diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 321b09b..43e78dc 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -63,6 +63,13 @@ jobs:
         run: bash testing/check-ci-parity.sh
       - name: Check test log matchers against the strings src/ emits
         run: python3 testing/check-log-strings.py
+      # Hermetic: synthetic ping functions, no containers, ~45s. Lives beside
+      # the other two so both runners gate on it identically — putting it in
+      # only one would create exactly the drift check-ci-parity.sh exists to
+      # catch, and it is invisible to that checker either way since it is not
+      # a matrix suite.
+      - name: Run convergence-gate unit tests
+        run: bash testing/lib/wait-converge-test.sh
 
   fmt:
     name: Format check
diff --git a/testing/ci-local.sh b/testing/ci-local.sh
index 083b783..f0137fb 100755
--- a/testing/ci-local.sh
+++ b/testing/ci-local.sh
@@ -1069,6 +1069,22 @@ run_log_strings() {
     record "log-strings" $rc
 }
 
+# Unit tests for the convergence gate every static suite waits on. Hermetic —
+# synthetic ping functions against the same SECONDS clock, no containers — but
+# it drives real timeouts, so it costs about 45 seconds rather than the "few
+# seconds" its own header used to claim.
+#
+# It is here with the other two rather than in the integration stage because it
+# needs nothing built. Note what that buys: wait_until_connected decides whether
+# every static suite proceeds or gives up, so a regression in it turns those
+# suites' verdicts into noise, and until now nothing ran this at all.
+run_wait_converge() {
+    local rc=0
+    info "[wait-converge] Running convergence-gate unit tests"
+    bash "$SCRIPT_DIR/lib/wait-converge-test.sh" || rc=$?
+    record "wait-converge" $rc
+}
+
 # ── Main ───────────────────────────────────────────────────────────────────
 
 main() {
@@ -1082,6 +1098,7 @@ main() {
     # local run means what a GitHub run means, whichever subset was asked for.
     run_ci_parity
     run_log_strings
+    run_wait_converge
 
     if [[ "$TEST_ONLY" == true ]]; then
         run_tests
diff --git a/testing/lib/wait-converge-test.sh b/testing/lib/wait-converge-test.sh
index 3abd2de..fda25c4 100755
--- a/testing/lib/wait-converge-test.sh
+++ b/testing/lib/wait-converge-test.sh
@@ -4,8 +4,12 @@
 # These tests drive the convergence gate with synthetic connectivity
 # checks (ping_fn stand-ins) that report scripted PASSED/FAILED counts
 # keyed off the same SECONDS clock the gate uses. No containers or
-# network are involved, so the whole suite runs in a few seconds and is
-# safe to run in CI.
+# network are involved, so the suite is hermetic and safe to run in CI.
+#
+# It is not fast, though: it drives real timeouts against the real clock
+# and takes about 45 seconds, measured 2026-07-23. The header claimed "a
+# few seconds" from the day it was written until then, which nothing had
+# contradicted because no runner had ever invoked it.
 #
 # Run:
 #   ./wait-converge-test.sh