diff --git a/.changeset/fe-1172-optional-link-targets.md b/.changeset/fe-1172-optional-link-targets.md
new file mode 100644
index 00000000000..dc49eb641b1
--- /dev/null
+++ b/.changeset/fe-1172-optional-link-targets.md
@@ -0,0 +1,5 @@
+---
+"@blockprotocol/graph": minor
+---
+
+Make `rightEntity` / `leftEntity` on `LinkEntityAndRightEntity` / `LinkEntityAndLeftEntity` possibly `undefined`, reflecting what `getOutgoingLinkAndTargetEntities` / `getIncomingLinkAndSourceEntities` actually return when a link's `has-right-entity` / `has-left-entity` edge is not resolved into the subgraph. Previously an unsafe cast hid this, allowing runtime crashes when consumers indexed into a missing target entity array.
diff --git a/apps/hash-api/src/graphql/resolvers/knowledge/org/shared.ts b/apps/hash-api/src/graphql/resolvers/knowledge/org/shared.ts
index e56150675e7..1e58782fea0 100644
--- a/apps/hash-api/src/graphql/resolvers/knowledge/org/shared.ts
+++ b/apps/hash-api/src/graphql/resolvers/knowledge/org/shared.ts
@@ -82,7 +82,7 @@ export const getPendingOrgInvitationsFromSubgraph = async (
       );
     }
 
-    const orgEntity = linkAndOrgEntities[0]?.leftEntity[0];
+    const orgEntity = linkAndOrgEntities[0]?.leftEntity?.[0];
 
     if (!orgEntity) {
       throw new Error(
diff --git a/apps/hash-frontend/src/components/hooks/use-account-pages.ts b/apps/hash-frontend/src/components/hooks/use-account-pages.ts
index e261cc67334..2757b5b7b09 100644
--- a/apps/hash-frontend/src/components/hooks/use-account-pages.ts
+++ b/apps/hash-frontend/src/components/hooks/use-account-pages.ts
@@ -71,12 +71,24 @@ export const useAccountPages = (
       );
 
       const parentLink = pageOutgoingLinks.find(({ linkEntity }) =>
-        linkEntity[0]!.metadata.entityTypeIds.includes(
+        linkEntity[0]?.metadata.entityTypeIds.includes(
           systemLinkEntityTypes.hasParent.linkEntityTypeId,
         ),
       );
 
-      const parentPage = parentLink?.rightEntity[0] ?? null;
+      const parentPage = parentLink ? parentLink.rightEntity?.[0] : null;
+
+      if (parentLink && !parentPage) {
+        /**
+         * The query resolves one level of outgoing `has-parent` links, so if
+         * the link is in the subgraph its target page must be too. A missing
+         * parent page means the subgraph is internally inconsistent, which we
+         * surface loudly rather than silently treating the page as parentless.
+         */
+        throw new Error(
+          `Invariant violation: has-parent link ${parentLink.linkEntity[0]?.metadata.recordId.entityId} on page ${latestPage.metadata.recordId.entityId} is missing its right (parent page) entity in the subgraph`,
+        );
+      }
 
       return {
         ...simplifyProperties(latestPage.properties as PageProperties),
diff --git a/apps/hash-frontend/src/lib/user-and-org.ts b/apps/hash-frontend/src/lib/user-and-org.ts
index 79821ea0962..7107fac6380 100644
--- a/apps/hash-frontend/src/lib/user-and-org.ts
+++ b/apps/hash-frontend/src/lib/user-and-org.ts
@@ -194,7 +194,11 @@ export const constructOrg = (params: {
       continue;
     }
 
-    const rightEntityRevision = rightEntity[0];
+    /**
+     * The right entity may be missing from the subgraph (e.g. if it was not
+     * resolved when the subgraph was produced) – skip the link in that case.
+     */
+    const rightEntityRevision = rightEntity?.[0];
 
     if (!rightEntityRevision) {
       continue;
@@ -269,11 +273,17 @@ export const constructOrg = (params: {
       continue;
     }
 
-    const userEntityRevision = leftEntity[0];
+    const userEntityRevision = leftEntity?.[0];
 
     if (!userEntityRevision) {
+      /**
+       * User entities are public – if the membership link is in the subgraph,
+       * its left (user) entity must be too. A missing user entity means the
+       * subgraph is internally inconsistent, which we surface loudly rather
+       * than silently dropping the membership.
+       */
       throw new Error(
-        `Failed to find the current user entity associated with the membership with entity ID: ${linkEntityRevision.metadata.recordId.entityId}`,
+        `Invariant violation: membership link ${linkEntityRevision.metadata.recordId.entityId} is missing its left (user) entity in the subgraph`,
       );
     }
 
@@ -450,14 +460,20 @@ export const constructUser = (params: {
     intervalForTimestamp(currentTimestamp()),
   );
 
