@@ -0,0 +1,13 @@
+---
+'@object-ui/app-shell': patch
+'@object-ui/plugin-gantt': patch
+---
+
+fix(app-shell, plugin-gantt): the home launcher tile draws the app's branding, and a gantt's name column is headed by its object
+
+Clause-②: no
+Metadata-protocol: none
+
+The console home's app tiles (and the `app:launcher` block, which draws the same strip) now follow the app's declared branding, the way the top-bar app pill and the app switcher already do: the `branding.logo` image when one is declared, else the app's icon on its `branding.primaryColor` when that is a hex, else the icon on the name-keyed gradient as before. A logo that fails to load falls back to the tile.
+
+A gantt bound to an object now heads its task list's name column with that object's label (translated like every other surface that names the object), so a campaign gantt reads "Campaign" rather than "Task Name". An inline data set, an object that declares no label, and a mixed-object tree (`objectField`) keep the generic heading.
@@ -22,7 +22,11 @@
  *
  * The strip's look is the Home artboard's apps section (objectui#12601): a
  * 15 px heading with a count pill, 112 px tiles with a 56 px icon on the app's
- * colour and a 13 px name on one line. Three optional parts ride along, all
+ * colour and a 13 px name on one line. The icon square follows the app's own
+ * branding, the way `AppMark` does in the top bar and the switcher: its
+ * `branding.logo` when it declares one, else its `icon` on its
+ * `branding.primaryColor` when that is a hex, else its `icon` on the
+ * name-keyed gradient. A logo that fails to load falls back to the tile. Three optional parts ride along, all
  * off unless the host asks: an 11 px "2 hr. ago" line under a tile's
  * name (`lastOpened`, which Home reads from the recent-items store), a muted
  * "System Settings" link at the heading's right (`settingsHref` — Home moves
@@ -32,7 +36,7 @@
  *
  * @module
  */
-import { useMemo, useState } from 'react';
+import { useMemo, useState, type ReactNode } from 'react';
 import { Link } from 'react-router-dom';
 import { LayoutGrid, Plus, Settings, Star } from 'lucide-react';
 import { cn } from '@object-ui/components';
@@ -43,13 +47,58 @@ import { timeAgo } from '../../utils/relativeTime.js';
 import { TILE_OPENED_TIME_FORMAT } from './appLastOpened.js';
 import type { FavoriteItem } from '../../hooks/useFavorites.js';
 import { ICON_BOX_CLASSES, TILE_CLASSES, launcherIconGradient } from './launcherTile.js';
+import { BRANDED_TILE_CLASSES, appTileColors, appTileStyle } from '../../layout/appTileColors.js';
 
 const COMPACT_LIMIT = 19;
 
 /** The 12 px links at the heading's right. */
 const HEADER_LINK_CLASSES =
   'inline-flex items-center gap-1.5 rounded-sm text-xs transition-colors hover:underline focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-ring';
 
