diff --git a/README.md b/README.md
index 91ebf9cf..0df9a404 100644
--- a/README.md
+++ b/README.md
@@ -47,7 +47,7 @@ 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, 1965 checks (GM_STEPS=20 for one step)
+node tools/seed-e2e.mjs && node tools/e2e.mjs      # the editor, 1966 checks (GM_STEPS=20 for one step)
                                                    #   every tool signs in first – see the Accounts page
 node tools/seed-jumprun.mjs && node tools/smoke-jumprun.mjs
 node tools/seed-tetris.mjs && node tools/smoke-tetris.mjs
diff --git a/src/editor/debug/uiHooks.ts b/src/editor/debug/uiHooks.ts
index 04e987f9..7e74a1e9 100644
--- a/src/editor/debug/uiHooks.ts
+++ b/src/editor/debug/uiHooks.ts
@@ -373,6 +373,32 @@ export function uiHooks({ app, state, editor }: HookContext) {
       if (ms !== undefined) keepGeneralSettings({ zoomTransitionMs: ms });
       return generalSettings().zoomTransitionMs;
     },
+    /**
+     * Whether each graph tab's magnet is on (#391); with `on` they are all switched first. The
+     * harness reads them on every load and then switches them off, so a drag lands where it is let go.
+     */
+    graphSnapping: (on?: boolean) => {
+      const tabs = {
+        logic: [editor.graphEditor.snap, editor.graphEditor.canvas],
+        stateMachine: [editor.stateMachineEditor.snap, editor.stateMachineEditor.canvas],
+        shader: [editor.shaderEditor.snap, editor.shaderEditor.canvas],
+        particles: [editor.particlesEditor.snap, editor.particlesEditor.canvas],
+        soundFx: [editor.soundFxEditor.snap, editor.soundFxEditor.canvas],
+        instrument: [editor.instrumentEditor.snap, editor.instrumentEditor.canvas],
+        song: [editor.songEditor.snap, editor.songEditor.routing],
+        routing: [editor.routingEditor.snap, editor.routingEditor.canvas],
+      } as const;
+      if (on !== undefined) for (const [snap] of Object.values(tabs)) snap.set(on);
+      // The magnet lit and the canvas snapping, or "mixed" where the two disagree.
+      return Object.fromEntries(
+        Object.entries(tabs).map(([tab, [snap, canvas]]) => [
+          tab,
+          snap.button.toggled === canvas.snapEnabled && snap.snapping === canvas.snapEnabled
+            ? canvas.snapEnabled
+            : 'mixed',
+        ]),
+      );
+    },
     /** The "Open project" dialog (#183): the projects it lists and the row picked. */
     projectPicker: () => editor.projectPickerDialog()?.info() ?? null,
     /** The "Snapshots" dialog (#231): its rows, newest first, the row picked and its name field. */
diff --git a/src/editor/graph/GraphCanvas.ts b/src/editor/graph/GraphCanvas.ts
index dc23d8c4..c511cd85 100644
--- a/src/editor/graph/GraphCanvas.ts
+++ b/src/editor/graph/GraphCanvas.ts
@@ -82,6 +82,7 @@ import { type PaletteEntry, paletteEntries } from './paletteEntries';
 import { NODE_WIDTH, NodeView, TITLE_HEIGHT } from './NodeView';
 import type { NodeFace } from './nodeFace';
 import { drawGraphGrid, FIT_MARGIN, inView, ZOOM_LIMITS, zoomedAbout } from './graphView';
+import { GRAPH_SNAPS_AT_FIRST } from './SnapToggle';
 import { GraphWiring } from './wiring';
 