-  const avatarLinkAndEntities: LinkEntityAndRightEntity[] = [];
-  const coverImageLinkAndEntities: LinkEntityAndRightEntity[] = [];
-  const hasBioLinkAndEntities: LinkEntityAndRightEntity[] = [];
+  /**
+   * These hold the latest revision of each link and its target entity, taken
+   * from the revision arrays after checking that both are present.
+   */
+  type LinkAndTargetRevision = { linkEntity: LinkEntity; rightEntity: Entity };
+
+  const avatarLinkAndEntities: LinkAndTargetRevision[] = [];
+  const coverImageLinkAndEntities: LinkAndTargetRevision[] = [];
+  const hasBioLinkAndEntities: LinkAndTargetRevision[] = [];
   const hasServiceAccounts: User["hasServiceAccounts"] = [];
 
   for (const linkAndEntity of outgoingLinkAndTargetEntities) {
     const linkEntity = linkAndEntity.linkEntity[0];
-    const rightEntity = linkAndEntity.rightEntity[0];
+    const rightEntity = linkAndEntity.rightEntity?.[0];
 
     if (!linkEntity || !rightEntity) {
       continue;
@@ -468,7 +484,7 @@ export const constructUser = (params: {
     if (
       entityTypeIds.includes(systemLinkEntityTypes.hasAvatar.linkEntityTypeId)
     ) {
-      avatarLinkAndEntities.push(linkAndEntity);
+      avatarLinkAndEntities.push({ linkEntity, rightEntity });
       continue;
     }
 
@@ -477,12 +493,12 @@ export const constructUser = (params: {
         systemLinkEntityTypes.hasCoverImage.linkEntityTypeId,
       )
     ) {
-      coverImageLinkAndEntities.push(linkAndEntity);
+      coverImageLinkAndEntities.push({ linkEntity, rightEntity });
       continue;
     }
 
     if (entityTypeIds.includes(systemLinkEntityTypes.hasBio.linkEntityTypeId)) {
-      hasBioLinkAndEntities.push(linkAndEntity);
+      hasBioLinkAndEntities.push({ linkEntity, rightEntity });
       continue;
     }
 
@@ -491,7 +507,7 @@ export const constructUser = (params: {
         systemLinkEntityTypes.hasServiceAccount.linkEntityTypeId,
       )
     ) {
-      const serviceAccountEntity = linkAndEntity.rightEntity[0]!;
+      const serviceAccountEntity = rightEntity;
 
       const { profileUrl } = simplifyProperties(
         serviceAccountEntity.properties as ServiceAccount["properties"],
@@ -510,31 +526,27 @@ export const constructUser = (params: {
     }
   }
 
-  const hasAvatar = avatarLinkAndEntities[0]
+  const [avatarLinkAndEntity] = avatarLinkAndEntities;
+  const hasAvatar = avatarLinkAndEntity
     ? {
-        // these are each arrays because each entity can have multiple revisions
-        linkEntity: avatarLinkAndEntities[0].linkEntity[0]!,
-        imageEntity: avatarLinkAndEntities[0]
-          .rightEntity[0]! as Entity<ImageFile>,
+        linkEntity: avatarLinkAndEntity.linkEntity,
+        imageEntity: avatarLinkAndEntity.rightEntity as Entity<ImageFile>,
       }
     : undefined;
 
-  const hasCoverImage = coverImageLinkAndEntities[0]
+  const [coverImageLinkAndEntity] = coverImageLinkAndEntities;
+  const hasCoverImage = coverImageLinkAndEntity
     ? {
-        // these are each arrays because each entity can have multiple revisions
-        linkEntity: coverImageLinkAndEntities[0].linkEntity[0]!,
-        imageEntity: coverImageLinkAndEntities[0]
-          .rightEntity[0]! as Entity<ImageFile>,
+        linkEntity: coverImageLinkAndEntity.linkEntity,
+        imageEntity: coverImageLinkAndEntity.rightEntity as Entity<ImageFile>,
       }
     : undefined;
 
-  const hasBio = hasBioLinkAndEntities[0]
+  const [hasBioLinkAndEntity] = hasBioLinkAndEntities;
+  const hasBio = hasBioLinkAndEntity
     ? {
-        // these are each arrays because each entity can have multiple revisions
-        linkEntity: hasBioLinkAndEntities[0]
-          .linkEntity[0]! as LinkEntity<HasBio>,
-        profileBioEntity: hasBioLinkAndEntities[0]
-          .rightEntity[0]! as Entity<ProfileBio>,
+        linkEntity: hasBioLinkAndEntity.linkEntity as LinkEntity<HasBio>,
+        profileBioEntity: hasBioLinkAndEntity.rightEntity as Entity<ProfileBio>,
       }
     : undefined;
 
