Complete Stage 3/4 push and post-push verification log

docs/operations/VPNRUNTIME_STAGE_EXECUTION_2026-05-12.md

@@ -58,3 +58,33 @@ Notes:
 Next:
 
 - Proceed to Stage 3 (remote push handoff readiness; auth-dependent).
+
+### Stage 3 - Completed
+
+Scope:
+
+- Verify remote push readiness and authentication.
+- Publish staged chain to `origin/main`.
+
+Result:
+
+- `git push --dry-run origin main`: PASS
+- `git push origin main`: PASS
+- Published branch: `main`
+
+### Stage 4 - Completed
+
+Scope:
+
+- Post-push integrity verification.
+
+Verification:
+
+- Local HEAD: `e94fc309fd3761d64bc670068c07e1f1c1116054`
+- `git ls-remote --heads origin main`:
+  `e94fc309fd3761d64bc670068c07e1f1c1116054 refs/heads/main`
+- Remote `main` matches local HEAD: YES
+
+Execution status:
+
+- All planned stages completed.