 /** One running instance's answer for a machine: which state it holds, and whose instance it is. */
@@ -136,7 +137,7 @@ export class GraphCanvas extends Widget {
     draw: () => this.applyView(),
   });
   private panning: { startX: number; startY: number; panX: number; panY: number } | null = null;
-  private snapping = false;
+  private snapping = GRAPH_SNAPS_AT_FIRST;
   private readonly wiring: GraphWiring;
   private readonly drags: GraphDrags;
   /** A rubber-band selection in progress, in graph coordinates. */
diff --git a/src/editor/graph/GraphEditor.ts b/src/editor/graph/GraphEditor.ts
index 8943fb70..24d622cc 100644
--- a/src/editor/graph/GraphEditor.ts
+++ b/src/editor/graph/GraphEditor.ts
@@ -4,14 +4,14 @@ import { AssetTabEditor } from '../AssetTabEditor';
 import type { EditorState } from '../state';
 import { Breadcrumb } from './Breadcrumb';
 import { GraphCanvas } from './GraphCanvas';
-import { SnapToggle } from './SnapToggle';
+import { GRAPH_SNAPS_AT_FIRST, SnapToggle } from './SnapToggle';
 import { backTo, descend, follow, type Trail } from './trail';
 
 /** Room kept for the "N nodes · M links" readout, wide enough for a three-digit graph. */
 const INFO_WIDTH = 150;
 
 export class GraphEditor extends AssetTabEditor<BehaviorAsset, GraphCanvas> {
-  readonly snap = new SnapToggle(() => this.canvas);
+  readonly snap = new SnapToggle(() => this.canvas, GRAPH_SNAPS_AT_FIRST);
   readonly breadcrumb = new Breadcrumb();
   private trail: Trail = [];
   /** A call followed into another behavior: the tab goes on to that document (#171). */
diff --git a/src/editor/graph/SnapToggle.ts b/src/editor/graph/SnapToggle.ts
index 7eacbd0b..73667ebf 100644
--- a/src/editor/graph/SnapToggle.ts
+++ b/src/editor/graph/SnapToggle.ts
@@ -6,12 +6,20 @@ export interface Snappable {
   setSnapping(on: boolean): void;
 }
 
-/** The magnet every tab that snaps carries in its header (#194): an icon toggle, off at first. */
+/** A graph, any of them, snaps from the start (#391); a curve and a vector art wait for the magnet. */
+export const GRAPH_SNAPS_AT_FIRST = true;
+
+/**
+ * The magnet every tab that snaps carries in its header (#194): an icon toggle, lit at first where
+ * its target starts snapping, as every graph does (#391).
+ */
 export class SnapToggle {
   readonly button: Button;
-  private on = false;
 
-  constructor(private readonly target: () => Snappable) {
+  constructor(
+    private readonly target: () => Snappable,
+    private on = false,
+  ) {
     this.button = new Button('', {
       width: Theme.controlHeight,
       icon: HEADER_ICON_SVG.snap,
@@ -19,6 +27,11 @@ export class SnapToggle {
       tooltip: 'Snap to the grid',
       onClick: () => this.set(!this.on),
     });
+    this.button.setToggled(on);
+  }
+
+  get snapping(): boolean {
+    return this.on;
   }
 
