point {
+  const u = direction(start, end);
+  return u ? { x: end.x - u.x * ARROW, y: end.y - u.y * ARROW } : end;
+}
+
+/** The three corners of the arrowhead at the target end, tip first. */
+export function arrowCorners(start: Point, end: Point): [Point, Point, Point] | null {
+  const u = direction(start, end);
+  if (!u) return null;
+  const base = arrowShaft(start, end);
+  const nx = -u.y * ARROW_HALF_WIDTH;
+  const ny = u.x * ARROW_HALF_WIDTH;
+  return [end, { x: base.x + nx, y: base.y + ny }, { x: base.x - nx, y: base.y - ny }];
+}
diff --git a/src/editor/inspector/nodeSection.ts b/src/editor/inspector/nodeSection.ts
index a7a2faaa..55143c97 100644
--- a/src/editor/inspector/nodeSection.ts
+++ b/src/editor/inspector/nodeSection.ts
@@ -3,13 +3,22 @@ import {
   declaresPropertyPorts,
   declaresVariablePorts,
   edgesInto,
+  edgesOfNode,
+  findNode,
+  type Graph,
+  type GraphEdge,
   type GraphNode,
   inlineInputDef,
   inlineInputs,
+  isStateNode,
+  MACHINE_PORT,
   OBJECT_BEHAVIOR_PARAM,
   OBJECT_TYPE_PARAM,
   portSignature,
   resolveDef,
+  STATE_TRANSITION,
+  stateName,
+  TRANSITION_PARAM,
 } from '../../core/graph';
 import type { GraphAsset } from '../../core/model/Asset';
 import { graphLookup } from '../../core/model/graphLookup';
@@ -21,6 +30,7 @@ import { createFieldRow, type FieldHandlers } from './fieldFactory';
 import { addNote, addTitle, type InspectorHost } from './host';
 import { buildPortSection, buildPropertyPortSection, buildVariablePortSection } from './portSection';
 import { listOpener, previewingHandlers } from './previewHandlers';
+import { buildTransitionPicker, buildTransitionSection } from './transitionSection';
 import { currentNode, nodeParamValue } from './valueSpecs';
 
 /** Structure-defining facts of a node selection: ports, connected inputs, declared variables. */
@@ -39,11 +49,24 @@ export function nodeSignature(project: Project, assetId: string, nodeId: string)
   const declared = (node.ports ?? []).map((p) => `${p.key}:${p.kind}${p.write ? ':set' : ''}`).join(',');
   // They decide which rows the inspector builds, and two behaviors may share a name in the title.
   const target = `${textOf(node.params[OBJECT_TYPE_PARAM] ?? '')}:${textOf(node.params[OBJECT_BEHAVIOR_PARAM] ?? '')}`;
+  // The transition rows and the picked name are drawn, not filled in by `refreshNodeSection`, so
+  // every part of them a command can change has to force a rebuild.
+  const transitions = isStateNode(node)
+    ? edgesOfNode(asset.graph, node.id)
+        .map((e) => `${e.id}:${e.label ?? ''}:${farStateName(asset.graph, e, node.id)}`)
+        .join(',')
+    : `${textOf(node.params[TRANSITION_PARAM] ?? '')}:${textOf(node.params[MACHINE_PORT] ?? '')}`;
   return `${portSignature(node, asset.graph, lookup, assetId)}|${declared}|${connected.join(',')}|${variablesOf(
     asset,
   )
     .map((v) => v.key)
-    .join(',')}|${target}`;
+    .join(',')}|${target}|${transitions}`;
+}
+
+/** The name of the state at the other end of an edge – what a transition row is labelled with. */
+function farStateName(graph: Graph, edge: GraphEdge, nodeId: string): string {
+  const far = findNode(graph, edge.from.node === nodeId ? edge.to.node : edge.from.node);
+  return far && isStateNode(far) ? stateName(far) : '';
 }
 
 /** A state machine declares no variables; its one node type has none to name. */
@@ -79,8 +102,13 @@ export function buildNodeSection(host: InspectorHost, assetId: string, nodeId: s
 
   if (!ownSettings && def.params.length > 0) {
     addTitle(host, 'SETTINGS');
-    for (const param of def.params) addSetting(param);
+    for (const param of def.params) {
+      if (param.key === TRANSITION_PARAM && node.type === STATE_TRANSITION)
+        buildTransitionPicker(host, assetId, node, asset.graph);
+      else addSetting(param);
+    }
   }
+  if (isStateNode(node)) buildTransitionSection(host, assetId, node, asset.graph);
 
   const free = inlineInputs(def).filter((p) => edgesInto(asset.graph, node.id, p.key).length === 0);
   if (free.length > 0) addTitle(host, 'INPUTS (unconnected)');
diff --git a/src/editor/inspector/transitionSection.ts b/src/editor/inspector/transitionSection.ts
new file mode 100644
index 00000000..1e53d0d0
--- /dev/null
+++ b/src/editor/inspector/transitionSection.ts
@@ -0,0 +1,131 @@
+import {
+  DisconnectCommand,
+  NameTransitionCommand,
+  SetNodeParamCommand,
+} from '../../core/commands/graphCommands';
+import {
+  findNode,
+  type Graph,
+  type GraphEdge,
+  type GraphNode,
+  isStateNode,
+  machineOf,
+  stateName,
+  TRANSITION_PARAM,
+  transitionNames,
+} from '../../core/graph';
+import { graphLookup } from '../../core/model/graphLookup';
+import { textOf } from '../../core/model/Properties';
+import { Dropdown, HStack, Label, Menu, Spacer, TextField, Theme } from '../../ui';
