diff --git a/ui/docs/renderer.md b/ui/docs/renderer.md
index dbcfb47..78c011c 100644
--- a/ui/docs/renderer.md
+++ b/ui/docs/renderer.md
@@ -280,14 +280,25 @@ Lifecycle (`RendererHandle.setPickMode(opts)`):
 
 1. **Open** (`opts !== null`): renderer marks `pickModeActive`,
    sets `alpha = 0.3` on every primitive whose id is neither the
-   source nor in `reachableIds`, mounts an overlay `Graphics` in
-   the origin tile, and subscribes to pointer-move + hover-change
-   + viewport `clicked` + document `keydown`.
+   source nor in `reachableIds`, mounts one overlay `Graphics`
+   per torus copy (nine total — matching the primitive layer's
+   wrap-copy layout), and subscribes to pointer-move +
+   hover-change + viewport `clicked` + document `keydown`. In
+   no-wrap mode the eight non-origin copies are `visible = false`,
+   so their overlay children render nothing automatically.
 2. **Tick** (every pointer-move and hover transition): the
    renderer asks `computePickOverlay(opts, cursorWorld,
-   hoveredId, points, allIds)` (`src/map/pick-mode.ts`) for a
-   draw spec — anchor ring + cursor line + optional hover
-   outline + dim set — and re-paints the overlay.
+   hoveredId, points, allIds, world)` (`src/map/pick-mode.ts`)
+   for a draw spec — anchor ring + cursor line + optional hover
+   outline + dim set — and re-paints every overlay graphic with
+   the same world-coord ops. Each copy's container already
+   applies its `(dx*W, dy*H)` transform, so the overlay shows in
+   whatever tile the user is panned over. In torus mode the
+   `world` argument switches the cursor-line endpoint to
+   `(sourceX + torusShortestDelta(...), sourceY + ...)` so the
+   line takes the short wrap path; anchor and hover-outline
+   coordinates stay canonical — the per-copy replication renders
+   them under the user's view in the matching tile.
 3. **Resolve**: a click on a primitive whose id is in
    `reachableIds` calls `opts.onPick(id)` and tears down. A click
    on empty space or a non-reachable primitive is a no-op
diff --git a/ui/frontend/src/map/cargo-routes.ts b/ui/frontend/src/map/cargo-routes.ts
index 6551322..8c943b9 100644
--- a/ui/frontend/src/map/cargo-routes.ts
+++ b/ui/frontend/src/map/cargo-routes.ts
@@ -22,10 +22,10 @@ import { DARK_THEME, type LinePrim, type PrimitiveID, type Style, type Theme } f
  */
 function routeStylesByLoadType(theme: Theme): Record<CargoLoadType, Style> {
 	return {
-		COL: { strokeColor: theme.routeCol, strokeAlpha: 0.95, strokeWidthPx: 2 },
-		CAP: { strokeColor: theme.routeCap, strokeAlpha: 0.95, strokeWidthPx: 2 },
-		MAT: { strokeColor: theme.routeMat, strokeAlpha: 0.95, strokeWidthPx: 2 },
-		EMP: { strokeColor: theme.routeEmp, strokeAlpha: 0.85, strokeWidthPx: 1 },
+		COL: { strokeColor: theme.routeCol, strokeAlpha: 0.95, strokeWidthPx: 0.6 },
+		CAP: { strokeColor: theme.routeCap, strokeAlpha: 0.95, strokeWidthPx: 0.6 },
+		MAT: { strokeColor: theme.routeMat, strokeAlpha: 0.95, strokeWidthPx: 0.6 },
+		EMP: { strokeColor: theme.routeEmp, strokeAlpha: 0.85, strokeWidthPx: 0.4 },
 	};
 }
 
diff --git a/ui/frontend/src/map/pick-mode.ts b/ui/frontend/src/map/pick-mode.ts
index 19e7c50..405e109 100644
--- a/ui/frontend/src/map/pick-mode.ts
+++ b/ui/frontend/src/map/pick-mode.ts
@@ -11,6 +11,7 @@
 // hover outline / click+Escape resolution) can be tested without
 // booting a Pixi `Application`.
 
