diff --git a/docs/validation.md b/docs/validation.md
index 14f46684..38055010 100644
--- a/docs/validation.md
+++ b/docs/validation.md
@@ -135,8 +135,11 @@ flowchart LR
   instance's own folder (the same `data-model.md` section). It's no
   violation: nothing is blocked or set aside, and the deck is still
   read and studied from. Those documents aren't
-  checked, under any spelling of their address (`isSameUrl`), since a
-  repair writes to the document. Solid Memo's data
+  checked, under any spelling of their address, since a
+  repair writes to the document. Each address is compared as a
+  request sends it (`canonicalUrlOf`), the unclaimed ones brought to
+  that form once per check, so a catalog of many decks costs one
+  lookup per document, not a comparison of every pair. Solid Memo's data
   check and the
   Studio's Health screen show them (`UnclaimedDecksNotice`) with "These
   are this deck's documents", which claims them once the user confirms
diff --git a/packages/application/src/instanceChecks.test.ts b/packages/application/src/instanceChecks.test.ts
index 09a01323..5dd586cd 100644
--- a/packages/application/src/instanceChecks.test.ts
+++ b/packages/application/src/instanceChecks.test.ts
@@ -11,6 +11,23 @@ import type { LibraryDeckContent } from "@solid-memo/domain/library";
 import { instance, deck, libraryContent, makeDeps } from "./testing/fakePorts";
 import { current, card2, setup } from "./testing/digestWorld";
 
+/** How many addresses the code under test brings to the form a request sends (canonicalUrlOf) or compares (isSameUrl). */
+const urlWork = vi.hoisted(() => ({ count: 0 }));
+vi.mock("@solid-memo/domain/instanceLayout", async (importOriginal) => {
+  const actual = await importOriginal<typeof import("@solid-memo/domain/instanceLayout")>();
+  return {
+    ...actual,
+    canonicalUrlOf: (text: string) => {
+      urlWork.count += 1;
+      return actual.canonicalUrlOf(text);
+    },
+    isSameUrl: (a: string, b: string) => {
+      urlWork.count += 2;
+      return actual.isSameUrl(a, b);
+    },
+  };
+});
+
 describe("instance checks", () => {
   it("planRepair plans from a report, and applyRepairs hands the repairs to the repository", async () => {
     const deps = makeDeps();
@@ -195,6 +212,43 @@ describe("instance checks", () => {
     expect(checked).toContain(`${instance.url}catalog.ttl`);
     expect(checked.filter((url) => url.includes("/notes/"))).toEqual([]);
   });
+  it("checks an address that is no URL, unclaimed or not", async () => {
+    const { deps, useCases } = setup();
+    const named = { ...deck, cardsDocumentUrl: "no url" };
+    deps.deckRepository.unclaimedDocuments = vi.fn(async () => ["also no url"]);
+    await useCases.checkDeck(instance.url, named, { plain: (value) => value, check: () => [] });
+    expect(
+      vi.mocked(deps.shapeValidator.validateDocumentSince).mock.calls.map(([url]) => url),
+    ).toEqual(expect.arrayContaining(["no url", deck.reviewsDocumentUrl]));
+  });
+  it("skips the unclaimed documents of many decks in work that grows with their number, not its square", async () => {
+    const unclaimedWork = async (count: number) => {
+      const { deps, useCases } = setup();
+      const decks = Array.from({ length: count }, (_, index) => ({
+        ...deck,
+        id: `deck-${index}`,
+        url: `${instance.url}catalog.ttl#deck-${index}`,
+        cardsDocumentUrl: `https://elsewhere.example/c${index}.ttl`,
+        reviewsDocumentUrl: `https://elsewhere.example/r${index}.ttl`,
+      }));
+      deps.deckRepository.listDecks = vi.fn(async () => decks);
+      deps.deckRepository.unclaimedDocuments = vi.fn(async (one) => [
+        one.cardsDocumentUrl,
+        one.reviewsDocumentUrl,
+      ]);
+      urlWork.count = 0;
+      const report = await useCases.checkInstance(instance.url);
+      const work = urlWork.count;
+      expect(report.unclaimed).toHaveLength(count);
+      expect(
+        vi.mocked(deps.shapeValidator.validateDocumentSince).mock.calls.map(([url]) => url),
+      ).not.toContain(decks[0]!.cardsDocumentUrl);
+      return work;
+    };
+    const few = await unclaimedWork(100);
+    // Ten times the decks, about ten times the work; comparing every pair would be about a hundred.
+    expect(await unclaimedWork(1000)).toBeLessThan(few * 20);
+  });
   describe("documents outside the instance's folder and any storage of the user's that holds it", () => {
     const ownElsewhere = "https://alice.example/notes/old-cards.ttl";
     const others = "https://bob.example/memo/";
diff --git a/packages/application/src/instanceChecks.ts b/packages/application/src/instanceChecks.ts
index e7b24c4d..245d62ad 100644
--- a/packages/application/src/instanceChecks.ts
+++ b/packages/application/src/instanceChecks.ts
@@ -5,11 +5,11 @@
 import { planRepair, type Repair, type RepairPlan } from "@solid-memo/domain/repair";
 import type { Deck } from "@solid-memo/domain/deck";
 import {
+  canonicalUrlOf,
   catalogUrlOf,
   historyUrlOf,
   instanceDocumentUrls,
   isDocumentIn,
-  isSameUrl,
 } from "@solid-memo/domain/instanceLayout";
 import {
   summarize,
@@ -33,6 +33,7 @@ import type {
 import type { AnswerStore } from "./answerStore";
 import { AppError } from "@solid-memo/domain/appError";
 import { documentUrlOf } from "@solid-memo/domain/subjectUrl";
+import { TextMap } from "@solid-memo/domain/pathKeys";
 import { mapAtOnce } from "./atOnce";
 import { noting } from "./digestStore";
 import type { DigestStore } from "./digestStore";
@@ -88,14 +89,32 @@ export interface InstanceCheckUseCases {
 }
 