   get widgets(): readonly Button[] {
diff --git a/src/editor/instrument/InstrumentEditor.ts b/src/editor/instrument/InstrumentEditor.ts
index c1beeb7d..fa8ab6dd 100644
--- a/src/editor/instrument/InstrumentEditor.ts
+++ b/src/editor/instrument/InstrumentEditor.ts
@@ -28,7 +28,7 @@ import { Button, Dropdown, Label, Menu, VStack, type Widget } from '../../ui';
 import { soundLibrary } from '../../viewport/SoundLibrary';
 import { AssetTabEditor } from '../AssetTabEditor';
 import { GraphCanvas } from '../graph/GraphCanvas';
-import { SnapToggle } from '../graph/SnapToggle';
+import { GRAPH_SNAPS_AT_FIRST, SnapToggle } from '../graph/SnapToggle';
 import { TOOLBAR_ICON_SVG } from '../panels/toolbarIcons';
 import { PreviewParams } from '../soundfx/PreviewParams';
 import type { EditorState } from '../state';
@@ -51,7 +51,7 @@ const AUDITION_DELAY_MS = 150;
  * them at once, a preset is heard on the keys.
  */
 export class InstrumentEditor extends AssetTabEditor<InstrumentAsset, GraphCanvas> {
-  readonly snap = new SnapToggle(() => this.canvas);
+  readonly snap = new SnapToggle(() => this.canvas, GRAPH_SNAPS_AT_FIRST);
   /** Public for the check scripts. */
   readonly keyboard = new PianoKeyboard();
   readonly stopButton: Button;
diff --git a/src/editor/particles/ParticlesEditor.ts b/src/editor/particles/ParticlesEditor.ts
index 5305a9d7..d41c0010 100644
--- a/src/editor/particles/ParticlesEditor.ts
+++ b/src/editor/particles/ParticlesEditor.ts
@@ -6,7 +6,7 @@ import { Button, HStack, Label, Slider, Spacer, type Splitter, Theme, VStack, ty
 import { AssetTabEditor } from '../AssetTabEditor';
 import { GraphCanvas } from '../graph/GraphCanvas';
 import { PreviewSplit } from '../PreviewSplit';
-import { SnapToggle } from '../graph/SnapToggle';
+import { GRAPH_SNAPS_AT_FIRST, SnapToggle } from '../graph/SnapToggle';
 import type { EditorState } from '../state';
 import { ParticlePreview } from './ParticlePreview';
 
@@ -25,7 +25,7 @@ const HOLD_WIDTH = 52;
  */
 export class ParticlesEditor extends AssetTabEditor<ParticlesAsset, GraphCanvas> {
   readonly preview: ParticlePreview;
-  readonly snap = new SnapToggle(() => this.canvas);
+  readonly snap = new SnapToggle(() => this.canvas, GRAPH_SNAPS_AT_FIRST);
   /** Public for the check scripts: the one control they have to hit rather than read. */
   readonly slider = new Slider(0, 0, MIN_SPAN, 120);
   private readonly holdButton = new Button('Hold', {
diff --git a/src/editor/routing/RoutingEditor.ts b/src/editor/routing/RoutingEditor.ts
index 110ee65f..8feaba77 100644
--- a/src/editor/routing/RoutingEditor.ts
+++ b/src/editor/routing/RoutingEditor.ts
@@ -2,7 +2,7 @@ import { masterRoutingProblems } from '../../core/music/projectRouting';
 import { ROUTING_ID } from '../../core/model/Project';
 import { Button, Label, Spacer, VStack } from '../../ui';
 import { GraphCanvas } from '../graph/GraphCanvas';
-import { SnapToggle } from '../graph/SnapToggle';
+import { GRAPH_SNAPS_AT_FIRST, SnapToggle } from '../graph/SnapToggle';
 import type { EditorState } from '../state';
 import { TabHeader } from '../TabHeader';
 
