feat(ui): port retail selected-stack quantity

Bind the authored stack count entry and horizontal slider to one Core split-quantity owner, preserve retail count-first naming and exact 1000-step rounding, refresh on stack changes, and consume the selected amount during merges. Conformance covers the production DAT fixture and retained pointer/focus paths.

Co-Authored-By: Codex <codex@openai.com>

docs/superpowers/plans/2026-07-10-retail-ui-fidelity-completion.md

@@ -505,12 +505,12 @@ overlay, while aliases stay neutral. Inventory now tries the pure named-retail
 stack-merge legality/amount planner before ordinary insertion, sends `0x0054`,
 broadcasts `FullMergingItem` immediately from the attempt owner, rekeys the toolbar
 with existing-destination removal, and selects the target. The notice is not a
-server confirmation despite its name. AP-101 still covers the absent shared split
-entry/slider; until it lands, merge requests use the whole source stack before the
-retail destination-capacity clamp. Release build is warning-free and 4,660 tests
-pass. The compatible-stack live gate passed 2026-07-11; it exposed the expected
-Wave 4.4/AP-101 gap that the selected strip still displays one instead of the
-stack count and has no split slider. The inventory-button live gate remains pending.
+server confirmation despite its name. Release build is warning-free and 4,660 tests
+pass. The compatible-stack live gate passed 2026-07-11 and exposed the expected
+Wave 4.4/AP-101 selected-stack gap. Wave 4.4a now implements that gap: exact count-first
+name formatting, authored entry/slider media, one Core split-quantity owner, live
+stack-size refresh, and selected-source merge amount. The inventory-button and
+selected-stack visual gates remain pending.
 
 ### 4.4 Finish toolbar controls
 
@@ -518,12 +518,24 @@ stack count and has no split slider. The inventory-button live gate remains pend
   Use, and Examine actions; dispatch panel buttons through the window registry,
   ghosting unavailable panels rather than constructing placeholders.
 - [ ] Make open/closed states event-driven from `RetailWindowManager`.
-- [ ] Complete selected-object item mana, formatted stack count, stack entry and
-  split slider; port `RecvNotice_UpdateItemMana`, `RecvNotice_SplitStack`, and
-  `HandleSelectionChanged` precedence.
+- [ ] Complete selected-object item mana and port `RecvNotice_UpdateItemMana`.
+- [x] Complete formatted stack count, stack entry and split slider, the applicable
+  `RecvNotice_SplitStack` activation behavior, and `HandleSelectionChanged` stack
+  precedence. Vendor-specific initial quantity remains naturally dormant until a
+  vendor panel owns an active vendor id.
 - [ ] Replace the PWD-only health gate with the exact attackable/player/pet policy.
-- [ ] Add item-mana query/cancel state, health query cancellation, and one shared
-  split-quantity owner for the entry, slider, and item drag payload.
+- [ ] Add item-mana query/cancel state and health query cancellation.
+- [x] Add one shared split-quantity owner for the entry, slider, and selected-source
+  item-holder merge payload.
+
+**Wave 4.4a implementation (2026-07-11):** static cdb against the matching retail
+binary pinned stack-name `"%d %hs"`, numeric entry `"%d"`, and the slider's exact
+1000-step truncation formula. `StackSplitQuantityState` is the single Core owner;
+`SelectedObjectController` binds authored elements `0x100001A3/A4`, and
+`InventoryController` consumes the value only when the dragged source is selected.
+The horizontal scrollbar remains the generic retained `UiScrollbar` in scalar mode,
+using the DAT track/thumb rather than panel-local drawing. The warning-free App Release
+build and 4,683-test suite are green; the live visual gate follows.
 
 **Wave 4.1 implementation (2026-07-11):** bare `1..9` now use slots 0..8,
 Ctrl+`1..9` selects them, Alt+`5..9` uses slots 13..17, and `0` creates a