+/**
+ * One app's 56 px icon square, drawn from the app's branding (see the module
+ * header). `children` is the favourite badge, which rides on every face.
+ */
+function LauncherAppIcon({ app, children }: { app: any; children?: ReactNode }) {
+  const logo = typeof app?.branding?.logo === 'string' && app.branding.logo ? app.branding.logo : undefined;
+  // The URL that failed to load, so a later, different logo is tried afresh.
+  const [failedLogo, setFailedLogo] = useState<string | undefined>(undefined);
+  const box = cn(ICON_BOX_CLASSES, 'shadow-sm transition-transform group-hover:scale-105');
+
+  if (logo && logo !== failedLogo) {
+    return (
+      <span className={cn(box, 'bg-card')} data-testid={`app-tile-logo-${app.name}`}>
+        <img
+          src={logo}
+          alt=""
+          aria-hidden
+          onError={() => setFailedLogo(logo)}
+          className="size-full rounded-[14px] object-contain"
+        />
+        {children}
+      </span>
+    );
+  }
+
+  const Icon = getIcon(app?.icon);
+  const colors = appTileColors(app?.branding?.primaryColor);
+  return (
+    <span
+      className={cn(
+        box,
+        colors ? BRANDED_TILE_CLASSES : cn('bg-gradient-to-br text-white', launcherIconGradient(app.name)),
+      )}
+      style={colors ? appTileStyle(colors) : undefined}
+      data-testid={`app-tile-icon-${app.name}`}
+      data-branded={colors ? 'true' : undefined}
+    >
+      {/* eslint-disable-next-line react-hooks/static-components -- getIcon returns a stable icon component from a static registry, not one created during render */}
+      <Icon className="size-[26px]" />
+      {children}
+    </span>
+  );
+}
+
 export function HomeAppsStrip({
   apps,
   favorites,
@@ -169,10 +218,8 @@ export function HomeAppsStrip({
       {/* `-ml-2` puts the first icon under the heading: a tile pads its icon 8 px. */}
       <div className="-ml-2 flex flex-wrap gap-1">
         {visible.map((app) => {
-          const Icon = getIcon(app.icon);
           const label = appLabel({ name: app.name, label: resolveKeyedI18nLabel(app.label, t) });
           const fav = favNames.has(app.name);
-          const grad = launcherIconGradient(app.name);
           const openedAgo = timeAgo(lastOpened?.get(app.name), displayLocale, TILE_OPENED_TIME_FORMAT);
           return (
             <Link
@@ -183,20 +230,13 @@ export function HomeAppsStrip({
               className={TILE_CLASSES}
               data-testid={`app-tile-${app.name}`}
             >
-              <span
-                className={cn(
-                  ICON_BOX_CLASSES,
-                  'bg-gradient-to-br text-white shadow-sm transition-transform group-hover:scale-105',
-                  grad,
-                )}
-              >
-                <Icon className="size-[26px]" />
+              <LauncherAppIcon app={app}>
                 {fav && (
                   <span className="absolute -right-1 -top-1 inline-flex h-4 w-4 items-center justify-center rounded-full bg-amber-400 ring-2 ring-background">
                     <Star className="h-2.5 w-2.5 fill-white text-white" />
                   </span>
                 )}
-              </span>
+              </LauncherAppIcon>
               <span className="w-full truncate text-[13px] font-medium">{label}</span>
               {openedAgo && (
                 <span
 
@@ -0,0 +1,84 @@
+// Copyright (c) 2026 ObjectStack. Licensed under the Apache-2.0 license.
+
+/**
+ * objectstack#27386 row 4 — a launcher tile draws the app's own branding.
+ *
+ * The 56 px icon square on Home (and the `app:launcher` block, which mounts the
+ * same strip) follows the ladder `AppMark` uses in the top bar and the app
+ * switcher: `branding.logo` when declared, else the app's `icon` on its
+ * `branding.primaryColor` when that is a hex, else the `icon` on the name-keyed
+ * gradient. A logo that fails to load falls back to the tile.
+ */
+
+import '@testing-library/jest-dom/vitest';
+import { describe, it, expect, afterEach } from 'vitest';
+import React from 'react';
+import { render, screen, fireEvent, cleanup } from '@testing-library/react';
+import { MemoryRouter } from 'react-router-dom';
+import { HomeAppsStrip } from '../HomeAppsStrip';
+import { launcherIconGradient } from '../launcherTile';
+import { appTileColors } from '../../../layout/appTileColors';
+
+function renderStrip(apps: Record<string, unknown>[], favorites: { id: string }[] = []) {
+  return render(
+    <MemoryRouter initialEntries={['/home']}>
+      <HomeAppsStrip
+        apps={apps}
+        favorites={favorites as any}
+        onBrowseMarketplace={() => {}}
+        isAdmin={false}
+      />
+    </MemoryRouter>,
+  );
+}
+
+describe('HomeAppsStrip — tile branding (objectstack#27386 row 4)', () => {
+  afterEach(cleanup);
+
+  it('draws a declared hex primaryColor instead of the name-keyed gradient', () => {
+    renderStrip([{ name: 'hotcrm', label: 'HotCRM', icon: 'Flame', branding: { primaryColor: '#ea580c' } }]);
+    const icon = screen.getByTestId('app-tile-icon-hotcrm');
+    expect(icon).toHaveAttribute('data-branded', 'true');
+    expect(icon.className).not.toContain('bg-gradient-to-br');
+    for (const cls of launcherIconGradient('hotcrm').split(' ')) expect(icon.className).not.toContain(cls);
+    const colors = appTileColors('#ea580c')!;
+    expect(icon.style.getPropertyValue('--os-app-tile-bg')).toBe(colors.bg);
+    expect(icon.style.getPropertyValue('--os-app-tile-fg')).toBe(colors.fg);
+    expect(icon.style.getPropertyValue('--os-app-tile-bg-dark')).toBe(colors.bgDark);
+    expect(icon.style.getPropertyValue('--os-app-tile-fg-dark')).toBe(colors.fgDark);
+  });
+
+  it('keeps the name-keyed gradient when no usable colour is declared', () => {
+    renderStrip([
+      { name: 'plain', label: 'Plain', icon: 'Box' },
+      // Not a hex: the spec's colour is a hex code, and `AppMark` reads only that.
+      { name: 'named', label: 'Named', icon: 'Box', branding: { primaryColor: 'orange' } },
+    ]);
+    for (const name of ['plain', 'named']) {
+      const icon = screen.getByTestId(`app-tile-icon-${name}`);
+      expect(icon).not.toHaveAttribute('data-branded');
+      expect(icon.className).toContain('bg-gradient-to-br');
+      for (const cls of launcherIconGradient(name).split(' ')) expect(icon.className).toContain(cls);
+      expect(icon.getAttribute('style')).toBeNull();
+    }
+  });
+
+  it('draws a declared logo, and falls back to the coloured tile when it fails to load', () => {
+    renderStrip(
+      [{ name: 'hotcrm', label: 'HotCRM', icon: 'Flame', branding: { logo: '/logo.png', primaryColor: '#ea580c' } }],
+      [{ id: 'app:hotcrm' }],
+    );
+    const logoBox = screen.getByTestId('app-tile-logo-hotcrm');
+    const img = logoBox.querySelector('img');
+    expect(img).toHaveAttribute('src', '/logo.png');
+    expect(screen.queryByTestId('app-tile-icon-hotcrm')).toBeNull();
+    // The favourite badge rides on the logo face too.
+    expect(logoBox.querySelector('.bg-amber-400')).not.toBeNull();
+
+    fireEvent.error(img!);
+    expect(screen.queryByTestId('app-tile-logo-hotcrm')).toBeNull();
+    const icon = screen.getByTestId('app-tile-icon-hotcrm');
+    expect(icon).toHaveAttribute('data-branded', 'true');
+    expect(icon.querySelector('.bg-amber-400')).not.toBeNull();
+  });
+});
@@ -33,7 +33,10 @@ function hashStr(s: string): number {
   return Math.abs(h);
 }
 