+import { NAME_WIDTH, removeButton } from './fieldFactory';
+import { addNote, addTitle, type InspectorHost } from './host';
+
+/** The name `State transition` asks for, picked from the machine on its `machine` input – the
+ *  options depend on another field, which no field kind can express. */
+export function buildTransitionPicker(
+  host: InspectorHost,
+  assetId: string,
+  node: GraphNode,
+  graph: Graph,
+): void {
+  const lookup = graphLookup(host.state.project);
+  const machine = machineOf({ node, graph, lookup });
+  const names = transitionNames(machine);
+  const chosen = textOf(node.params[TRANSITION_PARAM] ?? '');
+  const known = chosen === '' || names.includes(chosen);
+  const row = new HStack({ gap: Theme.gap, align: 'center' });
+  row.minHeight = Theme.rowHeight;
+  row.add(new Label('Transition', { style: 'muted' }));
+  row.add(new Spacer());
+  const choose = new Dropdown(chosen || UNNAMED, { variant: known ? 'default' : 'danger' });
+  choose.onClick = () => {
+    const items = [UNNAMED, ...names].map((name) => ({
+      label: name,
+      onSelect: () =>
+        host.state.execute(
+          new SetNodeParamCommand(assetId, node.id, TRANSITION_PARAM, name === UNNAMED ? '' : name),
+        ),
+    }));
+    new Menu(items, { searchable: names.length > 8 }).openBelow(choose);
+  };
+  row.add(choose);
+  host.body.add(row);
+  if (!machine) addNote(host, 'Pick a machine first.');
+  else if (!known) addNote(host, `"${chosen}" is not a transition of ${machine.name}.`, 'warning');
+}
+
+/** How the transition nobody named reads in a picker, where an empty row would look like a bug. */
+const UNNAMED = '(unnamed)';
+
+/** The transitions at a state, both ways round – the only handle they have, since a transition
+ *  hangs on ports the canvas never draws and so cannot be clicked out there. */
+export function buildTransitionSection(
+  host: InspectorHost,
+  assetId: string,
+  node: GraphNode,
+  graph: Graph,
+): void {
+  const out = transitionsAt(graph, node.id, true);
+  const into = transitionsAt(graph, node.id, false);
+  group(host, assetId, graph, 'TRANSITIONS OUT', out, true);
+  group(host, assetId, graph, 'TRANSITIONS IN', into, false);
+  const duplicate = firstDuplicate(out.map((e) => e.label ?? ''));
+  if (duplicate !== null)
+    addNote(
+      host,
+      duplicate
+        ? `Two transitions out of here are called "${duplicate}" – neither will be taken.`
+        : 'Two transitions out of here are unnamed – neither will be taken.',
+      'warning',
+    );
+}
+
+/** Edges joining this state to another one, on the given side. */
+function transitionsAt(graph: Graph, nodeId: string, outgoing: boolean): GraphEdge[] {
+  return graph.edges.filter((e) => {
+    const [mine, other] = outgoing ? [e.from.node, e.to.node] : [e.to.node, e.from.node];
+    const far = findNode(graph, other);
+    return mine === nodeId && far !== undefined && isStateNode(far);
+  });
+}
+
+/** The first name that appears twice, or null. An empty name counts: it is the unnamed transition. */
+function firstDuplicate(names: readonly string[]): string | null {
+  const seen = new Set<string>();
+  for (const name of names) {
+    if (seen.has(name)) return name;
+    seen.add(name);
+  }
+  return null;
+}
+
+function group(
+  host: InspectorHost,
+  assetId: string,
+  graph: Graph,
+  title: string,
+  edges: readonly GraphEdge[],
+  outgoing: boolean,
+): void {
+  addTitle(host, title);
+  if (edges.length === 0) {
+    addNote(host, outgoing ? 'Nothing leads out of this state yet.' : 'Nothing leads here yet.');
+    return;
+  }
+  for (const edge of edges) {
+    const far = findNode(graph, outgoing ? edge.to.node : edge.from.node);
+    const row = new HStack({ gap: Theme.gap, align: 'center' });
+    row.minHeight = Theme.rowHeight;
+    row.add(new Label(outgoing ? '→' : '←', { style: 'muted' }));
+    row.add(new Label(far ? stateName(far) : '?', { style: 'muted' }));
+    row.add(new Spacer());
+    row.add(
+      new TextField(edge.label ?? '', {
+        width: NAME_WIDTH,
+        onChange: (next) => host.state.execute(new NameTransitionCommand(assetId, edge.id, next)),
+      }),
+    );
+    row.add(removeButton(() => host.state.execute(new DisconnectCommand(assetId, edge.id))));
+    host.body.add(row);
+  }
+}
diff --git a/src/editor/statemachine/StateMachineEditor.ts b/src/editor/statemachine/StateMachineEditor.ts
index 0fac4bf2..b37475eb 100644
--- a/src/editor/statemachine/StateMachineEditor.ts
+++ b/src/editor/statemachine/StateMachineEditor.ts
@@ -9,9 +9,9 @@ import type { EditorState } from '../state';
 const INFO_WIDTH = 90;
 
 /**
- * The states of one state machine, on the graph canvas the Behavior tab uses: a state is a node,
- * so placing (right-click), moving, snapping, renaming, deleting and undo are the graph's.
