diff --git a/.changeset/authz-a4-managed-by-tristate.md b/.changeset/authz-a4-managed-by-tristate.md
new file mode 100644
index 000000000..559152c13
--- /dev/null
+++ b/.changeset/authz-a4-managed-by-tristate.md
@@ -0,0 +1,20 @@
+---
+"@object-ui/app-shell": patch
+---
+
+feat(app-shell): A4 — permission-provenance tri-state badge (framework#2920)
+
+The Studio permission-matrix editor's provenance badge was two-state
+(package / custom). It is now a **tri-state — platform / package / admin(custom)**,
+mirroring the unified `sys_*.managed_by` vocabulary landed in framework#2920 so
+the Studio matrix and the Setup record page read the same source-of-truth
+labels.
+
+- `PermissionMatrixEditor` — `managedBy === 'platform'` renders a **Platform**
+  badge; `'package'` (or an active `packageId`) renders **Package**; everything
+  else (including legacy `'user'`) falls through to **Custom**.
+- New `perm.badge.platform` i18n key (en + zh-CN).
+
+The Setup record page surfaces provenance via the framework object's now-`select`
+`managed_by` field (rendered by the generic record renderer), so no record-page
+change is required here.
diff --git a/packages/app-shell/src/views/metadata-admin/PermissionMatrixEditor.badge.test.tsx b/packages/app-shell/src/views/metadata-admin/PermissionMatrixEditor.badge.test.tsx
new file mode 100644
index 000000000..8fde8e835
--- /dev/null
+++ b/packages/app-shell/src/views/metadata-admin/PermissionMatrixEditor.badge.test.tsx
@@ -0,0 +1,76 @@
+// Copyright (c) 2026 ObjectStack. Licensed under the Apache-2.0 license.
+
+/**
+ * A4 (framework#2920) — the provenance badge in the Studio permission matrix is
+ * a TRI-STATE (platform / package / admin-custom), mirroring the unified sys_*
+ * `managed_by` vocabulary. This guards each branch of the ternary.
+ */
+
+import { describe, it, expect, vi, afterEach } from 'vitest';
+import { render, screen, cleanup } from '@testing-library/react';
+import { MemoryRouter } from 'react-router-dom';
+
+function makeClient(set: Record<string, unknown>) {
+  return {
+    layered: async () => ({ effective: set, code: null, overlay: null, overlayScope: null }),
+    getDraft: async () => null,
+    list: async (type: string) => (type === 'object' ? [{ item: { name: 'a_account' } }] : []),
+    get: async (type: string) => (type === 'object' ? { fields: [] } : null),
+    save: async (_t: string, _n: string, payload: Record<string, unknown>) => payload,
+  } as any;
+}
+
+let clientImpl: any;
+
+vi.mock('./useMetadata', () => ({
+  useMetadataClient: () => clientImpl,
+  useMetadataTypes: () => ({
+    loading: false,
+    error: null,
+    entries: [{ type: 'permission', label: 'Permission', allowOrgOverride: true }],
+  }),
+}));
+vi.mock('./AssignedUsersSection', () => ({ AssignedUsersSection: () => null }));
+
+import { PermissionMatrixEditPage } from './PermissionMatrixEditor';
+
+afterEach(cleanup);
+
+function baseSet(extra: Record<string, unknown>) {
+  return { name: 'sales_perms', label: 'Sales', isProfile: false, objects: {}, fields: {}, ...extra };
+}
+
+async function renderWith(extra: Record<string, unknown>) {
+  clientImpl = makeClient(baseSet(extra));
+  render(
+    <MemoryRouter>
+      <PermissionMatrixEditPage type="permission" name="sales_perms" />
+    </MemoryRouter>,
+  );
+  // Wait for the load to settle (the label input renders after the fetch).
+  await screen.findByDisplayValue('Sales');
+}
+
+describe('PermissionMatrixEditPage — provenance tri-state badge (A4 framework#2920)', () => {
+  it('managedBy "platform" renders the Platform badge', async () => {
+    await renderWith({ managedBy: 'platform' });
+    expect(screen.getByText('Platform')).toBeInTheDocument();
+    expect(screen.queryByText('Custom')).not.toBeInTheDocument();
+  });
+
+  it('managedBy "package" renders the Package badge', async () => {
+    await renderWith({ managedBy: 'package' });
+    expect(screen.getByText('Package')).toBeInTheDocument();
+  });
+
+  it('managedBy "admin" renders the Custom badge', async () => {
+    await renderWith({ managedBy: 'admin' });
+    expect(screen.getByText('Custom')).toBeInTheDocument();
+    expect(screen.queryByText('Platform')).not.toBeInTheDocument();
+  });
+
+  it('legacy managedBy "user" still falls through to Custom (read compat)', async () => {
+    await renderWith({ managedBy: 'user' });
+    expect(screen.getByText('Custom')).toBeInTheDocument();
+  });
+});
diff --git a/packages/app-shell/src/views/metadata-admin/PermissionMatrixEditor.tsx b/packages/app-shell/src/views/metadata-admin/PermissionMatrixEditor.tsx
index 225f3a81c..0ecae185f 100644
--- a/packages/app-shell/src/views/metadata-admin/PermissionMatrixEditor.tsx
+++ b/packages/app-shell/src/views/metadata-admin/PermissionMatrixEditor.tsx
@@ -527,10 +527,15 @@ export function PermissionMatrixEditPage({ type, name, packageId, onDraftSaved,
               WHO OWNS the set (provenance, ADR-0086 D3) and whether it is the
               package's suggested default (ADR-0090 D5). */}
           <div className="flex items-center gap-1.5 pb-1">
+            {/* [A4 framework#2920] Provenance tri-state — platform / package /
+                admin(custom) — mirrors the unified sys_* `managed_by` vocab so
+                the Studio matrix and the Setup record page read the same. */}
             <Badge variant="outline" className="text-[10px]">
-              {draft.managedBy === 'package' || packageId
-                ? t('perm.badge.package')
-                : t('perm.badge.custom')}
+              {draft.managedBy === 'platform'
+                ? t('perm.badge.platform')
+                : draft.managedBy === 'package' || packageId
+                  ? t('perm.badge.package')
+                  : t('perm.badge.custom')}
             </Badge>
             {!!draft.isDefault && (
               <Badge variant="secondary" className="text-[10px]">{t('perm.badge.default')}</Badge>
diff --git a/packages/app-shell/src/views/metadata-admin/i18n.ts b/packages/app-shell/src/views/metadata-admin/i18n.ts
index f95058a58..2e2f0ed04 100644
--- a/packages/app-shell/src/views/metadata-admin/i18n.ts
+++ b/packages/app-shell/src/views/metadata-admin/i18n.ts
@@ -720,6 +720,7 @@ const ENGINE_STRINGS_EN: Record<string, string> = {
   'perm.filter.empty': 'No objects match the filter.',
   'perm.field.name': 'Name',
   'perm.field.label': 'Label',
+  'perm.badge.platform': 'Platform',
   'perm.badge.package': 'Package',
   'perm.badge.custom': 'Custom',
   'perm.badge.default': 'Default for new users',
@@ -1927,6 +1928,7 @@ const ENGINE_STRINGS_ZH: Record<string, string> = {
   'perm.filter.empty': '没有匹配的对象。',
   'perm.field.name': '名称',
   'perm.field.label': '标签',
+  'perm.badge.platform': '平台内置',
   'perm.badge.package': '包内置',
   'perm.badge.custom': '本环境自定义',
   'perm.badge.default': '新用户默认',