-/** The icon gradient for a tile, chosen by a stable key (an app's `name`). */
+/**
+ * The icon gradient for a tile, chosen by a stable key (an app's `name`). An
+ * app tile draws it only when the app declares no branding (`HomeAppsStrip`).
+ */
 export function launcherIconGradient(key: string): string {
   return ICON_GRADIENTS[hashStr(key) % ICON_GRADIENTS.length];
 }
 
@@ -23,7 +23,7 @@
 import * as React from 'react';
 import { cn } from '@object-ui/components';
 import { getIcon } from '../utils/getIcon.js';
-import { appTileColors } from './appTileColors.js';
+import { BRANDED_TILE_CLASSES, appTileColors, appTileStyle } from './appTileColors.js';
 
 /** The app fields this glyph reads — the spec's `AppSchema` names. */
 export interface AppMarkApp {
@@ -42,16 +42,6 @@ const SIZE_CLASSES: Record<AppMarkSize, { box: string; glyph: string }> = {
   md: { box: 'size-[26px] rounded-md', glyph: 'size-4' },
 };
 
-/**
- * The tile for a declared `primaryColor`. The utility strings are literals so
- * Tailwind emits them at build time; the author's colour reaches them only as
- * CSS custom properties, so `dark:` stays a real variant the theme controls
- * (AGENTS.md section 2, the author-declared colour carve-out).
- */
-const BRANDED_TILE_CLASSES =
-  'bg-[color:var(--os-app-tile-bg)] text-[color:var(--os-app-tile-fg)] ' +
-  'dark:bg-[color:var(--os-app-tile-bg-dark)] dark:text-[color:var(--os-app-tile-fg-dark)]';
-
 /** The tile for an app that declares no usable colour — theme tokens only. */
 const NEUTRAL_TILE_CLASSES = 'border bg-muted text-muted-foreground';
 
@@ -92,16 +82,7 @@ export function AppMark({ app, size = 'sm', className }: AppMarkProps) {
         colors ? BRANDED_TILE_CLASSES : NEUTRAL_TILE_CLASSES,
         className,
       )}
-      style={
-        colors
-          ? ({
-              '--os-app-tile-bg': colors.bg,
-              '--os-app-tile-fg': colors.fg,
-              '--os-app-tile-bg-dark': colors.bgDark,
-              '--os-app-tile-fg-dark': colors.fgDark,
-            } as React.CSSProperties)
-          : undefined
-      }
+      style={colors ? appTileStyle(colors) : undefined}
     >
       {/* eslint-disable-next-line react-hooks/static-components -- getIcon returns a stable icon component from a static registry, not one created during render */}
       <Icon className={sizeClasses.glyph} />
 