- * Transitions are a later step.
+ * The states of one state machine, on the graph canvas the Behavior tab uses: a state is a node and
+ * a transition an edge, so placing (right-click), moving, snapping, renaming, connecting, deleting
+ * and undo are all the graph's.
  */
 export class StateMachineEditor extends AssetTabEditor<StateMachineAsset, GraphCanvas> {
   private readonly snap = new SnapToggle(() => this.canvas);
diff --git a/tests/core/graph.test.ts b/tests/core/graph.test.ts
index 0560984a..9140f308 100644
--- a/tests/core/graph.test.ts
+++ b/tests/core/graph.test.ts
@@ -72,8 +72,10 @@ describe('node registry', () => {
       const keys = [...def.inputs, ...def.outputs].map((p) => p.key);
       expect(new Set(def.inputs.map((p) => p.key)).size).toBe(def.inputs.length);
       expect(new Set(def.outputs.map((p) => p.key)).size).toBe(def.outputs.length);
-      // An event is seeded by the runtime, a state is a name in a machine: neither runs.
-      if (def.category === 'event' || def.category === 'state') expect(def.inputs).toHaveLength(0);
+      // An event is seeded by the runtime, so nothing flows into it.
+      if (def.category === 'event') expect(def.inputs).toHaveLength(0);
+      // A state is a name in a machine; its ports only anchor transitions, so it never runs.
+      else if (def.category === 'state') expect(def.run).toBeUndefined();
       // A shader node is compiled to GLSL and a particle node to a function: neither is ever run.
       else if (def.category === 'shader' || def.category === 'particles') expect('emit' in def).toBe(true);
       else expect(def.run).toBeTypeOf('function');
diff --git a/tests/core/node-catalog.test.ts b/tests/core/node-catalog.test.ts
index d08ebf10..6e849e3f 100644
--- a/tests/core/node-catalog.test.ts
+++ b/tests/core/node-catalog.test.ts
@@ -8,6 +8,7 @@ import { BUILT_IN_NODES } from '../../src/core/graph/nodes';
 import {
   createEmptyGraph,
   type DeclaredPort,
+  type GraphLookup,
   NO_LOOKUP,
   type NodeContext,
   resolveDef,
@@ -38,10 +39,19 @@ interface Case {
   repeat?: RunResult['repeat'] | null;
   /** Expected nested-behavior call; `null` asserts the node calls nothing. */
   call?: RunResult['call'] | null;
+  /** The project around the graph – for a node whose step is written in another asset. */
+  lookup?: GraphLookup;
   /** Assertions on what the node did to the context or to the handles it was given. */
   after?(ctx: FakeContext): void;
 }
 
+/** A lookup holding one machine "m" with the given transitions – what `State transition` reads. */
+const machineLookup = (transitions: { from: string; to: string; name?: string }[]): GraphLookup => ({
+  ...NO_LOOKUP,
+  machine: (id) =>
+    id === 'm' ? { name: 'M', states: [], transitions: transitions.map((t) => ({ name: '', ...t })) } : null,
+});
+
 const run = (type: string, c: Case): { result: RunResult; ctx: FakeContext } => {
   const ctx = fakeContext(c.context);
   const node = { id: 'n', type, x: 0, y: 0, params: c.params ?? {}, ports: c.ports };
@@ -52,7 +62,8 @@ const run = (type: string, c: Case): { result: RunResult; ctx: FakeContext } =>
     inputs: [...execPorts(c.derivedInputs), ...registered.inputs],
     outputs: [...registered.outputs, ...execPorts(c.derivedOutputs)],
   };
-  return { result: def.run!(ctx, c.inputs ?? {}, c.params ?? {}, def, c.entry ?? 'exec'), ctx };
+  const lookup = c.lookup ?? NO_LOOKUP;
+  return { result: def.run!(ctx, c.inputs ?? {}, c.params ?? {}, def, c.entry ?? 'exec', lookup), ctx };
 };
 
 const at = (name: string, x: number, y: number) => ({ ...fakeEntity(name), x, y });
@@ -140,6 +151,76 @@ const CASES: Record<string, Case[]> = {
       after: (ctx) => expect(ctx.states).toEqual({}),
     },
   ],
+  StateTransition: [
+    {
+      name: 'follows the transition of the asked-for name out of the current state',
+      inputs: { machine: 'm' },
+      params: { transition: 'alarm' },
+      context: { states: { m: 's1' } },
+      lookup: machineLookup([{ from: 's1', to: 's2', name: 'alarm' }]),
+      next: 'exec',
+      after: (ctx) => expect(ctx.states).toEqual({ m: 's2' }),
+    },
+    {
+      // The point of naming transitions: one node works from every state that has that name.