@@ -22,7 +22,7 @@ export class RoutingEditor extends VStack {
   constructor(private readonly state: EditorState) {
     super();
     this.canvas = new GraphCanvas(state, 'routing');
-    this.snap = new SnapToggle(() => this.canvas);
+    this.snap = new SnapToggle(() => this.canvas, GRAPH_SNAPS_AT_FIRST);
     this.fitButton = new Button('Fit', { onClick: () => this.canvas.fit() });
     this.info.minWidth = INFO_WIDTH;
     const header = new TabHeader();
diff --git a/src/editor/shader/ShaderEditor.ts b/src/editor/shader/ShaderEditor.ts
index 64ae75d7..00584264 100644
--- a/src/editor/shader/ShaderEditor.ts
+++ b/src/editor/shader/ShaderEditor.ts
@@ -19,7 +19,7 @@ import {
 import { shaderLibrary } from '../../viewport/ShaderLibrary';
 import { AssetTabEditor } from '../AssetTabEditor';
 import { GraphCanvas } from '../graph/GraphCanvas';
-import { SnapToggle } from '../graph/SnapToggle';
+import { GRAPH_SNAPS_AT_FIRST, SnapToggle } from '../graph/SnapToggle';
 import { PreviewSplit } from '../PreviewSplit';
 import type { EditorState } from '../state';
 import {
@@ -50,7 +50,7 @@ const FUNCTION_SUBJECT = 'A function shows in the shaders calling it';
  * frame – so the shader is judged on the image it is meant for; before that, a built-in test image.
  */
 export class ShaderEditor extends AssetTabEditor<ShaderTabAsset, GraphCanvas> {
-  readonly snap = new SnapToggle(() => this.canvas);
+  readonly snap = new SnapToggle(() => this.canvas, GRAPH_SNAPS_AT_FIRST);
   readonly preview: ShaderPreview;
   /** Assigned by `body`; public for the check scripts, which drag it. */
   splitter!: Splitter;
diff --git a/src/editor/song/SongEditor.ts b/src/editor/song/SongEditor.ts
index 190de2d0..40f39a9e 100644
--- a/src/editor/song/SongEditor.ts
+++ b/src/editor/song/SongEditor.ts
@@ -40,7 +40,7 @@ import {
 import { activateAsset } from '../actions';
 import { AssetTabEditor } from '../AssetTabEditor';
 import { GraphCanvas } from '../graph/GraphCanvas';
-import { SnapToggle } from '../graph/SnapToggle';
+import { GRAPH_SNAPS_AT_FIRST, SnapToggle } from '../graph/SnapToggle';
 import { BakeButton } from '../music/BakeButton';
 import { clockText } from '../music/timeView';
 import { claimTransport, releaseTransport } from '../music/transport';
@@ -93,7 +93,7 @@ export class SongEditor extends AssetTabEditor<SongAsset, SongTimeline> {
   readonly routingButton: Button;
   readonly bakeButton: BakeButton;
   readonly routing: GraphCanvas;
-  readonly snap = new SnapToggle(() => this.routing);
+  readonly snap = new SnapToggle(() => this.routing, GRAPH_SNAPS_AT_FIRST);
   private shown: SongView = 'timeline';
   private readonly pane = new VStack();
   /** Heard through the sound FX (#352), then straight into the master: a preview leaves the routing out (#368). */
diff --git a/src/editor/soundfx/SoundFxEditor.ts b/src/editor/soundfx/SoundFxEditor.ts
index ade26462..674c8816 100644
--- a/src/editor/soundfx/SoundFxEditor.ts
+++ b/src/editor/soundfx/SoundFxEditor.ts
@@ -10,7 +10,7 @@ import { soundLibrary } from '../../viewport/SoundLibrary';
 import { MASTER_MIX } from '../../core/music/mixer';
 import { AssetTabEditor } from '../AssetTabEditor';
 import { GraphCanvas } from '../graph/GraphCanvas';
-import { SnapToggle } from '../graph/SnapToggle';
+import { GRAPH_SNAPS_AT_FIRST, SnapToggle } from '../graph/SnapToggle';
 import { TOOLBAR_ICON_SVG } from '../panels/toolbarIcons';
 import type { EditorState } from '../state';
 import { PreviewParams } from './PreviewParams';
@@ -27,7 +27,7 @@ const PREVIEW_OWNER = 'soundfx-preview';
  * only there to listen with.
  */
 export class SoundFxEditor extends AssetTabEditor<SoundFxAsset, GraphCanvas> {
-  readonly snap = new SnapToggle(() => this.canvas);
+  readonly snap = new SnapToggle(() => this.canvas, GRAPH_SNAPS_AT_FIRST);
   /** Public for the check scripts. */
   readonly soundPicker: Dropdown;
   readonly playButton: Button;
diff --git a/src/editor/statemachine/StateMachineEditor.ts b/src/editor/statemachine/StateMachineEditor.ts
index c292d227..612e30a2 100644
--- a/src/editor/statemachine/StateMachineEditor.ts
+++ b/src/editor/statemachine/StateMachineEditor.ts
@@ -2,7 +2,7 @@ import { statesOf } from '../../core/graph';
 import type { Asset, StateMachineAsset } from '../../core/model/Asset';
 import { AssetTabEditor } from '../AssetTabEditor';
 import { GraphCanvas } from '../graph/GraphCanvas';
-import { SnapToggle } from '../graph/SnapToggle';
+import { GRAPH_SNAPS_AT_FIRST, SnapToggle } from '../graph/SnapToggle';
 import type { EditorState } from '../state';
 
