diff --git a/frontend/app/cycle/cycle.spec.ts b/frontend/app/cycle/cycle.spec.ts
index 748b3302..4b0108f3 100644
--- a/frontend/app/cycle/cycle.spec.ts
+++ b/frontend/app/cycle/cycle.spec.ts
@@ -142,22 +142,44 @@ test("the whole cycle, from opening the app to a downloaded export", async ({ pa
   // missing icon does in a headless run.
   const consoleErrors: string[] = [];
   const badRequests: string[] = [];
-  // Every API call the *app* made that the API refused. The walk contains such
-  // calls by design — `GET /projects/{id}/schema` answers 404 for a project that
-  // has no schema yet, which is how the editor knows to open on an empty draft —
-  // and Chrome logs a console error for each. Collected so those can be told from
-  // a resource the *browser* went looking for on its own, which is the only kind
-  // nothing else would notice.
+  // Every API call the *app* made that the API refused, exempted from the
+  // console assertion because the walk contains refused calls by design —
+  // `GET /projects/{id}/schema` answers 404 for a project that has no schema
+  // yet, which is how the editor knows to open on an empty draft — and Chrome
+  // logs a console error for each; a resource the *browser* went looking for
+  // on its own still stands out. The set is keyed by URL because that is what
+  // a console message's location carries; the list is keyed by route and
+  // status because that is what a person can check, and it is pinned in the
+  // final step. Without the list the exemption is unbounded: any route, any
+  // status, silently tolerated.
   const apiRefusals = new Set<string>();
+  const refusedApiCalls: string[] = [];
   // Requests the *app* issued that the network stack reported as aborted.
   // Asserted rather than ignored — see the final step for why they are not
   // `badRequests` and what the one expected member of this list is.
   const abortedApiCalls: string[] = [];
+  // Whether the curated model's size could be read on *this* installation, taken
+  // from what the form actually rendered. The probe reaches a hub through the
+  // optional local-inference runtime, so it answers 500 on an installation
+  // without it and 200 on one with it — and both are the product working. Read
+  // rather than assumed, because the two inference CI jobs install differently
+  // and a developer's machine matches neither.
+  let curatedSizeRefused = false;
   page.on("response", (response) => {
     const kind = response.request().resourceType();
     if (response.status() < 400) return;
-    if (kind === "fetch" || kind === "xhr") apiRefusals.add(response.url());
-    else badRequests.push(`${response.status()} ${kind} ${response.url()}`);
+    if (kind === "fetch" || kind === "xhr") {
+      apiRefusals.add(response.url());
+      // The path without its query, which is the part that identifies the route.
+      // A download-size query carries a model id and a revision that move with
+      // the catalog, and pinning those would fail on a bumped revision rather
+      // than on a refusal.
+      refusedApiCalls.push(
+        `${response.request().method()} ${new URL(response.url()).pathname} ${response.status()}`,
+      );
+      return;
+    }
+    badRequests.push(`${response.status()} ${kind} ${response.url()}`);
   });
   page.on("console", (message) => {
     if (message.type() !== "error") return;
@@ -534,6 +556,29 @@ test("the whole cycle, from opening the app to a downloaded export", async ({ pa
     // The trigger only exists once the real `/inference/providers` read has
     // answered — wait for it rather than racing the click against that request.
     await expect(page.getByTestId("connection-model")).toBeVisible();
+
+    // Whether the select lands on a curated model, or falls back to Custom
+    // model with an empty id, is a catalog fact `connection-model` being
+    // visible does not settle: `defaultEntry` seeds the first entry that
+    // answers a point prompt, but returns `undefined` when none does, and
+    // `DownloadSizeLine` renders nothing for an empty id — so the wait below
+    // would die on a bare, undiagnosable timeout on such an installation.
+    // Assert the seed landed on a curated model before waiting on the price
+    // probe only a curated model triggers.
+    await expect(page.getByTestId("connection-model")).not.toHaveText(/Custom model/);
+
+    // Let the seeded model's size probe settle before moving off it: clicking
+    // through the select faster than that request resolves leaves the
+    // refusal landing at whatever point the dialog happens to unmount, which
+    // is the difference between a pinned list and a flaky one. Waiting is
+    // also what makes the answer readable — `size-known` and
+    // `size-unavailable` are the form's own two outcomes, and the final step
+    // expects a refusal from this route exactly when the second one is what
+    // rendered.
+    const sizeLine = page.getByTestId(/^size-(known|unavailable)$/);
+    await expect(sizeLine).toBeVisible();
+    curatedSizeRefused = (await sizeLine.getAttribute("data-testid")) === "size-unavailable";
+
     await page.getByTestId("connection-model").click();
     await page.getByRole("option", { name: /Custom model/ }).click();
     await page.getByTestId("connection-custom-model").fill(STUB_MODEL_ID);
@@ -1498,6 +1543,46 @@ test("the whole cycle, from opening the app to a downloaded export", async ({ pa
       expect.stringMatching(/^DELETE .*\/batches\/[0-9a-f-]+$/),
       expect.stringMatching(/^DELETE .*\/annotations$/),
     ]);
+    /*
+     * **The refused API calls, pinned rather than merely tolerated.**
+     *
+     * Six 404s, all of them a screen asking for a document that does not exist
+     * yet: `GET /projects/{id}/schema` and its curated draft sibling are the
+     * schema editor's, opening on an empty draft for a project nobody has
+     * given a schema; the annotation draft pair belongs to the annotator's
+     * add-a-class dialog, gated on `addingClass` the same way. The walk asks
+     * each pair twice — a mount, then the remount or `page.reload()` that
+     * follows — because a saved draft is written straight into the cache
+     * rather than invalidated, so writing one never triggers a second read by
+     * itself. The project's id changes per run, so each is matched rather
+     * than compared.
+     *
+     * The seventh entry is conditional on the installation, and is the reason this
+     * list is worth pinning at all. `GET /inference/download-size` prices the
+     * curated model the connection form seeds itself with, and reading that price
+     * needs the optional local-inference runtime — so it answers 500 wherever the
+     * extra is absent, which is what `browser cycle (chromium)` installs, and 200
+     * wherever it is present. `curatedSizeRefused` carries what the form rendered,
+     * so the expectation follows the installation instead of guessing at it.
+     *
+     * Anything else — a route that starts refusing, a 404 that becomes a 500, a
+     * second refusal from a route allowed one — fails here with its method, its
+     * path and its status in the message. Before this list existed every one of
+     * them was added to a set, exempted from the console assertion, and never
+     * looked at again.
+     */
+    const schema = /^GET \/projects\/[0-9a-f-]+\/schema 404$/;
+    const curatedDraft = /^GET \/projects\/[0-9a-f-]+\/schema\/drafts\/curated 404$/;
+    const annotationDraft = /^GET \/projects\/[0-9a-f-]+\/schema\/drafts\/annotation 404$/;
+    expect(refusedApiCalls).toEqual([
+      expect.stringMatching(schema),
+      expect.stringMatching(curatedDraft),
+      expect.stringMatching(schema),
+      expect.stringMatching(curatedDraft),
+      ...(curatedSizeRefused ? ["GET /inference/download-size 500"] : []),
+      expect.stringMatching(annotationDraft),
+      expect.stringMatching(annotationDraft),
+    ]);
     // And the icon is genuinely served under the mount, rather than absent and
     // unnoticed: `vite preview` would answer 200 with `index.html` here, which is
     // the reason this is checked against the real server.