+      name: 'picks the same name out of whichever state the machine is in',
+      inputs: { machine: 'm' },
+      params: { transition: 'alarm' },
+      context: { states: { m: 'searching' } },
+      lookup: machineLookup([
+        { from: 'patrolling', to: 'chasing', name: 'alarm' },
+        { from: 'chasing', to: 'searching', name: 'lost' },
+        { from: 'searching', to: 'chasing', name: 'alarm' },
+      ]),
+      next: 'exec',
+      after: (ctx) => expect(ctx.states).toEqual({ m: 'chasing' }),
+    },
+    {
+      name: 'a name the current state does not carry moves nothing',
+      inputs: { machine: 'm' },
+      params: { transition: 'lost' },
+      context: { states: { m: 's1' } },
+      lookup: machineLookup([{ from: 's1', to: 's2', name: 'alarm' }]),
+      next: 'exec',
+      after: (ctx) => expect(ctx.states).toEqual({ m: 's1' }),
+    },
+    {
+      name: 'two of the name out of one state is no move: the graph never picked between them',
+      inputs: { machine: 'm' },
+      params: { transition: 'alarm' },
+      context: { states: { m: 's1' } },
+      lookup: machineLookup([
+        { from: 's1', to: 's2', name: 'alarm' },
+        { from: 's1', to: 's3', name: 'alarm' },
+      ]),
+      next: 'exec',
+      after: (ctx) => expect(ctx.states).toEqual({ m: 's1' }),
+    },
+    {
+      // An unnamed transition is a name too, so a machine nobody named still steps.
+      name: 'with no name asked for, follows the one unnamed transition',
+      inputs: { machine: 'm' },
+      context: { states: { m: 's1' } },
+      lookup: machineLookup([{ from: 's1', to: 's2' }]),
+      next: 'exec',
+      after: (ctx) => expect(ctx.states).toEqual({ m: 's2' }),
+    },
+    {
+      name: 'a state with nothing drawn out of it stays put',
+      inputs: { machine: 'm' },
+      context: { states: { m: 's2' } },
+      lookup: machineLookup([{ from: 's1', to: 's2' }]),
+      next: 'exec',
+      after: (ctx) => expect(ctx.states).toEqual({ m: 's2' }),
+    },
+    {
+      name: 'in no state yet there is nothing to move from',
+      inputs: { machine: 'm' },
+      lookup: machineLookup([{ from: 's1', to: 's2' }]),
+      next: 'exec',
+      after: (ctx) => expect(ctx.states).toEqual({}),
+    },
+  ],
   Repeat: [
     {
       name: 'asks for as many body rounds as it was given, then continues at done',
diff --git a/tests/core/state-machine.test.ts b/tests/core/state-machine.test.ts
index 32f9f214..e2719bd1 100644
--- a/tests/core/state-machine.test.ts
+++ b/tests/core/state-machine.test.ts
@@ -5,7 +5,13 @@
  */
 import { describe, expect, it } from 'vitest';
 import { CreateAssetCommand } from '../../src/core/commands/assetCommands';
-import { AddNodeCommand, ConnectCommand, SetNodeParamCommand } from '../../src/core/commands/graphCommands';
+import {
+  AddNodeCommand,
+  ConnectCommand,
+  NameTransitionCommand,
+  RemoveNodeCommand,
+  SetNodeParamCommand,
+} from '../../src/core/commands/graphCommands';
 import { AddVariableCommand } from '../../src/core/commands/variableCommands';
 import {
   BEHAVIOR_PARAM,
@@ -15,8 +21,13 @@ import {
   nextStateName,
   resolveDef,
   STATE,
+  STATE_IN,
   STATE_NAME_PARAM,
+  STATE_OUT,
   statesOf,
+  transitionNames,
+  transitionsOf,
+  transitionTo,
 } from '../../src/core/graph';
 import { BUILT_IN_NODES } from '../../src/core/graph/nodes';
 import type { StateMachineAsset } from '../../src/core/model/Asset';
@@ -289,3 +300,122 @@ describe('a running state machine', () => {
     ).toThrow('Port not found');
   });
 });
+
+describe('transitions between states', () => {
+  /** Draws a transition the way the canvas does: out of one state's `out`, into the other's `in`. */
+  const connect = (f: ProjectFixture, machineId: string, from: string, to: string) =>
+    f.stack.execute(
+      new ConnectCommand(machineId, { node: from, port: STATE_OUT }, { node: to, port: STATE_IN }),
+    );
+
+  it('hangs on the two exec ports every state carries', () => {
+    const f = makeProject();
+    const machine = makeMachine(f);
+    const node = machine.asset().graph.nodes[0]!;
+    const def = resolveDef(node, machine.asset().graph, graphLookup(f.project))!;
+    expect(def.inputs.map((p) => p.key)).toEqual([STATE_IN]);
+    expect(def.outputs.map((p) => p.key)).toEqual([STATE_OUT]);
+    // Without a port there is no anchor to draw, drag or right-click an edge on.