diff --git a/apps/hash-frontend/src/pages/notifications.page/notifications-with-links-context.tsx b/apps/hash-frontend/src/pages/notifications.page/notifications-with-links-context.tsx
index a5c2a7899e1..e312e0f068e 100644
--- a/apps/hash-frontend/src/pages/notifications.page/notifications-with-links-context.tsx
+++ b/apps/hash-frontend/src/pages/notifications.page/notifications-with-links-context.tsx
@@ -221,25 +221,25 @@ export const useNotificationsWithLinksContextValue =
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.occurredInEntity.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             const occurredInBlock = outgoingLinks.find(
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.occurredInBlock.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             const occurredInText = outgoingLinks.find(
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.occurredInText.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             const triggeredByUserEntity = outgoingLinks.find(
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.triggeredByUser.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             if (
               !occurredInEntity ||
@@ -260,7 +260,7 @@ export const useNotificationsWithLinksContextValue =
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.occurredInComment.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             if (occurredInComment) {
               return {
@@ -297,25 +297,25 @@ export const useNotificationsWithLinksContextValue =
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.occurredInEntity.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             const occurredInBlock = outgoingLinks.find(
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.occurredInBlock.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             const triggeredByComment = outgoingLinks.find(
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.triggeredByComment.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             const triggeredByUserEntity = outgoingLinks.find(
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.triggeredByUser.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             if (
               !occurredInEntity ||
@@ -336,7 +336,7 @@ export const useNotificationsWithLinksContextValue =
               isLinkAndRightEntityWithLinkType(
                 systemLinkEntityTypes.repliedToComment.linkEntityTypeId,
               ),
-            )?.rightEntity[0];
+            )?.rightEntity?.[0];
 
             if (repliedToComment) {
               return {
diff --git a/apps/hash-frontend/src/pages/settings/integrations/linear/use-linear-integrations.ts b/apps/hash-frontend/src/pages/settings/integrations/linear/use-linear-integrations.ts
index 8eef0e84a1b..a6142357b93 100644
--- a/apps/hash-frontend/src/pages/settings/integrations/linear/use-linear-integrations.ts
+++ b/apps/hash-frontend/src/pages/settings/integrations/linear/use-linear-integrations.ts
@@ -125,7 +125,19 @@ export const useLinearIntegrations = (): {
           })
           .map((linkAndTarget) => {
             const linkEntity = linkAndTarget.linkEntity[0]!;
-            const rightEntity = linkAndTarget.rightEntity[0]!;
+            const rightEntity = linkAndTarget.rightEntity?.[0];
+
+            if (!rightEntity) {
+              /**
+               * The target of a `syncLinearDataWith` link is a user or org
+               * (web) entity, which is public – if the link is in the
+               * subgraph its target must be too. A missing target means the
+               * subgraph is internally inconsistent.
+               */
+              throw new Error(
+                `Invariant violation: syncLinearDataWith link ${linkEntity.metadata.recordId.entityId} is missing its right (web) entity in the subgraph`,
+              );
+            }
 
             const { linearTeamId: linearTeamIds } = simplifyProperties(
               linkEntity.properties as SyncLinearDataWithProperties,
diff --git a/apps/hash-frontend/src/pages/shared/block-collection-contents.ts b/apps/hash-frontend/src/pages/shared/block-collection-contents.ts
index 57fcb9f572b..0cb23b28ff9 100644
--- a/apps/hash-frontend/src/pages/shared/block-collection-contents.ts
+++ b/apps/hash-frontend/src/pages/shared/block-collection-contents.ts
@@ -171,7 +171,7 @@ export const getBlockCollectionContents = (params: {
           linkEntityRevisions[0].metadata.entityTypeIds.includes(
             systemLinkEntityTypes.hasData.linkEntityTypeId,
           ),
-      )?.rightEntity[0];
+      )?.rightEntity?.[0];
 
       if (!blockChildEntity) {
         throw new Error("Error fetching block data");
diff --git a/apps/hash-frontend/src/pages/shared/block-collection/block-context-menu/block-select-data-modal.tsx b/apps/hash-frontend/src/pages/shared/block-collection/block-context-menu/block-select-data-modal.tsx
index 174b23174e4..87e80eb2eb5 100644
--- a/apps/hash-frontend/src/pages/shared/block-collection/block-context-menu/block-select-data-modal.tsx
+++ b/apps/hash-frontend/src/pages/shared/block-collection/block-context-menu/block-select-data-modal.tsx
@@ -81,12 +81,15 @@ export const BlockSelectDataModal: FunctionComponent<
       blockSubgraph,
       blockDataEntity.metadata.recordId.entityId,
     )
-      .filter(({ linkEntity: linkEntityRevisions }) =>
-        linkEntityRevisions[0]?.metadata.entityTypeIds.includes(
-          blockProtocolLinkEntityTypes.hasQuery.linkEntityTypeId,
-        ),
+      .filter(
+        ({ linkEntity: linkEntityRevisions, rightEntity }) =>
+          linkEntityRevisions[0]?.metadata.entityTypeIds.includes(
+            blockProtocolLinkEntityTypes.hasQuery.linkEntityTypeId,
+          ) &&
+          // the target entity may be missing from the subgraph – skip the link
+          !!rightEntity?.[0],
       )
-      .map(({ rightEntity }) => rightEntity[0] as HashEntity<Query>);
+      .map(({ rightEntity }) => rightEntity![0] as HashEntity<Query>);
 
     return existingQueries[0];
   }, [blockSubgraph, blockDataEntity]);
diff --git a/apps/hash-frontend/src/pages/shared/block-collection/mention-view/mention-display.tsx b/apps/hash-frontend/src/pages/shared/block-collection/mention-view/mention-display.tsx
index fc1c4a9f367..0c83aba73e0 100644
--- a/apps/hash-frontend/src/pages/shared/block-collection/mention-view/mention-display.tsx
+++ b/apps/hash-frontend/src/pages/shared/block-collection/mention-view/mention-display.tsx
@@ -139,7 +139,7 @@ export const MentionDisplay: FunctionComponent<MentionDisplayProps> = ({
           ),
       );
 