 /** Room kept for the "N states" readout. */
@@ -14,7 +14,7 @@ const INFO_WIDTH = 90;
  * and undo are all the graph's.
  */
 export class StateMachineEditor extends AssetTabEditor<StateMachineAsset, GraphCanvas> {
-  readonly snap = new SnapToggle(() => this.canvas);
+  readonly snap = new SnapToggle(() => this.canvas, GRAPH_SNAPS_AT_FIRST);
 
   constructor(state: EditorState) {
     super(state, { infoWidth: INFO_WIDTH });
diff --git a/tests/editor/snap-toggle.test.ts b/tests/editor/snap-toggle.test.ts
index 8b54b227..99328016 100644
--- a/tests/editor/snap-toggle.test.ts
+++ b/tests/editor/snap-toggle.test.ts
@@ -4,7 +4,7 @@
  */
 import { beforeAll, describe, expect, it, vi } from 'vitest';
 import { CanvasTextMetrics } from 'pixi.js';
-import { SnapToggle } from '../../src/editor/graph/SnapToggle';
+import { GRAPH_SNAPS_AT_FIRST, SnapToggle } from '../../src/editor/graph/SnapToggle';
 import { Theme } from '../../src/ui';
 
 // Node has no DOMParser to read the file with; what the magnet looks like is the icon tests' job.
@@ -40,6 +40,20 @@ describe('SnapToggle', () => {
     expect(canvas.calls).toEqual([true, false]);
   });
 