+    expect(def.inputs[0]?.type).toBe('exec');
+    expect(def.outputs[0]?.type).toBe('exec');
+  });
+
+  it('is an ordinary edge, so drawing, undo and a save round trip come for free', () => {
+    const f = makeProject();
+    const machine = makeMachine(f);
+    const [open, closed] = machine.ids as [string, string];
+    connect(f, machine.id, open, closed);
+    expect(transitionsOf(machine.asset().graph)).toEqual([{ from: open, to: closed, name: '' }]);
+
+    const loaded = findAssetOf(roundTrip(f.project), machine.id, 'statemachine')!;
+    expect(transitionsOf(loaded.graph)).toEqual([{ from: open, to: closed, name: '' }]);
+
+    f.stack.undo();
+    expect(transitionsOf(machine.asset().graph)).toEqual([]);
+  });
+
+  it('goes away with the state it hangs on, because both live in the one graph', () => {
+    const f = makeProject();
+    const machine = makeMachine(f);
+    const [open, closed] = machine.ids as [string, string];
+    connect(f, machine.id, open, closed);
+    f.stack.execute(new RemoveNodeCommand(machine.id, closed));
+    expect(transitionsOf(machine.asset().graph)).toEqual([]);
+    f.stack.undo();
+    expect(transitionsOf(machine.asset().graph)).toEqual([{ from: open, to: closed, name: '' }]);
+  });
+
+  it('is what the lookup hands a running graph', () => {
+    const f = makeProject();
+    const machine = makeMachine(f);
+    const [open, closed] = machine.ids as [string, string];
+    connect(f, machine.id, open, closed);
+    expect(graphLookup(f.project).machine(machine.id)?.transitions).toEqual([
+      { from: open, to: closed, name: '' },
+    ]);
+  });
+
+  it('moves the machine one step when a behavior runs State transition', () => {
+    const f = makeProject();
+    const machine = makeMachine(f);
+    const [open, closed] = machine.ids as [string, string];
+    connect(f, machine.id, open, closed);
+    const behavior = makeBehavior(f, 'B');
+    const edit = graphEditor(f, behavior);
+    const start = edit.addNode('OnStart');
+    const set = edit.addNode('SetState', { [MACHINE_PORT]: machine.id });
+    const next = edit.addNode('StateTransition', { [MACHINE_PORT]: machine.id });
+    edit.wire([
+      [start, 'exec', set, open],
+      [set, 'exec', next, 'exec'],
+    ]);
+    const ctx = fakeContext();
+    new GraphInterpreter(behavior.graph, graphLookup(f.project)).fire('OnStart', ctx);
+    expect(ctx.states).toEqual({ [machine.id]: closed });
+  });
+
+  it('carries the name it was given through a save, and undo takes it back', () => {
+    const f = makeProject();
+    const machine = makeMachine(f);
+    const [open, closed] = machine.ids as [string, string];
+    connect(f, machine.id, open, closed);
+    const edge = machine.asset().graph.edges[0]!;
+    f.stack.execute(new NameTransitionCommand(machine.id, edge.id, '  alarm  '));
+    // Trimmed on the way in, so a stray space never makes a second name that looks the same.
+    expect(transitionsOf(machine.asset().graph)).toEqual([{ from: open, to: closed, name: 'alarm' }]);
+
+    const loaded = findAssetOf(roundTrip(f.project), machine.id, 'statemachine')!;
+    expect(transitionsOf(loaded.graph)).toEqual([{ from: open, to: closed, name: 'alarm' }]);
+
+    f.stack.undo();
+    expect(transitionsOf(machine.asset().graph)).toEqual([{ from: open, to: closed, name: '' }]);
+  });
+
+  it('clears a name back to unnamed rather than keeping an empty one', () => {
+    const f = makeProject();
+    const machine = makeMachine(f);
+    const [open, closed] = machine.ids as [string, string];
+    connect(f, machine.id, open, closed);
+    const edge = machine.asset().graph.edges[0]!;
+    f.stack.execute(new NameTransitionCommand(machine.id, edge.id, 'alarm'));
+    f.stack.execute(new NameTransitionCommand(machine.id, edge.id, '   '));
+    expect(edge.label).toBeUndefined();
+    expect(transitionsOf(machine.asset().graph)).toEqual([{ from: open, to: closed, name: '' }]);
+  });
+
+  it('reads the same name out of whichever state the machine is in', () => {
+    const machine = {
+      name: 'Guard',
+      states: [],
+      transitions: [
+        { from: 'patrolling', to: 'chasing', name: 'alarm' },
+        { from: 'searching', to: 'chasing', name: 'alarm' },
+        { from: 'chasing', to: 'searching', name: 'lost' },
+      ],
+    };
+    expect(transitionTo(machine, 'patrolling', 'alarm')).toBe('chasing');
+    expect(transitionTo(machine, 'searching', 'alarm')).toBe('chasing');
+    expect(transitionTo(machine, 'chasing', 'alarm')).toBe('');
+    expect(transitionNames(machine)).toEqual(['alarm', 'lost']);
+  });
+});
diff --git a/tests/editor/transitions.test.ts b/tests/editor/transitions.test.ts
new file mode 100644
index 00000000..d9efaf9b
--- /dev/null
+++ b/tests/editor/transitions.test.ts
@@ -0,0 +1,129 @@
+/**
+ * The straight arrow between two states. It runs border to border because a diagonal line into a
+ * port passes under the target node and hides its own arrowhead there – the failure that made this
+ * geometry necessary, and the one these checks hold shut.