-      const targetEntity = outgoingLinkAndTargetEntities?.rightEntity[0];
+      const targetEntity = outgoingLinkAndTargetEntities?.rightEntity?.[0];
 
       const targetEntityLabel = targetEntity
         ? generateEntityLabel(entitySubgraph, targetEntity)
diff --git a/apps/hash-frontend/src/pages/shared/block-collection/shared/mention-suggester.tsx b/apps/hash-frontend/src/pages/shared/block-collection/shared/mention-suggester.tsx
index 4df9dbea351..7c290013fe1 100644
--- a/apps/hash-frontend/src/pages/shared/block-collection/shared/mention-suggester.tsx
+++ b/apps/hash-frontend/src/pages/shared/block-collection/shared/mention-suggester.tsx
@@ -398,7 +398,7 @@ export const MentionSuggester: FunctionComponent<MentionSuggesterProps> = ({
         ).map<Extract<SubMenuItem, { kind: "outgoing-link" }>>(
           ({
             linkEntity: linkEntityRevisions,
-            rightEntity: rightEntityRevisions,
+            rightEntity: rightEntityRevisions = [],
           }) => {
             const [linkEntity] = linkEntityRevisions;
             const [rightEntity] = rightEntityRevisions;
diff --git a/apps/hash-frontend/src/pages/shared/claims-table.tsx b/apps/hash-frontend/src/pages/shared/claims-table.tsx
index 720f3db3581..c389d81697c 100644
--- a/apps/hash-frontend/src/pages/shared/claims-table.tsx
+++ b/apps/hash-frontend/src/pages/shared/claims-table.tsx
@@ -429,13 +429,13 @@ export const ClaimsTable = memo(
               systemLinkEntityTypes.hasObject.linkEntityTypeId,
             )
           ) {
-            objectEntityId = rightEntity[0]?.entityId;
+            objectEntityId = rightEntity?.[0]?.entityId;
           } else if (
             linkEntity[0]?.metadata.entityTypeIds.includes(
               systemLinkEntityTypes.hasSubject.linkEntityTypeId,
             )
           ) {
-            subjectEntityId = rightEntity[0]?.entityId;
+            subjectEntityId = rightEntity?.[0]?.entityId;
           }
         }
 
diff --git a/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/incoming-links-section.tsx b/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/incoming-links-section.tsx
index 4bbcbfacd02..03a3896a135 100644
--- a/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/incoming-links-section.tsx
+++ b/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/incoming-links-section.tsx
@@ -140,7 +140,7 @@ export const IncomingLinksSection = ({
         !draftLinksToArchive.includes(
           incomingLinkAndSource.linkEntity[0].entityId,
         ) &&
-        incomingLinkAndSource.leftEntity[0] &&
+        incomingLinkAndSource.leftEntity?.[0] &&
         !incomingLinkAndSource.leftEntity[0].metadata.entityTypeIds.includes(
           systemEntityTypes.claim.entityTypeId,
         )
diff --git a/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/incoming-links-section/incoming-links-table.tsx b/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/incoming-links-section/incoming-links-table.tsx
index cc3096f117e..785c63216b9 100644
--- a/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/incoming-links-section/incoming-links-table.tsx
+++ b/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/incoming-links-section/incoming-links-table.tsx
@@ -362,9 +362,14 @@ export const IncomingLinksTable = memo(
           linkEntityTypeIds.add(linkType.$id);
         }
 
-        const leftEntity = leftEntityRevisions[0];
+        const leftEntity = leftEntityRevisions?.[0];
         if (!leftEntity) {
-          throw new Error("Expected at least one left entity revision");
+          /**
+           * The source entity may be missing from the subgraph (e.g. if it
+           * was not resolved when the subgraph was produced) – skip the link
+           * rather than crashing.
+           */
+          continue;
         }
 
         const leftEntityClosedMultiType = getClosedMultiEntityTypeFromMap(
diff --git a/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/outgoing-links-section/readonly-outgoing-links-table.tsx b/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/outgoing-links-section/readonly-outgoing-links-table.tsx
index 336903f8b02..cbd6924c2e2 100644
--- a/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/outgoing-links-section/readonly-outgoing-links-table.tsx
+++ b/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/outgoing-links-section/readonly-outgoing-links-table.tsx
@@ -341,9 +341,14 @@ export const OutgoingLinksTable = memo(
           linkEntityTypeIds.add(linkType.$id);
         }
 
