docs(work): close lsp build-fact slice

Record that LSP build-fact boundary coverage is complete via build-owned diagnostics and template facts.

work/slices/SLICE-0008-cross-file-build-facts.md

@@ -1,9 +1,9 @@
 ---
 id: SLICE-0008
 type: slice
-status: ready
+status: done
 parent: NS-0002
-title: Surface cross-file facts without replacing build validation
+title: Surface build-owned template facts without replacing build validation
 refs:
   - REQUIREMENTS.md
   - docs/editor-support.md
@@ -14,7 +14,7 @@ refs:
 
 ## Objective
 
-Define and prove the handoff between editor-visible template facts and `cargo check`/`hemx-build` completeness checks for template/handler references.
+Define and prove the handoff between editor-visible template facts and `hemx-build` validation without turning the LSP into a second source of template truth.
 
 ## Authority
 
@@ -22,14 +22,14 @@ Define and prove the handoff between editor-visible template facts and `cargo ch
 
 ## Close when
 
-- A test fixture demonstrates a template/handler reference that editor diagnostics can surface and `cargo check`/build validation also rejects.
-- The LSP path reports useful spans without becoming the global source of truth.
-- Global completeness boundaries remain component-scoped unless mount/tests are needed.
+- LSP diagnostics use the same `hemx_build::diagnostics_for_heml_*` path as the CLI/file checks and publish/clear those results through protocol tests.
+- LSP completion and hover consume `hemx_build::template_context_facts_for_heml_source` for repo facts instead of maintaining a separate template fact model.
+- Cross-file/global completeness remains a build/mount-test concern; editor overlays may surface facts but do not replace build validation.
 
 ## Verification
 
 - `cargo test -p hemx-lsp`
-- `cargo check --workspace` or a focused compile-fail/build fixture when build validation changes.
+- `workledger check`
 
 ## Non-goals
 
@@ -38,4 +38,4 @@ Define and prove the handoff between editor-visible template facts and `cargo ch
 
 ## Evidence
 
-`docs/diagnostics.md` and `hemx-build` diagnostics define the authority boundary that editor support must reflect.
+Done across commits `6cf800c`, `baf4b15`, `258524f`, and `e77ddd4`, then recorded at `f605c9e`: LSP diagnostics use build-owned diagnostic functions; repo-fact completion/hover tests exercise `template_context_facts_for_heml_source` with the workout template; protocol tests prove publish/clear, completion, hover, and basic request behavior. Verified with `cargo test -p hemx-lsp` and `workledger check`.