 /**
- * Whether the document at `url` is one of these decks' unclaimed ones,
- * in whatever spelling (isSameUrl): a deck may name one document twice,
- * and only the first spelling is listed as unclaimed.
+ * A test of whether the document at an address is one of these decks'
+ * unclaimed ones, in whatever spelling: a deck may name one document
+ * twice, and only the first spelling is listed as unclaimed. Each
+ * address is compared as a request would send it (canonicalUrlOf), the
+ * unclaimed ones brought to that form once for the test, so that a
+ * catalog naming many decks costs one lookup per address, not a
+ * comparison with every unclaimed document.
  */
-function isUnclaimed(url: string, unclaimed: readonly UnclaimedDeck[]): boolean {
-  return unclaimed.some((deck) =>
-    deck.documents.some((document) => isSameUrl(documentUrlOf(document), documentUrlOf(url))),
-  );
+function unclaimedTest(unclaimed: readonly UnclaimedDeck[]): (url: string) => boolean {
+  // Keyed by pieces (TextMap): an address as a request sends it may be longer than V8 hashes all of.
+  const skipped = new TextMap<true>();
+  for (const deck of unclaimed) {
+    for (const document of deck.documents) {
+      const canonical = canonicalDocumentOf(document);
+      if (canonical !== null) skipped.set(canonical, true);
+    }
+  }
+  return (url) => {
+    const canonical = canonicalDocumentOf(url);
+    return canonical !== null && skipped.has(canonical);
+  };
+}
+
+/** The address of the document `url` is in, as a request sends it (canonicalUrlOf); null for one that is no URL. */
+function canonicalDocumentOf(url: string): string | null {
+  return canonicalUrlOf(documentUrlOf(url));
 }
 
 /**
@@ -195,7 +214,7 @@ export function createInstanceCheckUseCases({
   /**
    * The instance's documents, then its drafts': each with where it is,
    * which picks its shapes. An unclaimed document is not checked, in any
-   * spelling of its address (isUnclaimed): it may be anyone's, and a
+   * spelling of its address (unclaimedTest): it may be anyone's, and a
    * repair of what the check finds writes to it.
    */
   function documentsToCheck(
@@ -204,9 +223,10 @@ export function createInstanceCheckUseCases({
     drafts: readonly string[],
     unclaimed: readonly UnclaimedDeck[],
   ): { url: string; context: Exclude<DocumentContext, "library"> }[] {
+    const isUnclaimed = unclaimedTest(unclaimed);
     return [
       ...instanceDocumentUrls(instanceUrl, decks)
-        .filter((url) => !isUnclaimed(url, unclaimed))
+        .filter((url) => !isUnclaimed(url))
         .map((url) => ({ url, context: "pod" as const })),
       ...drafts.map((url) => ({ url, context: "draft" as const })),
     ];
@@ -288,8 +308,9 @@ export function createInstanceCheckUseCases({
       const [report, cards, release] = await Promise.all([
         Promise.all([digestStore.of(instanceUrl), unclaimedDecksOf(instanceUrl, [deck])]).then(
           async ([digest, unclaimed]) => {
+            const isUnclaimed = unclaimedTest(unclaimed);
             const urls = [deck.cardsDocumentUrl, deck.reviewsDocumentUrl].filter(
-              (url) => !isUnclaimed(url, unclaimed),
+              (url) => !isUnclaimed(url),
             );
             return withUnclaimed(
               await checkDocuments(