-        const rightEntity = rightEntityRevisions[0];
+        const rightEntity = rightEntityRevisions?.[0];
         if (!rightEntity) {
-          throw new Error("Expected at least one right entity revision");
+          /**
+           * The target entity may be missing from the subgraph (e.g. if it
+           * was not resolved when the subgraph was produced) – skip the link
+           * rather than crashing.
+           */
+          continue;
         }
 
         const rightEntityClosedMultiType = getClosedMultiEntityTypeFromMap(
diff --git a/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/outgoing-links-section/use-rows.ts b/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/outgoing-links-section/use-rows.ts
index 11c69d00872..caa2ed268ad 100644
--- a/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/outgoing-links-section/use-rows.ts
+++ b/apps/hash-frontend/src/pages/shared/entity/entity-editor/links-section/outgoing-links-section/use-rows.ts
@@ -145,7 +145,7 @@ export const useRows = ({
             );
           }
 
-          const targetEntityRevisions = [...entities.rightEntity];
+          const targetEntityRevisions = [...(entities.rightEntity ?? [])];
           targetEntityRevisions.sort((entityA, entityB) =>
             intervalCompareWithInterval(
               entityA.metadata.temporalVersioning[variableAxis],
@@ -156,9 +156,12 @@ export const useRows = ({
           const latestTargetEntityRevision = targetEntityRevisions.at(-1);
 
           if (!latestTargetEntityRevision) {
-            throw new Error(
-              `Couldn't find a target link entity revision from ${entity.metadata.recordId.entityId}, this is likely an implementation bug in the stdlib`,
-            );
+            /**
+             * The target entity may be missing from the subgraph (e.g. if it
+             * was not resolved when the subgraph was produced) – skip the
+             * link rather than crashing.
+             */
+            continue;
           }
 
           const { entityTypeIds, recordId } = latestLinkEntityRevision.metadata;
diff --git a/apps/hash-frontend/src/pages/shared/entity/get-entity-multi-type-dependencies.ts b/apps/hash-frontend/src/pages/shared/entity/get-entity-multi-type-dependencies.ts
index 797dedcf686..7c444bba1a7 100644
--- a/apps/hash-frontend/src/pages/shared/entity/get-entity-multi-type-dependencies.ts
+++ b/apps/hash-frontend/src/pages/shared/entity/get-entity-multi-type-dependencies.ts
@@ -83,7 +83,7 @@ export const getEntityMultiTypeDependencies = ({
       console.warn(`Link entity not found in subgraph`);
     }
 
-    const rightEntityRevision = rightEntity[0];
+    const rightEntityRevision = rightEntity?.[0];
 
     if (rightEntityRevision) {
       addEntityTypeIdsToSet(
@@ -110,7 +110,7 @@ export const getEntityMultiTypeDependencies = ({
       console.warn(`Link entity not found in subgraph`);
     }
 
-    const leftEntityRevision = leftEntity[0];
+    const leftEntityRevision = leftEntity?.[0];
 
     if (leftEntityRevision) {
       addEntityTypeIdsToSet(uniqueJoinedMultiEntityTypeIds, leftEntityRevision);
diff --git a/apps/hash-frontend/src/pages/shared/use-flow-runs-usage.ts b/apps/hash-frontend/src/pages/shared/use-flow-runs-usage.ts
index 57f13dd4818..864172aaea3 100644
--- a/apps/hash-frontend/src/pages/shared/use-flow-runs-usage.ts
+++ b/apps/hash-frontend/src/pages/shared/use-flow-runs-usage.ts
@@ -131,7 +131,7 @@ export const useFlowRunsUsage = ({
           );
         }
 
-        const incurredInEntity = incurredInLinkAndEntities[0]!.rightEntity[0];
+        const incurredInEntity = incurredInLinkAndEntities[0]!.rightEntity?.[0];
 
         if (!incurredInEntity) {
           return false;
diff --git a/apps/hash-frontend/src/pages/signin.page.tsx b/apps/hash-frontend/src/pages/signin.page.tsx
index 9226bf85fab..4a59c29acce 100644
--- a/apps/hash-frontend/src/pages/signin.page.tsx
+++ b/apps/hash-frontend/src/pages/signin.page.tsx
@@ -571,6 +571,9 @@ const SigninPage: NextPageWithLayout = () => {
                       <Button
                         type="submit"
                         variant="tertiary_quiet"
+                        // The login flow is fetched asynchronously – submitting
+                        // before it has loaded cannot succeed.
+                        disabled={!flow}
                         sx={{
                           /** @todo: replace this with a blue from the design system */
                           color: "#2482FF",
diff --git a/apps/hash-frontend/src/pages/types/[[...type-kind]].page.tsx b/apps/hash-frontend/src/pages/types/[[...type-kind]].page.tsx
index dfdf28736cb..22ada4efe3c 100644
--- a/apps/hash-frontend/src/pages/types/[[...type-kind]].page.tsx
+++ b/apps/hash-frontend/src/pages/types/[[...type-kind]].page.tsx
@@ -2,11 +2,11 @@ import { Box, Container, Stack, Typography } from "@mui/material";
 import { NextSeo } from "next-seo";
 import { useCallback, useEffect, useMemo, useState } from "react";
 