@@ -1,11 +1,13 @@
 /**
  * The fallback app tile's colours, derived from an app's declared
- * `branding.primaryColor` (objectui#12201). `AppMark` publishes them as CSS
- * custom properties on the tile; see that component for why.
+ * `branding.primaryColor` (objectui#12201). `AppMark` and the home launcher's
+ * tiles publish them as CSS custom properties on the tile (`appTileStyle`),
+ * which the static `BRANDED_TILE_CLASSES` utilities consume.
  *
  * @module
  */
 
+import type { CSSProperties } from 'react';
 import { contrastRatio, hexToHSL } from '@object-ui/core';
 
 /** The two foregrounds `AppShell` pairs with a brand colour (`--primary-foreground`). */
@@ -47,3 +49,23 @@ export function appTileColors(primaryColor: unknown): AppTileColors | undefined
     fgDark: ON_BRAND_DARK,
   };
 }
+
+/**
+ * The tile for a declared `primaryColor`. The utility strings are literals so
+ * Tailwind emits them at build time; the author's colour reaches them only as
+ * CSS custom properties, so `dark:` stays a real variant the theme controls
+ * (AGENTS.md section 2, the author-declared colour carve-out).
+ */
+export const BRANDED_TILE_CLASSES =
+  'bg-[color:var(--os-app-tile-bg)] text-[color:var(--os-app-tile-fg)] ' +
+  'dark:bg-[color:var(--os-app-tile-bg-dark)] dark:text-[color:var(--os-app-tile-fg-dark)]';
+
+/** The custom properties `BRANDED_TILE_CLASSES` reads, for a tile's `style`. */
+export function appTileStyle(colors: AppTileColors): CSSProperties {
+  return {
+    '--os-app-tile-bg': colors.bg,
+    '--os-app-tile-fg': colors.fg,
+    '--os-app-tile-bg-dark': colors.bgDark,
+    '--os-app-tile-fg-dark': colors.fgDark,
+  } as CSSProperties;
+}
@@ -735,6 +735,11 @@ export interface GanttViewProps {
    * overwriting each other in the Downloads folder.
    */
   exportFileName?: string
+  /**
+   * Heading of the task list's name column — what the rows are, e.g. the bound
+   * object's label ("Campaign"). Falls back to the generic "Task Name".
+   */
+  taskColumnLabel?: string
   /**
    * Per-interaction switches. Omit for all-on. See
    * {@link GanttInteractions}: e.g. `{ resize: false }` keeps bars movable and
@@ -928,6 +933,7 @@ export function GanttView({
   dependencyTypes = true,
   timeZone,
   exportFileName,
+  taskColumnLabel,
   interactions,
   onBeforeTaskUpdate,
 }: GanttViewProps) {
@@ -3821,7 +3827,7 @@ export function GanttView({
             className="flex items-center font-medium text-xs text-muted-foreground px-2 sm:px-4 border-r bg-card z-20 shadow-sm"
             style={{ width: taskListWidth, minWidth: taskListWidth }}
           >
-            <div className="flex-1 truncate">{t('gantt.column.taskName')}</div>
+            <div className="flex-1 truncate" data-testid="gantt-task-column-heading">{taskColumnLabel || t('gantt.column.taskName')}</div>
             {showSEColumns && (
               <>
                 <div className="w-16 gantt-sm-w20 text-right">{t('gantt.column.start')}</div>
Original file line number	Diff line number	Diff line change
`@@ -33,7 +33,10 @@ function hashStr(s: string): number {`
`33`	`33`	`return Math.abs(h);`
`34`	`34`	`}`
`35`	`35`
`36`		-/** The icon gradient for a tile, chosen by a stable key (an app's `name`). */
	`36`	`+/**`
	`37`	+ * The icon gradient for a tile, chosen by a stable key (an app's `name`). An
	`38`	+ * app tile draws it only when the app declares no branding (`HomeAppsStrip`).
	`39`	`+ */`
`37`	`40`	`export function launcherIconGradient(key: string): string {`
`38`	`41`	`return ICON_GRADIENTS[hashStr(key) % ICON_GRADIENTS.length];`
`39`	`42`	`}`