diff --git a/src/layers/rail/cockpitSubject.js b/src/layers/rail/cockpitSubject.js
index c30228118..e076779b9 100644
--- a/src/layers/rail/cockpitSubject.js
+++ b/src/layers/rail/cockpitSubject.js
@@ -2,6 +2,29 @@ import { pointAtS } from '../../data/railPaths.js';
 import { getRegisteredRailFeed } from '../../data/railFeeds.js';
 import { displayMotion } from '../transit/movement.js';
 
+/** Each line's read-only copy for a snapshot's `path.line` (lineOf). */
+const lines = new WeakMap();
+
+/**
+ * A line as a snapshot hands it out: a frozen copy of the layer's path, its
+ * number arrays frozen arrays, built once per line. `pointAtS` and
+ * `projectOnPath` read it as they read the path, and nothing written to it
+ * reaches the layer.
+ */
+function lineOf(path) {
+  let line = lines.get(path);
+  if (!line) {
+    const copy = {};
+    for (const [name, value] of Object.entries(path))
+      copy[name] = ArrayBuffer.isView(value)
+        ? Object.freeze(Array.from(value))
+        : value;
+    line = Object.freeze(copy);
+    lines.set(path, line);
+  }
+  return line;
+}
+
 const NO_STOPS = Object.freeze([]);
 /** Each stops list's frozen copy for a snapshot's `stops` (stopsOf). */
 const stopLists = new WeakMap();
@@ -44,8 +67,9 @@ function reuse(previous, next) {
  * and the held one as a frozen snapshot, read again on each call: where it is
  * along its line, how fast it moves and how that is known, and its stops. A
  * call while nothing in it changed returns the snapshot it returned before,
- * and a part that did not change (its feed, its stops) is the same object in
- * the next one, so a view can read it on every frame.
+ * and a part that did not change (its feed, its line, its stops) is the same
+ * object in the next one, so a view can read it on every frame. `path.line`
+ * is a frozen copy of the train's line for `pointAtS` and `projectOnPath`.
  * `setCockpitSubject(key)` holds a train: its marker, card and selected line
  * are hidden, it stays selected (so its stops stay fresh and its feed stays
  * polled at any distance) and clicks and Escape no longer change the
@@ -164,7 +188,7 @@ export function createRailCockpitSubject({
       path.lengthM = binding.path.length;
       path.via = binding.via;
       path.builtAt = state._pathPacks.get(entry.feedId)?.pack?.builtAt ?? null;
-      path.line = binding.path;
+      path.line = lineOf(binding.path);
     }
 
     const motion = draft.motion;
diff --git a/src/layers/rail/cockpitSubject.test.mjs b/src/layers/rail/cockpitSubject.test.mjs
index a88052b2e..2f9630007 100644
--- a/src/layers/rail/cockpitSubject.test.mjs
+++ b/src/layers/rail/cockpitSubject.test.mjs
@@ -12,6 +12,7 @@ import {
 } from '../../testSupport/railLayerHarness.mjs';
 import { RAIL_SELECTED_OVERLAY_SOURCE_ID } from './policy.js';
 import { publicRailCatalog } from '../../data/railFeeds.js';
+import { pointAtS } from '../../data/railPaths.js';
 
 const M_PER_DEG = 111_320;
 const LAT = 42.36;
@@ -154,6 +155,26 @@ test('a snapshot read again while nothing changed is the one read before', async
   );
 });
 
+test('a snapshot’s line is a frozen copy: writing to it leaves the layer’s line', async (t) => {
+  const app = await onTheLine(t);
+  app.parts().selection.selectTrain(T1);
+  const { line, s } = app.layer.getSelectedTrain().path;
+  const own = app.entry(T1).path.path;
+  assert.notEqual(line, own, 'not the layer’s own');
+  assert.ok(Object.isFrozen(line));
+  for (const name of ['lat', 'lon', 'x', 'y', 's', 'box'])
+    assert.ok(Object.isFrozen(line[name]), name);
+  const lat = own.lat[1];
+  assert.throws(() => {
+    line.lat[1] = 0;
+  }, TypeError);
+  assert.equal(own.lat[1], lat, 'the layer’s line is as it was');
+  assert.deepEqual(pointAtS(line, s), pointAtS(own, s), 'it reads the same');
+  // Copied once per line: T2 runs on the same one.
+  app.parts().selection.selectTrain(T2);
+  assert.equal(app.layer.getSelectedTrain().path.line, line);
+});
+
 test('a held train hides its marker and card and keeps the selection', async (t) => {
   const app = await onTheLine(t);
   assert.equal(app.layer.setCockpitSubject('rail:mbta-rail:nope'), false);