### Environment

- Omarchy 4.0.2-1 (packages, installed on CachyOS; `omarchy-settings` 4.0.2-1)
- Lenovo Legion Go 2 (83N0, Ryzen Z2 Extreme, Radeon 890M), kernel 7.2.2-1-cachyos
- Plymouth 26.134.222-2.1, theme `omarchy`, LUKS root (`sd-encrypt`), Limine
- Internal panel eDP-1: 1920x1200, 190x120 mm → **257 DPI**
- External DP-1: 1920x1080, 600x330 mm → 81 DPI

### What happens

At the LUKS passphrase prompt the whole theme — logo, lock icon, entry box, progress bar —
is bunched into the upper-left corner instead of being centred. It is wrong on **both**
outputs at once: the logo is cropped off the left edge of the internal panel, and sits in
the top-left quadrant of the external monitor.

### Why

`plymouthd` picks a device scale automatically from the panel's DPI, and that scale is a
single daemon-wide value — there is no per-output form. The 257 DPI internal panel puts it
at 2, and the external 27" monitor inherits it.

With scale 2 the script module reports 960x600 to the theme instead of 1920x1200, so
`omarchy.script` computes:

```
logo X = Window.GetWidth()  / 2 - 800 / 2 = 960/2 - 400 =  80   (should be 560)
logo Y = Window.GetHeight() / 2 - 188 / 2 = 600/2 -  94 = 206   (should be 506)
```

Those are exactly the offsets observed on screen. Every other element derives from the
logo position, so the whole layout follows it into the corner.

### Steps to reproduce

1. Install Omarchy on a machine whose internal panel is above ~192 DPI (any 8"-class
   1920x1200 handheld; a 13" 4K laptop should do too).
2. Encrypt the root filesystem so Plymouth shows the passphrase prompt.
3. Boot.

### Workaround (verified)

```ini
# /etc/plymouth/plymouthd.conf
[Daemon]
DeviceScale=1
Theme=omarchy
```

then `sudo mkinitcpio -P`. The initramfs rebuild is required — the passphrase prompt is
drawn by Plymouth from inside the image, so editing the on-disk file alone changes
nothing. After that the theme is correctly centred on both outputs.

### Suggested fix

Make the theme scale-aware rather than assuming device pixels, or ship `DeviceScale=1`
with the theme.

### Secondary observation

Independently of the above, `omarchy.script` centres with

```lua
logo.sprite.SetX(Window.GetWidth() / 2 - logo.image.GetWidth() / 2);
```

while Plymouth's own reference theme (`/usr/share/plymouth/themes/script/script.script`)
uses

```lua
logo.sprite.SetX(Window.GetX() + Window.GetWidth() / 2 - logo.image.GetWidth() / 2);
```

The missing `Window.GetX()` / `Window.GetY()` makes no difference on a single-head setup,
so it was not the cause here — with `DeviceScale=1` the layout is correct on both outputs —
but it is a real divergence from upstream and may matter on other multi-monitor
arrangements. Affected lines: 8, 9, 111, 187, 196.

---

*Investigated and written with Claude Code (Claude Opus 5). Every command output, file
excerpt and measurement quoted above was taken from the affected machine.*