+ */
+import { describe, expect, it } from 'vitest';
+import {
+  ARROW,
+  arrowCorners,
+  arrowShaft,
+  BORDER_GAP,
+  boxExit,
+  centreOf,
+  direction,
+  PARALLEL_SEP,
+  transitionEnds,
+  transitionOffsets,
+  transitionPreview,
+} from '../../src/editor/graph/transitions';
+
+/** Two states side by side, 100 x 40 each, 200 apart on x. */
+const left = { x: 0, y: 0, w: 100, h: 40 };
+const right = { x: 300, y: 0, w: 100, h: 40 };
+/** Directly below the first, which is where a pin-to-pin line would cut through a node. */
+const below = { x: 0, y: 200, w: 100, h: 40 };
+
+describe('transition geometry', () => {
+  it('leaves a box on the side the ray points at', () => {
+    expect(boxExit(left, { x: 1, y: 0 })).toEqual({ x: 100, y: 20 });
+    expect(boxExit(left, { x: -1, y: 0 })).toEqual({ x: 0, y: 20 });
+    expect(boxExit(left, { x: 0, y: 1 })).toEqual({ x: 50, y: 40 });
+    expect(boxExit(left, { x: 0, y: -1 })).toEqual({ x: 50, y: 0 });
+  });
+
+  it('runs border to border, so neither end sits inside a node', () => {
+    const ends = transitionEnds(left, right)!;
+    expect(ends.start).toEqual({ x: 100 + BORDER_GAP, y: 20 });
+    expect(ends.end).toEqual({ x: 300 - BORDER_GAP, y: 20 });
+  });
+
+  it('leaves through the bottom and the top when one state sits under the other', () => {
+    const ends = transitionEnds(left, below)!;
+    // The whole point: straight down, out of the lower border and into the upper one – never
+    // across the body of either node.
+    expect(ends.start).toEqual({ x: 50, y: 40 + BORDER_GAP });
+    expect(ends.end).toEqual({ x: 50, y: 200 - BORDER_GAP });
+  });
+
+  it('keeps both ends clear of the borders they leave', () => {
+    const ends = transitionEnds(left, right)!;
+    expect(ends.start.x).toBeGreaterThan(left.x + left.w);
+    expect(ends.end.x).toBeLessThan(right.x);
+  });
+
+  it('pushes a there-and-back pair to opposite sides of the line', () => {
+    const offsets = transitionOffsets([
+      { id: 'there', from: 'a', to: 'b' },
+      { id: 'back', from: 'b', to: 'a' },
+    ]);
+    const there = offsets.get('there')!;
+    const back = offsets.get('back')!;
+    // Same sign in each arrow's own frame, which is opposite sides on screen, since the normal
+    // turns with the direction.
+    expect(there).toBe(back);
+    expect(Math.abs(there)).toBe(PARALLEL_SEP / 2);
+
+    const a = transitionEnds(left, right, there)!;
+    const b = transitionEnds(right, left, back)!;
+    expect(a.start.y).not.toBe(b.end.y);
+    expect(Math.abs(a.start.y - b.end.y)).toBeCloseTo(PARALLEL_SEP);
+  });
+
+  it('leaves a lone transition on the line between the centres', () => {
+    const offsets = transitionOffsets([{ id: 'only', from: 'a', to: 'b' }]);
+    expect(offsets.get('only')).toBe(0);
+    expect(transitionEnds(left, right, 0)).toEqual(transitionEnds(left, right));
+  });
+
+  it('fans three between the same pair evenly around the centre line', () => {
+    const offsets = transitionOffsets([
+      { id: 'one', from: 'a', to: 'b' },
+      { id: 'two', from: 'a', to: 'b' },
+      { id: 'three', from: 'a', to: 'b' },
+    ]);
+    expect([...offsets.values()]).toEqual([-PARALLEL_SEP, 0, PARALLEL_SEP]);
+  });
+
+  it('keeps transitions between different pairs on their own centre lines', () => {
+    const offsets = transitionOffsets([
+      { id: 'ab', from: 'a', to: 'b' },
+      { id: 'cd', from: 'c', to: 'd' },
+    ]);
+    expect(offsets.get('ab')).toBe(0);
+    expect(offsets.get('cd')).toBe(0);
+  });
+
+  it('has no ends when the two boxes share a centre', () => {
+    expect(transitionEnds(left, { ...left })).toBeNull();
+    expect(direction({ x: 5, y: 5 }, { x: 5, y: 5 })).toBeNull();
+  });
+
+  it('stops the line one arrowhead short of the tip', () => {
+    const shaft = arrowShaft({ x: 0, y: 0 }, { x: 100, y: 0 });
+    expect(shaft).toEqual({ x: 100 - ARROW, y: 0 });
+  });
+
+  it('points the head at the target, across the line', () => {
+    const [tip, a, b] = arrowCorners({ x: 0, y: 0 }, { x: 100, y: 0 })!;
+    expect(tip).toEqual({ x: 100, y: 0 });
+    // Both base corners sit at the shaft's end, one on each side of the line.