+import { torusShortestDelta } from "./math";
 import { DEFAULT_POINT_RADIUS_PX, type PointPrim, type PrimitiveID } from "./world";
 
 /**
@@ -87,6 +88,20 @@ export const HOVER_PADDING_WORLD = 4;
  * computePickOverlay produces a `PickOverlaySpec` for the current
  * pick state. Pure: no DOM access, no Pixi calls. Callers prepare
  * `pointPrimitivesById` from the active world before invoking.
+ *
+ * `world` enables torus-wrap geometry for the cursor line: in torus
+ * mode the renderer paints the overlay graphic into every torus copy
+ * (`render.ts.openPickMode`), so the line endpoint is computed as
+ * `(sourceX + torusShortestDelta(...), sourceY + ...)` — extending
+ * beyond `[0, W) × [0, H)` when the short path crosses the seam. With
+ * 9-copy replication the user sees a short line in whatever copy is
+ * under the cursor. Pass `null` (the default) for no-wrap mode, where
+ * the line goes straight from source to canonical cursor.
+ *
+ * `anchor` and `hoverOutline` stay at the canonical source / target
+ * coordinates regardless of mode: the copy with the offset that puts
+ * them under the user's view gets rendered by the renderer's
+ * per-copy graphics, the others fall off-screen and consume nothing.
  */
 export function computePickOverlay(
 	options: PickModeOptions,
@@ -94,6 +109,7 @@ export function computePickOverlay(
 	hoveredId: PrimitiveID | null,
 	pointPrimitivesById: ReadonlyMap<PrimitiveID, PointPrim>,
 	allPrimitiveIds: Iterable<PrimitiveID>,
+	world: { width: number; height: number } | null = null,
 ): PickOverlaySpec {
 	const sourcePrim = pointPrimitivesById.get(options.sourcePrimitiveId);
 	const sourceRadius =
@@ -107,15 +123,34 @@ export function computePickOverlay(
 		dimmed.add(id);
 	}
 
-	const line =
-		cursorWorld === null
-			? null
-			: {
-					x1: options.sourceX,
-					y1: options.sourceY,
-					x2: cursorWorld.x,
-					y2: cursorWorld.y,
-				};
+	let line: PickOverlaySpec["line"] = null;
+	if (cursorWorld !== null) {
+		if (world !== null) {
+			const dx = torusShortestDelta(
+				options.sourceX,
+				cursorWorld.x,
+				world.width,
+			);
+			const dy = torusShortestDelta(
+				options.sourceY,
+				cursorWorld.y,
+				world.height,
+			);
+			line = {
+				x1: options.sourceX,
+				y1: options.sourceY,
+				x2: options.sourceX + dx,
+				y2: options.sourceY + dy,
+			};
+		} else {
+			line = {
+				x1: options.sourceX,
+				y1: options.sourceY,
+				x2: cursorWorld.x,
+				y2: cursorWorld.y,
+			};
+		}
+	}
 
 	let hoverOutline: PickOverlaySpec["hoverOutline"] = null;
 	if (
diff --git a/ui/frontend/src/map/render.ts b/ui/frontend/src/map/render.ts
index 5c7a811..a85b4ab 100644
--- a/ui/frontend/src/map/render.ts
+++ b/ui/frontend/src/map/render.ts
@@ -596,10 +596,16 @@ export async function createRenderer(opts: RendererOptions): Promise<RendererHan
 