-import { getRoots } from "@blockprotocol/graph/stdlib";
+import { getEntityTypes, getRoots } from "@blockprotocol/graph/stdlib";
 
 import { useBlockProtocolQueryDataTypes } from "../../components/hooks/block-protocol-functions/ontology/use-block-protocol-query-data-types";
-import { useLatestEntityTypesOptional } from "../../shared/entity-types-context/hooks";
-import { useEntityTypesContextRequired } from "../../shared/entity-types-context/hooks/use-entity-types-context-required";
+import { useBlockProtocolQueryEntityTypes } from "../../components/hooks/block-protocol-functions/ontology/use-block-protocol-query-entity-types";
+import { isSpecialEntityType } from "../../shared/entity-types-context/shared/is-special-entity-type";
 import { FilesLightIcon } from "../../shared/icons/files-light-icon";
 import { PlusRegularIcon } from "../../shared/icons/plus-regular";
 import { getLayoutWithSidebar } from "../../shared/layout";
@@ -22,7 +22,10 @@ import {
 
 import type { NextPageWithLayout } from "../../shared/layout";
 import type { DataTypeRootType } from "@blockprotocol/graph";
-import type { DataTypeWithMetadata } from "@blockprotocol/type-system";
+import type {
+  DataTypeWithMetadata,
+  EntityTypeWithMetadata,
+} from "@blockprotocol/type-system";
 import type { GetServerSideProps } from "next";
 
 type ParsedQueryKindParam =
@@ -52,33 +55,73 @@ export const getServerSideProps: GetServerSideProps<
 };
 
 const TypesPage: NextPageWithLayout<TypesPageProps> = ({ currentTab }) => {
-  const { latestEntityTypes } = useLatestEntityTypesOptional({
-    includeArchived: true,
-  });
+  const { queryEntityTypes } = useBlockProtocolQueryEntityTypes();
 
-  const { isSpecialEntityTypeLookup } = useEntityTypesContextRequired();
+  const [latestEntityTypesByKind, setLatestEntityTypesByKind] = useState<{
+    nonLink: EntityTypeWithMetadata[];
+    link: EntityTypeWithMetadata[];
+  }>();
 
-  const latestNonLinkEntityTypes = useMemo(
-    () =>
-      isSpecialEntityTypeLookup
-        ? latestEntityTypes?.filter(
-            (entityType) =>
-              !isSpecialEntityTypeLookup[entityType.schema.$id]?.isLink,
-          )
-        : undefined,
-    [isSpecialEntityTypeLookup, latestEntityTypes],
-  );
+  /**
+   * This page only lists the latest version of each entity type, so it runs
+   * its own `latestOnly` query rather than waiting on the entity types
+   * context, which fetches all versions of all entity types (including
+   * archived ones) – a much heavier query.
+   *
+   * Constraint resolve depths are zeroed because only the inheritance chain
+   * (`inheritsFrom`, kept at its default depth) is needed to decide whether a
+   * type is a link type.
+   */
+  const fetchEntityTypes = useCallback(async () => {
+    const { data: subgraph } = await queryEntityTypes({
+      data: {
+        latestOnly: true,
+        includeArchived: true,
+        graphResolveDepths: {
+          constrainsValuesOn: 0,
+          constrainsPropertiesOn: 0,
+          constrainsLinksOn: 0,
+          constrainsLinkDestinationsOn: 0,
+        },
+      },
+    });
 
-  const latestLinkEntityTypes = useMemo(
-    () =>
-      isSpecialEntityTypeLookup
-        ? latestEntityTypes?.filter(
-            (entityType) =>
-              isSpecialEntityTypeLookup[entityType.schema.$id]?.isLink,
-          )
-        : undefined,
-    [isSpecialEntityTypeLookup, latestEntityTypes],
-  );
+    if (!subgraph) {
+      return;
+    }
+
+    const latestEntityTypes = getRoots(subgraph);
+
+    /**
+     * All (transitive) parents of the latest entity types are resolved into
+     * the subgraph via its `inheritsFrom` depth, so the lookup by versioned
+     * URL contains everything `isSpecialEntityType` needs to walk each
+     * type's inheritance chain.
+     */
+    const typesByVersion = Object.fromEntries(
+      getEntityTypes(subgraph).map((type) => [type.schema.$id, type]),
+    );
+
+    const nonLink: EntityTypeWithMetadata[] = [];
+    const link: EntityTypeWithMetadata[] = [];
+
+    for (const entityType of latestEntityTypes) {
+      if (isSpecialEntityType(entityType.schema, typesByVersion).isLink) {
+        link.push(entityType);
+      } else {
+        nonLink.push(entityType);
+      }
+    }
+
+    setLatestEntityTypesByKind({ nonLink, link });
+  }, [queryEntityTypes]);
+
+  useEffect(() => {
+    void fetchEntityTypes();
+  }, [fetchEntityTypes]);
+
+  const latestNonLinkEntityTypes = latestEntityTypesByKind?.nonLink;
+  const latestLinkEntityTypes = latestEntityTypesByKind?.link;
 