+    expect(a.x).toBeCloseTo(100 - ARROW);
+    expect(b.x).toBeCloseTo(100 - ARROW);
+    expect(Math.sign(a.y)).toBe(-Math.sign(b.y));
+    expect(Math.abs(a.y)).toBeCloseTo(Math.abs(b.y));
+  });
+
+  it('previews from the source border to the pointer until it finds a state', () => {
+    const loose = transitionPreview(left, null, { x: 300, y: 20 });
+    expect(loose.start).toEqual({ x: 100 + BORDER_GAP, y: 20 });
+    expect(loose.end).toEqual({ x: 300, y: 20 });
+
+    const snapped = transitionPreview(left, right, { x: 280, y: 20 });
+    expect(snapped).toEqual(transitionEnds(left, right));
+  });
+
+  it('centres a box where both halves meet', () => {
+    expect(centreOf(left)).toEqual({ x: 50, y: 20 });
+  });
+});
diff --git a/tests/helpers.ts b/tests/helpers.ts
index 277fd157..da966538 100644
--- a/tests/helpers.ts
+++ b/tests/helpers.ts
@@ -9,7 +9,9 @@ import {
   type DeclaredPort,
   ENTITY_HANDLE,
   type EntityHandle,
+  type GraphLookup,
   type GraphNode,
+  NO_LOOKUP,
   type NodeContext,
   type PointerState,
   type Value,
@@ -216,9 +218,10 @@ export function runDef(
   inputs: Record<string, Value>,
   params: PropertyBag = {},
   entry = 'exec',
+  lookup: GraphLookup = NO_LOOKUP,
 ): RunResult {
   const def = requireNodeDef(type);
-  return def.run!(ctx, inputs, params, def, entry);
+  return def.run!(ctx, inputs, params, def, entry, lookup);
 }
 
 /** Runs one node definition in isolation and returns its data outputs. */
diff --git a/tools/e2e/26-state-machine.mjs b/tools/e2e/26-state-machine.mjs
index af7eb229..681a0e45 100644
--- a/tools/e2e/26-state-machine.mjs
+++ b/tools/e2e/26-state-machine.mjs
@@ -191,8 +191,138 @@ export async function stateMachine(t) {
   await press('Escape');
   await sleep(200);
 
-  // 26f. A behavior reads the machine: Set state on start, State branch every frame.
+  // 26e2. A transition is an ordinary edge, but it hangs on ports the editor never draws: a
+  // transition joins two whole states, so there is no socket to aim at and none to grab.
   const [first, second] = (await states()).map((s) => s.id);
+  const outPin = await json(`__gm.stateMachine.portAt(${JSON.stringify(first)}, 'out', true)`);
+  const inPin = await json(`__gm.stateMachine.portAt(${JSON.stringify(second)}, 'in', false)`);
+  check(
+    'every state still carries the out and in port an edge needs to exist at all',
+    outPin !== null && inPin !== null,
+    JSON.stringify({ outPin, inPin }),
+  );
+  const grabbable = async (id, port, isOutput) =>
+    json(`__gm.stateMachine.portGrabbable(${JSON.stringify(id)}, ${JSON.stringify(port)}, ${isOutput})`);
+  check(
+    'but neither can be grabbed, because neither is drawn',
+    (await grabbable(first, 'out', true)) === false && (await grabbable(second, 'in', false)) === false,
+  );
+
+  const transitions = () =>
+    json(`__gm.state.project.assets.find((a) => a.id === ${JSON.stringify(made.id)}).graph.edges`);
+  const centreOfState = async (id) => {
+    const r = await json(`__gm.stateMachine.nodeRect(${JSON.stringify(id)})`);
+    return { x: r.x + r.w / 2, y: r.y + r.h / 2 };
+  };
+  const makeTransition = async (fromId, toId) => {
+    const from = await centreOfState(fromId);
+    await click(from.x, from.y, 'right');
+    await sleep(300);
+    await clickLast('Make transition');
+    await sleep(250);
+    const to = await centreOfState(toId);
+    await click(to.x, to.y);
+    await sleep(350);
+  };
+
+  // The right-click way in, since there is no pin to drag from any more.
+  const firstCentre = await centreOfState(first);
+  await click(firstCentre.x, firstCentre.y, 'right');
+  await sleep(300);
+  check(
+    "a state's menu offers Make transition",
+    (await json('__gm.overlayTexts()')).includes('Make transition'),
+    JSON.stringify(await json('__gm.overlayTexts()')),
+  );
+  await clickLast('Make transition');
+  await sleep(250);
+  check(
+    'armed, the canvas says which click it is waiting for',
+    (await json('__gm.stateMachine.hint()')).includes('Click the state'),
+    JSON.stringify(await json('__gm.stateMachine.hint()')),
+  );
+  check(
+    'and the line to the pointer is already on screen',
+    (await json('__gm.stateMachine.danglingEdge()')) === true,
+  );
+  await shot('05a-armed');
+  await press('Escape');
+  await sleep(250);
+  check(
+    'Escape drops the attempt, drawing nothing',
+    (await transitions()).length === 0 && (await json('__gm.stateMachine.danglingEdge()')) === false,
+  );
+
+  await makeTransition(first, second);
+  const drawn = await transitions();
+  check(
+    'clicking the other state connects them',
+    drawn.length === 1 && drawn[0]?.from.node === first && drawn[0]?.to.node === second,
+    JSON.stringify(drawn),
+  );
+  check(
+    'the transition is really stroked, not dropped for want of an anchor',
+    (await json(`__gm.stateMachine.edgeDrawn(${JSON.stringify(drawn[0]?.id)})`)) === true,
+  );
+  await undo();
+  await sleep(300);
+  check('undo takes the transition back', (await transitions()).length === 0);
+  await redo();
+  await sleep(300);
+  check('redo puts it back', (await transitions()).length === 1);
+  await shot('05-transition');
+
+  // 26e3. Naming a transition, from the list the inspector shows on the state it leaves.
