docs: finalize product search integration

.project-docs/30-worklog/tasks/20260902-integrate-product-search-3b7f6a20.md

@@ -8,7 +8,7 @@
 - Worktree: /Users/inmanx/Documents/lwltAPI-integrate-product-search-3b7f6a20
 - Base commit: fff9171ba2f08c4638a0753c60a079ec9eccd774
 - Owner: codex
-- Status: In progress
+- Status: Ready for integration
 
 ## Scope
 
@@ -32,6 +32,7 @@
 - Kept the source feature task record on its source branch, so this integration changes no other task-owned project document.
 - Promoted the durable `S_chanpinming` lookup order and its search-only evidence into canonical current state, business rules, evidence, and rollout commitments while preserving the distinction between read-only search proof and write proof.
 - The combined integration tree passed all repository, contract, regression, build, and release checks and is ready for a guarded normal push.
+- A fresh fetch confirmed `origin/main` was still `fff9171`; the normal non-force push advanced it to verified integration commit `a045701dfcb596df104587212d1b8a755c66ab5a`.
 - No runtime, browser-extension, service, task, or ERP state was changed.
 
 ## Verification
@@ -45,6 +46,8 @@
 - `node --run build`: passed.
 - `dist/ltjt-order-assistant-0.5.165.zip` SHA-256 is `14f3150ab26d99131e32321ddc805a85550438bc2810a1e20921f7922b25aaac`, exactly matching `dist/release-manifest.json`.
 - The temporary `node_modules` symlink used for isolated-worktree verification was removed.
+- Fresh pre-push fetch showed divergence `0 3` and proved `origin/main` was an ancestor of the integration tip. After the normal push, local `HEAD`, the `origin/main` tracking ref, and `git ls-remote --heads origin main` all returned `a045701dfcb596df104587212d1b8a755c66ab5a`.
+- This task record is finalized in a documentation-only follow-up commit after that remote-equality check.
 
 ## Follow-ups