   const { queryDataTypes } = useBlockProtocolQueryDataTypes();
 
diff --git a/apps/plugin-browser/src/shared/get-user.ts b/apps/plugin-browser/src/shared/get-user.ts
index 7adfa3e04fe..2726173a553 100644
--- a/apps/plugin-browser/src/shared/get-user.ts
+++ b/apps/plugin-browser/src/shared/get-user.ts
@@ -44,7 +44,7 @@ const getAvatarForEntity = (
       systemLinkEntityTypes.hasAvatar.linkEntityTypeId,
     ),
   );
-  return avatarLinkAndEntities[0]?.rightEntity[0] as
+  return avatarLinkAndEntities[0]?.rightEntity?.[0] as
     | Entity<ImageFile>
     | undefined;
 };
@@ -102,10 +102,10 @@ export const getUser = (): Promise<LocalStorage["user"] | null> => {
           linkEntity[0]?.metadata.entityTypeIds.includes(
             systemLinkEntityTypes.has.linkEntityTypeId,
           ) &&
-          rightEntity[0]?.metadata.entityTypeIds.includes(
+          rightEntity?.[0]?.metadata.entityTypeIds.includes(
             systemEntityTypes.browserPluginSettings.entityTypeId,
           ),
-      )[0]?.rightEntity[0];
+      )[0]?.rightEntity?.[0];
 
       let settingsEntityId: EntityId;
 
@@ -223,8 +223,18 @@ export const getUser = (): Promise<LocalStorage["user"] | null> => {
         });
       }
 
-      const orgs = orgLinksAndEntities.map(({ rightEntity }) => {
-        const org = rightEntity[0]!;
+      const orgs = orgLinksAndEntities.map(({ linkEntity, rightEntity }) => {
+        const org = rightEntity?.[0];
+        if (!org) {
+          /**
+           * Org entities are public – if the membership link is in the
+           * subgraph, its right (org) entity must be too. A missing org
+           * entity means the subgraph is internally inconsistent.
+           */
+          throw new Error(
+            `Invariant violation: membership link ${linkEntity[0]?.metadata.recordId.entityId} is missing its right (org) entity in the subgraph`,
+          );
+        }
         const orgAvatar = getAvatarForEntity(
           subgraph,
           org.metadata.recordId.entityId,
diff --git a/libs/@blockprotocol/graph/src/stdlib/subgraph/edge/link-entity.ts b/libs/@blockprotocol/graph/src/stdlib/subgraph/edge/link-entity.ts
index 8fccf6fc359..e442790124f 100644
--- a/libs/@blockprotocol/graph/src/stdlib/subgraph/edge/link-entity.ts
+++ b/libs/@blockprotocol/graph/src/stdlib/subgraph/edge/link-entity.ts
@@ -330,6 +330,8 @@ export const getOutgoingLinkAndTargetEntities = <
     ([linkEntityId, linkEntityRevisions]) => {
       return {
         linkEntity: linkEntityRevisions,
+        // `undefined` if the link's `has-right-entity` edge is not resolved
+        // into the subgraph
         rightEntity: getRightEntityForLinkEntity(
           subgraph,
           linkEntityId,
@@ -337,7 +339,10 @@ export const getOutgoingLinkAndTargetEntities = <
         ),
       };
     },
-  ) as LinkAndRightEntities; // @todo consider fixing generics in functions called within
+    // The cast is only needed for the caller-provided generic – the mapped
+    // value is a valid `LinkEntityAndRightEntity[]`.
+    // @todo consider fixing generics in functions called within
+  ) as LinkAndRightEntities;
 };
 
 /**
@@ -386,6 +391,8 @@ export const getIncomingLinkAndSourceEntities = <
     ([linkEntityId, linkEntityRevisions]) => {
       return {
         linkEntity: linkEntityRevisions,
+        // `undefined` if the link's `has-left-entity` edge is not resolved
+        // into the subgraph
         leftEntity: getLeftEntityForLinkEntity(
           subgraph,
           linkEntityId,
@@ -393,5 +400,8 @@ export const getIncomingLinkAndSourceEntities = <
         ),
       };
     },
-  ) as LinkAndLeftEntities; // @todo consider fixing generics in functions called within
+    // The cast is only needed for the caller-provided generic – the mapped
+    // value is a valid `LinkEntityAndLeftEntity[]`.
+    // @todo consider fixing generics in functions called within
+  ) as LinkAndLeftEntities;
 };
diff --git a/libs/@blockprotocol/graph/src/types/entity.ts b/libs/@blockprotocol/graph/src/types/entity.ts
index 4c0344b22e7..96ab6b52848 100644
--- a/libs/@blockprotocol/graph/src/types/entity.ts
+++ b/libs/@blockprotocol/graph/src/types/entity.ts
@@ -36,7 +36,12 @@ export type LinkEntityAndRightEntity<
   LinkEntityImpl extends LinkEntity = LinkEntity,
 > = {
   linkEntity: LinkEntityImpl[];
-  rightEntity: EntityImpl[];
+  /**
+   * The revisions of the link's target entity, or `undefined` if the link's
+   * `has-right-entity` edge was not resolved into the subgraph (e.g. because
+   * of resolve depths, or because the subgraph is only partially consistent).
+   */
+  rightEntity?: EntityImpl[];
 };
 