 	// Pick-mode state. Owned by the renderer so all callers funnel
 	// through `setPickMode`; tests for the pure overlay math live in
-	// `pick-mode.ts`.
+	// `pick-mode.ts`. The overlay graphic is replicated across all nine
+	// torus copies — identical world-coord ops drawn into each copy's
+	// container, which already carries the wrap offset — so the
+	// anchor / cursor line / hover outline always render in whatever
+	// copy the user is panned over. In no-wrap mode the eight wrap
+	// copies are `visible = false`, so their overlay children render
+	// nothing for free; no special-case path is needed.
 	let pickModeActive = false;
 	let pickOptions: PickModeOptions | null = null;
-	let pickOverlay: Graphics | null = null;
+	let pickOverlays: Graphics[] = [];
 	const dimmedAlphaBackup = new Map<Graphics, number>();
 	const dimmedTintBackup = new Map<Graphics, number>();
 	const detachPickListeners: Array<() => void> = [];
@@ -631,7 +637,7 @@ export async function createRenderer(opts: RendererOptions): Promise<RendererHan
 	};
 	viewport.on("clicked", handleViewportClicked);
 	const redrawPickOverlay = (): void => {
-		if (pickOverlay === null || pickOptions === null) return;
+		if (pickOverlays.length === 0 || pickOptions === null) return;
 		const cursorWorld =
 			lastCursorPx === null
 				? null
@@ -640,41 +646,48 @@ export async function createRenderer(opts: RendererOptions): Promise<RendererHan
 						handle.getCamera(),
 						handle.getViewport(),
 					);
+		// Pass the world dims only in torus mode: the function
+		// switches to torus-shortest line geometry when world is
+		// non-null, so the line endpoint goes the wrap-short way.
 		const spec = computePickOverlay(
 			pickOptions,
 			cursorWorld,
 			lastHoveredId,
 			pointPrimitivesById,
 			allPrimitiveIds,
+			mode === "torus"
+				? { width: opts.world.width, height: opts.world.height }
+				: null,
 		);
-		const g = pickOverlay;
-		g.clear();
-		g.circle(spec.anchor.x, spec.anchor.y, spec.anchor.radius);
-		g.stroke({
-			color: theme.pickHighlight,
-			alpha: PICK_OVERLAY_STYLE.anchor.alpha,
-			width: PICK_OVERLAY_STYLE.anchor.width,
-		});
-		if (spec.line !== null) {
-			g.moveTo(spec.line.x1, spec.line.y1);
-			g.lineTo(spec.line.x2, spec.line.y2);
+		for (const g of pickOverlays) {
+			g.clear();
+			g.circle(spec.anchor.x, spec.anchor.y, spec.anchor.radius);
 			g.stroke({
 				color: theme.pickHighlight,
-				alpha: PICK_OVERLAY_STYLE.line.alpha,
-				width: PICK_OVERLAY_STYLE.line.width,
-			});
-		}
-		if (spec.hoverOutline !== null) {
-			g.circle(
-				spec.hoverOutline.x,
-				spec.hoverOutline.y,
-				spec.hoverOutline.radius,
-			);
-			g.stroke({
-				color: theme.pickHighlight,
-				alpha: PICK_OVERLAY_STYLE.hover.alpha,
-				width: PICK_OVERLAY_STYLE.hover.width,
+				alpha: PICK_OVERLAY_STYLE.anchor.alpha,
+				width: PICK_OVERLAY_STYLE.anchor.width,
 			});
+			if (spec.line !== null) {
+				g.moveTo(spec.line.x1, spec.line.y1);
+				g.lineTo(spec.line.x2, spec.line.y2);
+				g.stroke({
+					color: theme.pickHighlight,
+					alpha: PICK_OVERLAY_STYLE.line.alpha,
+					width: PICK_OVERLAY_STYLE.line.width,
+				});
+			}
+			if (spec.hoverOutline !== null) {
+				g.circle(
+					spec.hoverOutline.x,
+					spec.hoverOutline.y,
+					spec.hoverOutline.radius,
+				);
+				g.stroke({
+					color: theme.pickHighlight,
+					alpha: PICK_OVERLAY_STYLE.hover.alpha,
+					width: PICK_OVERLAY_STYLE.hover.width,
+				});
+			}
 		}
 		requestRender();
 	};
@@ -687,10 +700,8 @@ export async function createRenderer(opts: RendererOptions): Promise<RendererHan
 		dimmedAlphaBackup.clear();
 		for (const [g, tint] of dimmedTintBackup) g.tint = tint;
 		dimmedTintBackup.clear();
-		if (pickOverlay !== null) {
-			pickOverlay.destroy();
-			pickOverlay = null;
-		}
+		for (const g of pickOverlays) g.destroy();
+		pickOverlays = [];
 		pickOptions = null;
 		// Un-dimming primitives and removing the overlay are scene
 		// changes that do not move the camera.
@@ -717,12 +728,18 @@ export async function createRenderer(opts: RendererOptions): Promise<RendererHan
 				g.tint = theme.pickDimTint;
 			}
 		}
-		// Overlay graphic. Lives in the origin copy so the central
-		// tile owns it; the camera always wraps back into this tile
-		// (`wrapTorusCamera`), so the user sees the overlay
-		// regardless of how far they have panned.
-		pickOverlay = new Graphics();
-		copies[ORIGIN_COPY_INDEX]!.addChild(pickOverlay);
+		// Overlay graphics — one per torus copy. Every copy receives an
+		// identical set of draw ops in world coords, and each copy's
+		// container already applies its `(dx*W, dy*H)` transform, so
+		// the anchor / cursor line / hover outline render in whatever
+		// copy the user is currently panned over. In no-wrap mode the
+		// non-origin copies are `visible = false`, so their overlay
+		// children are invisible without extra wiring.
+		pickOverlays = copies.map((c) => {
+			const g = new Graphics();
+			c.addChild(g);
+			return g;
+		});
 		redrawPickOverlay();
 		// Pointer-move drives the cursor line; hover changes drive
 		// the outline. Both go through the renderer's existing
diff --git a/ui/frontend/tests/map-pick-mode.test.ts b/ui/frontend/tests/map-pick-mode.test.ts
index 0ec66ac..3a3f1b6 100644
--- a/ui/frontend/tests/map-pick-mode.test.ts
+++ b/ui/frontend/tests/map-pick-mode.test.ts
@@ -100,7 +100,7 @@ describe("computePickOverlay", () => {
 		expect(spec.line).toBeNull();
 	});
 