+  it('starts lit where its target snaps from the start, as every graph does (#391)', () => {
+    const canvas = target();
+    const snap = new SnapToggle(() => canvas, GRAPH_SNAPS_AT_FIRST);
+    expect(GRAPH_SNAPS_AT_FIRST).toBe(true);
+    expect(snap.button.toggled).toBe(true);
+    expect(snap.snapping).toBe(true);
+    // Nothing is asked of the target before a click: it snaps by itself from the start.
+    expect(canvas.calls).toEqual([]);
+
+    snap.button.onClick?.();
+    expect(snap.button.toggled).toBe(false);
+    expect(canvas.calls).toEqual([false]);
+  });
+
   it('asks for the target at the click, so a canvas mounted later is the one switched', () => {
     let canvas = target();
     const snap = new SnapToggle(() => canvas);
diff --git a/tools/e2e/06-graph.mjs b/tools/e2e/06-graph.mjs
index 34bebe79..80970819 100644
--- a/tools/e2e/06-graph.mjs
+++ b/tools/e2e/06-graph.mjs
@@ -27,6 +27,7 @@ export async function graph(t) {
     asset,
     api,
     navigate,
+    graphSnapAtFirst,
     projectId,
     showTab,
   } = t;
@@ -447,7 +448,16 @@ export async function graph(t) {
   //       current zoom – the canvas is not wide enough here for a zoom of 1.
   const GRID = 24;
   const onGrid = (n) => n.x % GRID === 0 && n.y % GRID === 0;
-  check('snapping is off until it is asked for', (await json('__gm.graph.snapping()')) === false);
+  // Every graph tab comes up snapping, magnet lit (#391); the harness has switched them all off since.
+  const atFirst = graphSnapAtFirst();
+  check(
+    'every graph tab starts with snapping on and its magnet lit',
+    atFirst !== null &&
+      Object.keys(atFirst).length === 8 &&
+      Object.values(atFirst).every((on) => on === true),
+    JSON.stringify(atFirst),
+  );
+  check('snapping is off as the harness left it', (await json('__gm.graph.snapping()')) === false);
   // The switch is a magnet (#194): a square icon button that stays lit while snapping is on.
   const magnet = await json('__gm.graph.snapButton()');
   await click(magnet.x, magnet.y);
diff --git a/tools/e2e/26-state-machine.mjs b/tools/e2e/26-state-machine.mjs
index b3cc2cd7..e40b33e8 100644
--- a/tools/e2e/26-state-machine.mjs
+++ b/tools/e2e/26-state-machine.mjs
@@ -110,7 +110,10 @@ export async function stateMachine(t) {
   // 26b2. The header's magnet is the graph's: on, a dragged state lands on the 24 px grid.
   const GRID = 24;
   const stateXY = async (id) => (await states()).find((s) => s.id === id) ?? { x: NaN, y: NaN };
-  check('snapping is off until it is asked for', (await json('__gm.stateMachine.snapping()')) === false);
+  check(
+    'snapping is off as the harness left it (#391)',
+    (await json('__gm.stateMachine.snapping()')) === false,
+  );
   const magnet = await json('__gm.stateMachine.snapButton()');
   const preSnap = JSON.stringify(await states());
   await click(magnet.x, magnet.y);
diff --git a/tools/e2e/45-login.mjs b/tools/e2e/45-login.mjs
index 0c8c9880..041508b9 100644
--- a/tools/e2e/45-login.mjs
+++ b/tools/e2e/45-login.mjs
@@ -285,4 +285,7 @@ export async function login(t) {
     restored.dialog === null && restored.notice.startsWith('Password changed'),
     restored,
   );
+  // The editor came up through the sign-in screen, not `navigate()`: its graphs snap (#391), and
+  // the steps after this one drag nodes to exact spots.
+  await evaluate('__gm.graphSnapping(false)');
 }
diff --git a/tools/e2e/65-song.mjs b/tools/e2e/65-song.mjs
index ecf74687..e2ca512e 100644
--- a/tools/e2e/65-song.mjs
+++ b/tools/e2e/65-song.mjs
@@ -954,7 +954,8 @@ export async function song(t) {
   p = await json("__gm.song.viewAt('routing')");
   await click(p.x, p.y);
   await sleep(300);
-  // The magnet is the routing's, as in every graph tab: off at first, greyed out on the timeline.
+  // The magnet is the routing's, as in every graph tab: off as the harness left it (#391), greyed
+  // out on the timeline.
   const magnet = await json('__gm.song.routing.snapButton()');
   const snapOff = await json('__gm.song.routing.snapping()');
   await click(magnet.x, magnet.y);
diff --git a/tools/lib/harness.mjs b/tools/lib/harness.mjs
index ac1aa7ac..7f8e92bc 100644
--- a/tools/lib/harness.mjs
+++ b/tools/lib/harness.mjs
@@ -491,7 +491,14 @@ function makeTools({ cdp, projectId, baseUrl, consoleLog, check, shotPrefix }) {
     check('debug hook present', Boolean(await evaluate('Boolean(window.__gm?.state)')));
     // The zoom is shown as a transition (#309); a check reads the step it lands on, not the way.
     await evaluate('__gm.zoomTransition?.(0)');
+    // Every graph snaps from the start (#391); the checks drag nodes to exact spots, so the magnets
+    // go off here. What they started at stays readable for the check that wants it.
+    snapAtFirst = (await json('__gm.graphSnapping?.() ?? null')) ?? null;
+    await evaluate('__gm.graphSnapping?.(false)');
   };
+  /** Each graph tab's magnet as the last load left it, before the harness switched it off (#391). */
+  let snapAtFirst = null;
+  const graphSnapAtFirst = () => snapAtFirst;
 
   return {
     cdp,
@@ -545,6 +552,7 @@ function makeTools({ cdp, projectId, baseUrl, consoleLog, check, shotPrefix }) {
     signIn,
     sceneOf,
     navigate,
+    graphSnapAtFirst,
   };
 }