+  const edgeId = (await transitions())[0]?.id;
+  await evaluate(
+    `__gm.state.select({ kind: 'node', assetId: ${JSON.stringify(made.id)}, nodeId: ${JSON.stringify(first)}, nodeIds: [${JSON.stringify(first)}] })`,
+  );
+  await sleep(400);
+  check(
+    'the inspector lists the transitions of the selected state, both ways round',
+    (await has('TRANSITIONS OUT')) && (await has('TRANSITIONS IN')),
+  );
+  await evaluate(`__gm.stateMachine.nameTransition(${JSON.stringify(edgeId)}, 'alarm')`);
+  await sleep(400);
+  check(
+    'a named transition carries the name on the edge itself',
+    (await transitions())[0]?.label === 'alarm',
+    JSON.stringify(await transitions()),
+  );
+  check(
+    'and the name is drawn on the arrow, not only listed in the panel',
+    (await json(`__gm.stateMachine.transitionLabel(${JSON.stringify(edgeId)})`)) === 'alarm',
+  );
+  // The field is only findable once it holds text, so the rename is what proves it is really a field.
+  const field = await locate('alarm', true);
+  // Double-click, so the name is selected and replaced – a single click only parks the caret in it.
+  await doubleClick(field.x, field.y);
+  await sleep(200);
+  await typeText('lost');
+  await press('Enter');
+  await sleep(400);
+  check(
+    'and the panel row is a real field: typing in it renames the transition',
+    (await transitions())[0]?.label === 'lost',
+    JSON.stringify(await transitions()),
+  );
+  await evaluate(`__gm.stateMachine.nameTransition(${JSON.stringify(edgeId)}, 'alarm')`);
+  await sleep(300);
+  await shot('05b-named');
+
+  // 26e4. Both ways round between the same pair: the two arrows must not lie on top of each other.
+  await makeTransition(second, first);
+  const both = await transitions();
+  check('a transition back is allowed alongside the one there', both.length === 2, JSON.stringify(both));
+  const drawnBoth = await Promise.all(
+    both.map((e) => json(`__gm.stateMachine.edgeDrawn(${JSON.stringify(e.id)})`)),
+  );
+  check('both arrows are stroked', drawnBoth.every(Boolean), JSON.stringify(drawnBoth));
+  await shot('05c-both-ways');
+  await undo();
+  await sleep(300);
+
+  // 26f. A behavior reads the machine: Set state on start, State branch every frame.
   const rig = await scaffoldBehavior(t, {
     assetId: 'sm-logic',
     name: 'Doors logic',
@@ -248,6 +378,50 @@ export async function stateMachine(t) {
   );
   await stop();
 
+  // 26f2. What a named transition is for at runtime: State transition takes the step called "alarm".
+  await mutate(`
+    const b = __gm.state.project.assets.find((a) => a.id === 'sm-logic');
+    b.graph.nodes.push({
+      id: 'sm-next', type: 'StateTransition', x: 600, y: 0,
+      params: { machine: ${JSON.stringify(made.id)}, transition: 'alarm' },
+    });
+    b.graph.edges.push({
+      id: 'sm-e5', from: { node: 'sm-set', port: 'exec' }, to: { node: 'sm-next', port: 'exec' },
+    });
+  `);
+  await sleep(300);
+  await play();
+  await sleep(600);
+  const moved = (await world())?.log ?? [];
+  check(
+    'State transition follows the transition of that name, so the branch takes the state it points at',
+    moved.includes('second state') && !moved.includes('first state'),
+    JSON.stringify([...new Set(moved)]),
+  );
+  await stop();
+
+  // A name the current state does not carry moves nothing – the machine stays where it was put.
+  await mutate(`
+    const b = __gm.state.project.assets.find((a) => a.id === 'sm-logic');
+    b.graph.nodes.find((n) => n.id === 'sm-next').params.transition = 'no such transition';
+  `);
+  await sleep(300);
+  await play();
+  await sleep(600);
+  const stayed = (await world())?.log ?? [];
+  check(
+    'a name the state does not carry leaves the machine where it was',
+    stayed.includes('first state') && !stayed.includes('second state'),
+    JSON.stringify([...new Set(stayed)]),
+  );
+  await stop();
+  await mutate(`
+    const b = __gm.state.project.assets.find((a) => a.id === 'sm-logic');
+    b.graph.nodes.find((n) => n.id === 'sm-next').params.transition = 'alarm';
+  `);
+  await sleep(200);
+  await sleep(200);
+
   // 26g. An unconnected machine input shows a picker; picking a machine grows the state ports.
   await mutate(`
     const a = __gm.state.project.assets.find((x) => x.id === 'sm-logic');