-	test("line endpoints follow the cursor when present", () => {
+	test("line endpoints follow the cursor when present (no-wrap)", () => {
 		const spec = computePickOverlay(
 			makeOptions(),
 			{ x: 250, y: 320 },
@@ -116,6 +116,100 @@ describe("computePickOverlay", () => {
 		});
 	});
 
+	test("torus line endpoint uses torusShortestDelta — short path matches direct cursor", () => {
+		// Source at (100,100), cursor at (150,120). Wrap world 201×201
+		// — the direct delta is already the shortest, so the endpoint
+		// equals the cursor.
+		const spec = computePickOverlay(
+			makeOptions(),
+			{ x: 150, y: 120 },
+			null,
+			points,
+			allIds,
+			{ width: 201, height: 201 },
+		);
+		expect(spec.line).toEqual({ x1: 100, y1: 100, x2: 150, y2: 120 });
+	});
+
+	test("torus line endpoint wraps when the short path crosses the seam (x axis)", () => {
+		// Issue #50 repro: source A3 near the left edge (x=1.44) of a
+		// 201-wide world, cursor over a wrap copy of an A1-like planet
+		// at world x ≈ -15 (the user is panned to the left side, seeing
+		// the wrap copy that A1's canonical x=184 produces at x=184-201
+		// = -17 in the screen-space the renderer paints in the -W tile).
+		// torusShortestDelta(1.44, -15, 201) is -16.44 — the line endpoint
+		// is the source + that delta, extending left past x=0.
+		const spec = computePickOverlay(
+			makeOptions({ sourceX: 1.44, sourceY: 146 }),
+			{ x: -15, y: 137 },
+			null,
+			points,
+			allIds,
+			{ width: 201, height: 201 },
+		);
+		expect(spec.line).not.toBeNull();
+		expect(spec.line!.x1).toBe(1.44);
+		expect(spec.line!.y1).toBe(146);
+		expect(spec.line!.x2).toBeCloseTo(-15);
+		expect(spec.line!.y2).toBe(137);
+	});
+
+	test("torus line endpoint wraps the long-way cursor back through the seam (x axis)", () => {
+		// Source at x=184 (canonical A1), cursor at x=200 (just inside
+		// the [0, W) tile near the right edge). Direct delta is +16
+		// (no wrap), but if the cursor sits in a wrap copy of an
+		// A3-like planet at world x ≈ 202.44, the torus-shortest delta
+		// from 184 is +18.44 and the endpoint extends past the seam.
+		const spec = computePickOverlay(
+			makeOptions({ sourceX: 184, sourceY: 137 }),
+			{ x: 202.44, y: 146 },
+			null,
+			points,
+			allIds,
+			{ width: 201, height: 201 },
+		);
+		expect(spec.line!.x1).toBe(184);
+		expect(spec.line!.x2).toBeCloseTo(202.44);
+	});
+
+	test("torus line endpoint wraps when the short path crosses the seam (y axis)", () => {
+		// Symmetric coverage on the y axis — source near the bottom,
+		// cursor pulled across the seam via the negative-y wrap.
+		const spec = computePickOverlay(
+			makeOptions({ sourceX: 50, sourceY: 3 }),
+			{ x: 50, y: -10 },
+			null,
+			points,
+			allIds,
+			{ width: 100, height: 50 },
+		);
+		expect(spec.line!.y1).toBe(3);
+		expect(spec.line!.y2).toBeCloseTo(-10);
+		expect(spec.line!.x1).toBe(50);
+		expect(spec.line!.x2).toBe(50);
+	});
+
+	test("torus mode preserves canonical anchor and hover-outline coords", () => {
+		// The renderer paints the overlay into every torus copy with
+		// its own offset, so the spec stays in canonical coords; the
+		// torus argument must only affect the cursor line. This test
+		// guards the contract for the future-careless reader.
+		const spec = computePickOverlay(
+			makeOptions(),
+			{ x: 250, y: 320 },
+			2,
+			points,
+			allIds,
+			{ width: 400, height: 400 },
+		);
+		expect(spec.anchor).toEqual({ x: 100, y: 100, radius: 6 + ANCHOR_PADDING_WORLD });
+		expect(spec.hoverOutline).toEqual({
+			x: 200,
+			y: 100,
+			radius: 5 + HOVER_PADDING_WORLD,
+		});
+	});
+
 	test("hoverOutline is null when nothing is hovered", () => {
 		const spec = computePickOverlay(
 			makeOptions(),