 export type LinkEntityAndLeftEntity<
@@ -44,7 +49,12 @@ export type LinkEntityAndLeftEntity<
   LinkEntityImpl extends LinkEntity = LinkEntity,
 > = {
   linkEntity: LinkEntityImpl[];
-  leftEntity: EntityImpl[];
+  /**
+   * The revisions of the link's source entity, or `undefined` if the link's
+   * `has-left-entity` edge was not resolved into the subgraph (e.g. because
+   * of resolve depths, or because the subgraph is only partially consistent).
+   */
+  leftEntity?: EntityImpl[];
 };
 
 export type CreateEntityData = {
diff --git a/libs/@local/hash-isomorphic-utils/src/save.ts b/libs/@local/hash-isomorphic-utils/src/save.ts
index f1df878df69..817d39cae58 100644
--- a/libs/@local/hash-isomorphic-utils/src/save.ts
+++ b/libs/@local/hash-isomorphic-utils/src/save.ts
@@ -463,7 +463,7 @@ const mapEntityToGqlBlock = (
       linkEntityRevisions[0].metadata.entityTypeIds.includes(
         systemLinkEntityTypes.hasData.linkEntityTypeId,
       ),
-  )?.rightEntity[0];
+  )?.rightEntity?.[0];
 
   if (!blockChildEntity) {
     throw new Error(
diff --git a/libs/@local/hash-isomorphic-utils/src/service-usage.ts b/libs/@local/hash-isomorphic-utils/src/service-usage.ts
index 785c39b7e01..be23f03d6a1 100644
--- a/libs/@local/hash-isomorphic-utils/src/service-usage.ts
+++ b/libs/@local/hash-isomorphic-utils/src/service-usage.ts
@@ -48,7 +48,13 @@ const getServiceFeatureForUsage = ({
   }
 
   const serviceFeatureEntity = serviceFeatureLinkAndEntities[0]!
-    .rightEntity[0]! as HashEntity<ServiceFeature>;
+    .rightEntity?.[0] as HashEntity<ServiceFeature> | undefined;
+
+  if (!serviceFeatureEntity) {
+    throw new Error(
+      `Service feature entity missing from subgraph for service usage record ${usageRecord.metadata.recordId.entityId}.`,
+    );
+  }
 
   const { featureName, serviceName, serviceUnitCost } = simplifyProperties(
     serviceFeatureEntity.properties,
diff --git a/tests/hash-playwright/global-setup.ts b/tests/hash-playwright/global-setup.ts
index 60ff553e083..9282dac452b 100644
--- a/tests/hash-playwright/global-setup.ts
+++ b/tests/hash-playwright/global-setup.ts
@@ -12,9 +12,22 @@ const signInAndSaveState = async (
   const context = await browser.newContext({ baseURL });
   const page = await context.newPage();
 
+  /**
+   * The signin page fetches a Kratos login flow asynchronously after mount
+   * (`createBrowserLoginFlow` hits `/self-service/login/browser`). Submitting
+   * before the flow has loaded throws "No sign in flow available" and no
+   * navigation ever happens. Register the wait before navigating so the
+   * response can't be missed, and await it before clicking Submit.
+   */
+  const loginFlowResponse = page.waitForResponse(
+    (response) =>
+      response.url().includes("/self-service/login") && response.ok(),
+  );
+
   await page.goto("/signin");
   await page.fill('[placeholder="Enter your email address"]', email);
   await page.fill('[type="password"]', "password");
+  await loginFlowResponse;
   await page.click("text=Submit");
   await page.waitForURL("/", { timeout: 30_000 });
 
diff --git a/tests/hash-playwright/tests/features/types-page.spec.ts b/tests/hash-playwright/tests/features/types-page.spec.ts
index d0de0b05fe3..050d7beb980 100644
--- a/tests/hash-playwright/tests/features/types-page.spec.ts
+++ b/tests/hash-playwright/tests/features/types-page.spec.ts
@@ -19,9 +19,7 @@ test("/types page renders and loads types", async ({ page }) => {
     "Data Types": `${pathPrefix}data-type`,
   };
 
-  /**
-   * Check that all tabs have a non-zero type count
-   */
+  // Check that all tabs have a non-zero type count
   for (const [tabTitle, href] of Object.entries(hrefByTabTitle)) {
     await expect(page.locator(`[href*="${href}"]`)).toHaveText(
       new RegExp(`^${tabTitle}[1-9]\\d*$`),